Design, fabrication, and dynamic mechanical responses of fiber‐reinforced composite lattice materials

Fiber‐reinforced composites are a popular lightweight materials used in a variety of engineering applications, such as aerospace, architecture, automotive, and marine construction, due to their attractive mechanical properties. Constructing lattice materials from fiber‐reinforced composites is an efficient approach for developing ultra‐lightweight structural systems with superior mechanical properties and multifunctional benefits. In contrast to corrugated, foam, and honeycomb core materials, composite lattice materials can be manufactured with various architectural designs, such as woven, grid, and truss cores. Moreover, lattice materials with open‐cell topology provide multifunctional advantages over conventional closed‐cell honeycomb and foam structures and are thus highly desirable for developing aerospace systems, hypersonic vehicles, long‐range rockets and missiles, ship and naval structures, and protective systems. The objective of this study is to review and analyze dynamic mechanical behavior performed by different researchers in the area of composite lattice materials and to highlight topics for future research.

these porous materials can be further improved by covering them with thin and dense layers of skin, resulting in a structure with significantly improved bending stiffness and strength for a relatively small increase in weight.For example, human bones have structures with a strong outer skin layer that is used to support our weight and a lightweight interior that houses other tissues while maintaining a high bending resistance. 4Similarly, bird beaks have evolved to resist buckling through a structure consisting of a thin outer shell supported by bone trusses. 5is basic design template has also traditionally been used in sandwich structures, where stiff, thin face sheets enclose a porous core.These structures are primarily desirable due to the considerable weight reduction achieved without significantly compromising the mechanical characteristics of the structure. 6These highly porous materials also possess combinations of multifunctional properties that are not possible to achieve in traditional monolithic materials. 7erefore, in the past century, honeycombs and foams were developed as typical lightweight core materials and are still widely used in land, sea, and air vehicles.With the recent emphasis on developing multifunctional structures, these materials seem to be naturally suited for adoption.However, traditional honeycomb and foam cores suffer from some limitations due to their closed cell architecture, which impedes easy installation of sensory, thermal, or electromagnetic components, such as electrical wires, electronic components, fire retardant foam, or a circulating cooling liquid.In addition, the air and water vapor trapped in the honeycomb structure can accelerate damage to key spacecraft components.
These well-known structural advantages and difficulties of extending cellular structures to multifunctional applications have led to an increased focus on lattice materials with an open-cell topology.1][12][13] In contrast to metallic materials, composite materials, which achieve even higher stiffness and a strength-to-weight ratio, can provide a template for fabricating advanced ultralight composite lattice materials. 14Such materials are needed to create lightweight, high-strength, corrosionresistant, and high-temperature-resistant structures that are highly sought after in modern technological applications.Particularly, fiberreinforced composite lattice structures have gained a lot of interest in recent years because of their superior mechanical properties and multifunctional capabilities that far surpass those of traditional layered, laminated, chopped, or woven fiber composite materials.The exponential growth in the number of publications on this topic, including those in high-impact journals with a wide scientific readership, is indicative of the intensifying study of these materials. 15,16Despite the rapidly advancing development and design of these materials, as reflected in the rich publication record, there are no comprehensive reviews of recent progress in the area of composite lattice materials.This work systematically evaluates and highlights the most recent developments in the dynamic mechanical behavior of fiber-reinforced composite lattice structures.It aims to provide a systematic and comprehensive analysis of low-density and high-performance composite sandwich structures.According to the structural form, we divide the existing composite lattice into three categories: integrated hollow core, lattice grid, and lattice truss.In the subsequent content, we will discuss the current research progress of related structures.Section 2 presents an introduction to the impact of composite lattice materials.Section 3 reviews the vibration characteristics of composite lattice materials.Section 4 then proposes future directions for developing ultra-lightweight and high-performance composite lattice materials.
The discussion in Section 2 highlights the significant advances that have been made in the manufacturing technology of composite lattice materials.These advances made it possible to mass-produce composite materials with increasingly complex geometries.In parallel, progress in the dynamic mechanical characterization of these materials is also essential for design and predictive prognosis.
Mechanical characterization invariably requires deepening the understanding of the underlying heterogeneity, nonlinearities, and failure behavior under various loading conditions.Such characterization, together with modeling and simulations, furthers the integration of these materials into the realm of practical applications.Even for multifunctional applications, the underlying mechanics is the bedrock for furthering our understanding of these materials.Thus, the current literature on the dynamic mechanics of these structures, including analytical models and computational investigations, is summarized for impact and vibration.

| Integrated hollow core materials
Traditionally, reinforcing structural members such as pins have been utilized to improve the mechanical properties of classical foam core sandwich structures, which frequently display poor transverse stiffness and catastrophic core compressive failure.Pultruded glass and carbon tow rods are implanted in the foam core to build a 3D truss network in the noncontinuous interweaving approach for a Z-pin reinforced core. 17The struts formed by the noncontinuous intertwining method are unable to transfer load among themselves.This causes a relative instability of the pins under loading, eliminating some of the structural gains due to the reinforcement.Thus, if the fiber-reinforced struts can be made continuous and part of a larger order, their structural performance can be significantly improved.The 3D fabric consists of upper and lower fabric face sheets, which are set at a given fixed distance from each other and mechanically woven together by fusing vertical pile threads.This method is hereinafter referred to as the woven fabric method of intertwining. 18According to this method, the fabrication generally includes a hand lay-up and a vacuum-assisted resin infusion molding process, as shown in Figure 1.
Composite integrated hollow core materials are typically made up of two parallel top and bottom skins and a middle core, which are woven together with pile yarn, maintaining a specified distance between the skins and the core.The final mechanical performance of sandwich architecture is heavily influenced by the characteristics of the skin, the core, and the strength of the skin-core connection.The integrated connection provides through-thickness reinforcement, strengthening shear stiffness and removing a significant shortcoming of many other core materials.The warp and weft make up the skin, while the pile yarn forms a hollow core layer the thickness of which depends on the length of the pile yarn.Mechanically, this structure results in an integral weaving of the upper and lower skin layers with the core and ensures a firm bond among the layers, preventing the delamination of skin and core.This mechanical advantage is in addition to the benefit of open spaces available for multifunctional applications.
The design of integrated hollow-core foam structures intends to inherit the benefits of classical foam core sandwich structures while overcoming their weak points by improving compressive, 20 shear 21 and bending properties, 22 energy absorption, 23 and delamination resistance under fatigue. 24A large number of experimental and computational investigations have demonstrated that Z-pins with carbon or glass rods can significantly increase the delamination toughness, compressive strength, 25 bending characteristics, and shock resistance performance of sandwiches compared to their plain foam counterparts. 23,24Thus, most of the research has focused on the abovementioned typical loadings to show the advantages of these innovative designs compared to traditional foam cores.The influence of Z-pinning on the compression responses of composite sandwich materials has received a lot of attention. 23,26In these cited studies, composite columns and rods/pins have been demonstrated to be the key components of foam sandwich structures.The following discussion focuses on the mechanical behavior of sandwich constructions composed entirely of columns without foam to pave the way for composite lattice truss structures (sandwich structures with foam and composite rods/pins are not covered in this part).
A range of typical low-strain rate shocks, such as tool slips, hail hits, debris bombardments, and impacts from high-velocity bullet damage, cause a variety of local damages that greatly reduce the structure's mechanical strength.Under low-velocity impact conditions, the breakdown of the bond between the panel and the core frequently results in a decrease in the structure's bearing capacity, which is one of the main problems in the operation of composite sandwich structures, due to which it cannot be used.Many researchers have investigated the impact resistance of composite integrated hollow core materials.
Azadian et al. 27 used a knitting machine to fabricate the E-glass integrated weft-knitted fabrics and experimentally studied the low-velocity impact behavior of sandwich structures.Under the drop hammer impact, all the sandwiches demonstrated matrix fracture and transverse damage to the connecting layer.However, no face-core F I G U R E 1 Fabrication steps for three-dimensional integrated hollow sandwich structure.Reproduced with permission. 19 debonding occurred in all the structures, indicating that the 3D woven fabric has good resistance to low-impact energy.Similarly, Vaidya et al. 28 analyzed the low energy shock response of E-glass/epoxyintegrated hollow core composites.The findings of the experiments demonstrate that both hollow and functionally inserted cores exhibit regional failure, although the damage region is confined by the warhead's impact area.Furthermore, the peak strength under static compressing and low-velocity impact were calculated using the Euler formula for long columns.In addition, they found that damage spread primarily due to the tearing of the top face sheet and the localized micro-buckling of the glass/epoxy core members.For the thickness considered in the study, critical energy for sandwich skin fracture is primarily determined by the resin of the core layer.Shiah et al. 29 created a composite sandwich construction with hollow cores utilizing a machine-braided three-dimensional core structure.The modulus and impact resistance of the sandwich construction were tested experimentally.The skin materials affect the impact resistance of a sandwich structure.For the sandwich structure with skin made of chopped strand mat, the core shear fracture occurs when there is no delamination between the core and the skin of the loaded sample.Additionally, for sandwich structures with woven roving skin, not only does the core fails but also delamination occurs between the core and skin due to the shear stress in the connection area.Karahan et al. 30 concluded that shear failure of cores and buckling failure of thin walls under impact stress happen primarily due to the low resistance of sandwich samples with hollow cores.As the core layer's thickness increases, the peak load of the core resistance decreases, preventing the skin from achieving optimal mechanical performance.With an increase in the thickness of the core in an empty sample, the shear deformation of the cores becomes higher, which leads to a decrease in the absorbed energy.
These findings indicated that core-skin delamination was fully prevented. 31Wang et al. 32 investigated the blast resistance of the integrated hollow core sandwich structure.Explosion tests revealed that the woven panel-core integrated sandwich structure had good blast resistance, as shown in Figure 2. When the scaled distance was below 1.026 m/kg 1/3 , the panels could maintain their integrity and no debonding was observed for the structure.Excellent blast resistance depends on the high fracture toughness of the composite material and the high interfacial strength of the sandwich structure.

| Composite lattice grid materials
The hollow sandwich structure's core geometry is often quite simple due to weaving process limitations.Therefore, researchers created the interlocking method to construct lattice core layers with more complicated geometries.This approach creates lattice structures with specific spatial forms via interlock operations on various sheets with slots.Weaving needs precise control over the orientation and sequencing of the tows.The interlocked structure is based only on mechanical manipulation and is not material-specific.Furthermore, Failure mode of the woven sandwich structure under blast impact.Reproduced with permission. 32Copyright 2022, Elsevier.by controlling the machine instrument's cutting path, a variety of open-hole grid structures other than the typical closed-hole twodimensional honeycomb structure can be achieved.The interlocking method is an inexpensive and highly scalable processing method.
The technology may be used to quickly create open-cell composite lattice structures with three-dimensional configurations 33,34 (Figure 3 depicts the assembly sheet and procedure).Xiong et al. 35 devised and constructed an open-hole carbon fiber composite lattice structure.
The laminate was made from T700 carbon fiber reinforced epoxy resin composite material.It was cut by an engraving machine according to the design drawing to generate preform inserts with specific slots and holes, and then the preform was assembled by interlocking.Furthermore, the egg structure (Figure 3A) and the pyramid structure (Figure 3B) of lattice grid structures were generated by altering the inlay location of the slots of the inserts.Since the same type of inlay is utilized for both lattice grid structures, tiresome processing is reduced and preparation efficiency is improved.
To investigate the high-velocity impact response of a sandwich beam structure, Russell et al. 36 impacted the mid-span of a simply supported beam with metal foam bullets to create local explosive loads.Under blast impact, the composite beam structure filled with a square honeycomb core exhibited multiple failure modes, including fracture and punch plug shear failure of the internal cores, debonding between the skin and the cores, and panel fragmentation at the fixed support location.In contrast, for some beam structures, only facecore delamination and tensile fracture of the panel at the support location were observed.Furthermore, the experimentally measured deflections of the beam structure under impact loading agree well with the finite element results.Park et al. 37 prepared a carbon fiber composite square honeycomb material by grooving, interlocking assembly, and gluing.The authors studied the strain rate effects.
The compression response of the structure was also systematically analyzed for static compression, dynamic impact, and other loads.It was concluded that the composite topological form is beneficial as a lightweight sandwich structure.The failure of the structure originates from stress concentration at the root of the slot, leading to the early appearance of micro-flexion.It was also found that the obvious shock wave effect appeared when the impact velocity was too large.
Zhu et al. 38 studied the interlocked square grid core sandwich structures by utilizing experiments and simulation.It is found that these structures have a variety of damage responses and damage modes under low-velocity impact.At the rib-plate intersection, the sandwich structure shows progressive fragmentation failure, and the failure mode is dominated by matrix damage.However, the shock response curve shows a double peak and a valley when the load is applied in the center of the unit cell (see Figure 4).Additionally, a refined numerical model was developed, and damage modes not observed in the experiments were discovered.Moreover, to prevent water vapor condensation in the closed-hole structure, Cao et al. 39 designed openings in cell walls and cross-shaped inserts.They also studied the impact progressive damage of the sandwich structure and evaluated its impact performance by combining simulations with low-velocity impact experiments.
In addition to the square honeycomb, the hexagonal structure is also of interest as a common architecture of grid structure.Petrone et al. 40 investigated the effect of fiber type on the impact resistance of the structure.They prepared a corrugated panel sandwich structure by molding with short and long fiber-reinforced composites as the matrix materials.It is demonstrated that the long fiber composites have significant superiority in resisting impact.Lv et al. 41 designed a combination of square and hexagonal grid honeycombs.
They investigated the low-energy impact mechanical behavior of the combined grid construction using experiments and numerical simulations.It is found that a sandwich structure with both mechanical performance and lightweight could be obtained by optimizing the structural parameters.
The aircraft fuselage structure is a typical cylindrical shell.
Composite lattice structure can improve the weight efficiency and load-carrying capacity of the fuselage structure.Kondakov et al. 42,43 F I G U R E 3 Interlock assembly composite lattice grid material.Reproduced with permission. 34,35Copyright 2014, Elsevier.(A) Egg shape structure; (B) pyramidal shape structure.
| 217 applied a composite lattice grid to a civil aircraft fuselage and investigated the resistance of the structure to low-speed impact.It was found that the impact resistance of the lattice grid structure was low and additional protective structures needed to be used.An elastomeric material protection mat was used to separate the aerodynamic cover from the lattice grid.A finite element model of the unidirectional carbon fiber grid ribs was developed to determine the parameters of the protective structure under a 50J impact.The impact test agrees well with the finite element results.

| Composite lattice truss materials
There are many studies on lattice truss materials made from carbon fiber composites using different fabrication methods, such as the intertwining method, 44,45 interlocking method, 46,47 assembly method, 48,49 hot press mold method, 50,51 3D printing, 52,53 and others, as shown in Figure 5.More detailed information can be found in the review of Hunt et al. 54 Compared with metallic materials (e.g., stainless steel, aluminum alloy), composites have considerable benefits in static mechanical characteristics at low apparent densities.However, it is not yet known whether composites still have advantages in the mechanical response at high-impact velocities.
Therefore, Wang et al. 55 used carbon fiber-reinforced polymer composites and 304 stainless steel to evaluate the impact resistance of the materials at various impact rates using experimental and finite element methods.At low rates of impact, stainless steel has a high energy absorption capability.Carbon fiber composites demonstrate substantial superiority under bullet impact at high rates (velocities surpassing 950 m/s), indicating that the composites exhibit excellent mechanical response at high rates of impact.Furthermore, an impactresistant structure with both lightweight and good protective performance is created by optimizing the arrangement of the multilayer plates consisting of laminating carbon fiber composites and metal plates.Thus, the multilayer composite structure of composite-metal-composite is lighter in weight than pure metal plates with the same protective effect.This work provides a new viewpoint for the development of existing armor protection systems.
Under the same weight conditions, the sandwich structure has better blast resistance than the monolithic laminate.The high-performance advantage of carbon fiber composites can further enhance the impact resistance of sandwich constructions.Therefore, increasing attention has been drawn to the research on the impact response of carbon fiber composite sandwich construction.Zhang et al. 56 assembled machined carbon fiber composite plates to obtain a composite pyramid truss lattice structure.Then, they glued the upper and bottom skins together to create a pyramid lattice sandwich structure.The effect of impact on the residual strength of the pyramid lattice sandwich structure was investigated in terms of load energy, loading position, and core geometry.The loading location had a major effect on the failure mode of the structure.Due to the high restraint of the panel at the nodes of the lattice core, the damage to the panel was relatively minor when the punch impacted the lattice nodes.In contrast, impacted on the blank region, where the lattice core was unsupported, the panel was less restrained and showed noticeable splits extending around the panel.After the punch strikes the blank zone, the remaining mechanical characteristics of the core structure worsen substantially.
Owing to the weak connection between the core and the panel, the lattice sandwich structure often has problems with the separation of the core from the panel during impact.Filling the blank area with solid lightweight material is an effective method for improving the connection effect.Zhang et al. 57 fabricated a foam-filled composite pyramidal lattice sandwich structure and investigated the low-energy impact behavior (see Figure 6).The addition of polyurethane foam improves the load-bearing capacity of the structure.However, preliminary experiments showed that the foam addition has little effect on the impact resistance performance since the energy is too small and the structure is loaded mainly on the high-stiffness lattice.
Yungwirth et al. 58  with various solid materials, such as polyurethane, ballistic fibers, and ceramics.At a high-velocity impact of 600 m/s, the hollow lattice sandwich core structure practically did not resist the bullet and was completely penetrated.Adding polyurethane and ballistic fibers could reduce the bullet's residual velocity, but stopping the bullet from penetrating remains challenging.Although using ceramic to replace the blank region helps suppress the bullet in the proximal panel, the high apparent density of ceramic material increases the surface density of the sandwich construction from 27.7 to 105 kg/m 2 .To reduce the weight of the protective system, a hybrid lattice filled with multiple materials (such as polyurethane, ballistic fabric, and ceramic) is proposed, making it possible to create a system with density and high blast resistance.Furthermore, to improve the ballistic performance of the aforementioned hybrid multimaterial lattice sandwich and increase the ballistic limit, Yungwirth et al. 59 filled the blank area of the lattice core with a ceramic-Kevlar fiber mixture while maintaining the same surface density.As a result, the ballistic limit of the hybrid structure was twice as high as that of the metal panel, and the residual velocity of the panel fragments was further reduced due to the mixture of ballistic fibers.Thus, the protective effect of the sandwich construction is strengthened.
Yin et al. 60 also designed a composite pyramid hollow rod lattice truss structure with hollow rods filled with silicone rubber, and the core empty area is also filled with rubber.After filling with soft material (rubber), the dynamics of the structure was investigated using low-velocity impact experiments, which showed that the F I G U R E 5 Composite lattice truss materials obtained by various fabrication methods: (A) Intertwining method.Reproduced with permission. 45Copyright 2014, Elsevier.(B) Interlocking method.Reproduced with permission. 47Copyright 2022, Elsevier.(C) Assembly method.Reproduced with permission. 49Copyright 2018, Wiley.(D) Hot press mold method.Reproduced with permission. 51Copyright 2010, Elsevier.(E) Three dimensional printing.Reproduced with permission. 52Copyright 2018, Elsevier.In the low-energy impact test, although the total failure zone (125 mm 2 ) was more extensive than in the unfilled and filled composite pyramidal lattice structures (about 80 mm 2 ), the damaged part of the filled lattice structure was smaller.In addition, the rubber filler inside the truss boosts the truss core's compression resistance under greater energy impacts, while the filler between the trusses inhibits top penetration.Thus, impact resistance is higher in constructions with more robust struts or structures packed with additional rubber.
In actual engineering applications, component structures are often cylindrical objects with a certain curvature.Yin et al. 61 developed a composite lattice truss sandwich shell structure for automotive engine hood applications.The sandwich structure is a combination of a carbon fiber panel and a plant fiber composite lattice truss core.The protection effect of the sandwich shell when colliding with the human body was investigated using head injury criteria.The experimental and finite element results show that the incorporation of the fractional truss core improves the protective effect of the structure.Therefore, the lattice truss sandwich shell has the potential to be applied to automotive parts coverings.

| Integrated hollow core materials
The inside core of a 3D woven integrated sandwich structure is hollow.It allows injecting foam and liquid damping materials to improve the overall structural sound/vibration isolation capability.
3][64] Compared to other structural forms of lattice materials, the vibration response of integrated hollow sandwich structures is less studied, which is not favorable to the structure against mechanical vibrations.Abedzade Atar et al. 65 investigated the effect of structural topology and core-panel integrity on the vibration of the structure.Modal tests and numerical simulations determined the inherent frequencies of the specimens.
The highest inherent frequencies were found for the triangular structure.The inherent frequencies of the integral structure are higher than those of the nonintegral structure.Thus, core-panel integral design is necessary for practical engineering applications.
Liu 66 used the finite element method to study the influence of system parameters on the sound insulation performance of the integrated hollow sandwich.The inherent characteristics of the sandwich structure were analyzed, including the first-tenth-order inherent frequencies and vibration modes of the structure.With the increase in frequency, the sound insulation volume of the sound insulation valley gradually increases.With the increase of vibration order, the overall displacement amplitude of the structure decreases, which indicates that the high mode has less influence on the sound insulation performance of the structure.
Adding foam to the hollow core can further improve the stiffness of the integrated hollow sandwich structure.Thus, the inherent frequency of the structure can be increased.Vaidya et al. 67 investigated the bending vibration response of hollow sandwich structures with E-glass cores.The bending vibration mode dominates when the excitation point is at the geometric center of the specimen.Also, the frequency response function and damping ratio parameters were investigated.The damping ratio of polyurethane-filled foam increased by 150% and the weight by 77%.The structural resonant frequency decreased by 35% when the core was damaged by about 6%, which provides a quantitative reference for nondestructive vibration testing.Besides, the internal structural parameters of the core affect the structural characteristic frequency.Core rod diameter is the principal influencing factor of structural characteristic frequency. 68Furthermore, Arunkumar et al. 69  structure is more significant in square and trapezoidal honeycombs.This provides a reference for the design of aerospace structures with high static and dynamic vibration performance requirements.

| Composite lattice grid materials
Stiffness is critical in the structural design of spacecraft components.
On the one hand, the structure must match the high stiffness requirement for less mass and high load-bearing while having a high intrinsic frequency to eliminate resonance problems.On the other hand, the vibrational response of cylindrical shells is related to the efficiency of using the structure.Most existing research employs a combination of test and numerical approaches for assessing the vibratory behavior of cylindrical shells.In practice, only the minimum intrinsic frequency is needed to calculate the stiffness characteristics of a structure.Lopatin et al. 70 utilized mathematical analysis to compute the first-order intrinsic frequency of the composite cylindrical shell construction, as well as the deflection of the cylindrical shell during vibration.Furthermore, the influence of shell shape and solid material on shell vibration was investigated, and the theoretical model was validated using finite elements.The basic frequency computation approach is demonstrated to be simple and efficient.
Based on the single-shell structure, the grid structure is filled inside the cylindrical shell to improve the overall structural buckling resistance.Zhang et al. 71 prepared a carbon fiber composite grid cylinder and then studied the quasi-static compression behavior and free vibration characteristics of the cylinder (see Figure 7).The structural profile changed from circular to elliptical under vibration.
The first-order principal frequency and vibration pattern of the cylinder were successfully predicted.The potential of the carbon fiber grid cylinder in the development of new lighter and stronger spacecraft cylinder shell structures is demonstrated.These lattice grid cylindrical shells of the same weight and dimensions were always much stiffer than traditional lattice grid cylindrical shells with a single skin. 72ggesting that cylindrical lattice shells had a higher base frequency and may have been designed to be lighter to meet the initial frequency requirement for astronautic applications.An analogous technique was also shown to be accurate enough.Consequently, a practical way has been found to predict the fundamental frequencies and vibration mode morphology of lattice grid cylindrical shells.Sun et al. 73 investigated the effect of notching on the vibration performance of composite conical cylinders.Skin failure occurs under compression load.It extends circumferentially from the notch location.Vibration tests showed that notching does not affect the lower-order modes of the structure, but notching leads to more complex higher-order modes.Numerical simulations further demonstrate the small effect of notching on the free vibration performance.Similarly, Han et al. 74 and Shahgholian-Ghahfarokhi et al. 75 investigated the vibration modes and intrinsic frequencies of the lattice grid core sandwich cylinders.They found that changing the grid structure form can tailor the vibration characteristics of the cylinder.These studies can provide a reference for the design of spacecraft load-bearing structures.
Vibration correlation technique (VCT) technology can be used for nondestructive testing of structural parameters. 76Shahgholian-Ghahfarokhi et al. 77 developed a nondestructive method to calculate the flexural loading of thin-walled lattice cylindrical shell structures using VCT.They investigated the modal behavior of composite lattice grid cylindrical shells under various external pressurized loads using the modal drop hammer method.The VCT technique was found to be effective for analyzing grid cylindrical shells.Further, Zarei et al. 78 used testing, analytical, and mathematical methods to study the free vibration characteristics of the composite grid conical shell.The structure has been altered into a conical shell with changeable elastic F I G U R E 7 Mode shapes of composite lattice grid shell.Reproduced with permission. 71Copyright 2014, Elsevier.
XIONG ET AL.
| 221 parameters and varying thickness, taking into account the particular geometry of the cone.The Ritz technique is utilized to derive the governing equations from first-order deformation theory.Experiments and finite elements are used to validate the analytical conclusions.Finally, the authors discuss the effect of shell geometric parameters and cross angle on natural frequency.The inherent frequency of the grid conical shell is larger than that of the unreinforced conical shell when the skin thickness is smaller and the modal number is higher, indicating that the shell boundary conditions impact the inherent frequency of the structure.In actual engineering applications, when operating with loadbearing structural elements, a resonance that may occur at high amplitudes must be avoided.It is critical to reduce the vibration amplitude of the structure to ensure the service life of the loadbearing structural parts.Therefore, Yang et al. 80 used viscoelastic layers to explore the vibration and damping response of a carbon fiber pyramidal lattice (see Figure 8).The carbon fiber lattice sandwich construction was created by first preparing the thin rods and panels of the lattice structure using T700 unidirectional fabric and then bonding and recombining them.The equivalency concept was employed to compare the sandwich structure to a monolithic plate.Modal experiments combined with the finite element approach were performed to capture the structure's modal forms of different orders and the vibration performance of its lattice sandwich.When compared to the prior sandwich construction, the addition of the damping layer enhances the damping factor and allows the structure to swiftly recuperate from vibration.Tests have shown that the hybrid sandwich structure performs more rapid vibration attenuation when filled with rubber in the composite lattice structure. 60en et al. 81 investigated the dynamic response of the composite tetrahedral lattice structure.They derived the nonlinear control equations for the lattice sandwich structure.Thus, the mathematical expression for the entire structure's frequency response is obtained.Also, they analyzed the effects of the structural geometric parameters of the internal core (core thickness, lattice rod diameter, and rod tilt angle) on the frequency response of the overall structure.When the core thickness increases, the stiffness of the overall structure increases, and the structure hardens.However, the hardening phenomenon caused by fixing the height of the overall structure and expanding the thickness of the core becomes less pronounced, indicating that the stiffness change pattern of the overall structure is primarily controlled by the overall weight of the structure and the stiffness of the panel.Damage to composite structures is complex and varied, making the cracks inside challenging to visualize.The structure's stiffness changes after damage, which indirectly leads to changes in the structure's intrinsic frequency, mode shape, and damping characteristics.The damage pattern of the structure can be judged based on the analysis of the vibration of the damaged structure.Thus, extraction of the time domain signal and imaging is an effective measure for the detection of composite structure damage.To this end, Lou et al. 82 demonstrated the feasibility of using vibration analysis to assess structural damage failure.They studied the vibration response of a pyramidal lattice sandwich construction with localized damage, including the frequency and vibration mode of the structure.A failure factor indicating the degree of structural damage was established and set as a reference for the internal damage of the lattice sandwich.Moreover, the internal damage to the structure leads to the reduction of the stiffness in the damaged area.The vibration analysis reveals local deformation behavior, which is beneficial to the determination of the damage location.In addition, when the sandwich structure's border constraint is substantial, the fluctuation in the intrinsic frequency of the locally damaged structure is greater than that of the undamaged structure.This provides an excellent experimental reference for a quantitative description of the internal damage to the structure.5][86] Li and Lyu 87 researched the proactive vibration management of sandwich construction with a middle pyramidal lattice layer (see Figure 9).Piezoelectric materials were used for the actuator and sensor by bonding these materials onto the upper and lower layers of the beam.The discrete lattice truss core was modeled by homogeneous continuous material, and typical frequencies have been identified utilizing vibrational models and eigenvalue analysis.The vibration of the structural system was controlled using the velocity feedback control approach and a linear quadratic regulator.The frequency and time domain responses evaluated the control effectiveness of the sandwich construction with middle pyramidal lattice mesh.The results demonstrated that the speed feedback regulation and linear quadratic regulator management techniques successfully eliminated vibration in these constructions.Furthermore, Guo et al. 88 studied the dynamic response and vibration management of a multilayer lattice sandwich structure.The hourglass sandwich structure's dynamic properties were studied using a simplified calculation method.The vibration of the structure was actively controlled using piezoelectric materials, and a theoretical model of the natural frequency was established using the Hamilton principle.Also, the impact of geometric parameters and material characteristics on the dynamic performance of the sandwich structure was investigated.

| Composite lattice truss materials
A Rayleigh-Ritz analytical model and FE numerical model based on the modal energy approach were developed by Yang et al. 89 to predict the modal characteristics of three types of free-free composite sandwich cylindrical shells with pyramidal truss-like cores (see Figure 10).Three types of specimens were fabricated using a hot press molding method, and the relevant modal properties were obtained from modal tests.The predicted modal properties of the composite sandwich cylindrical shell with pyramidal truss-like cores agree well with experimental ones.The influence of the fiber ply angles on the natural frequency and damping loss factor was also investigated.The modal strain energy approach effectively estimated the structural damping loss factors.Furthermore, it adequately explained the damping variation for each vibration mode by considering the contributions of each strain energy component.The structural damping loss factors depend on vibration modes as well as the inherent material damping.The natural frequencies of the composite sandwich cylindrical shells increased with increasing ply angles of the inner and outer curved face sheets.In contrast, the damping loss factors of the shells did not increase monotonically.
For the application of cylindrical shell structure, 90 Zhang et al. 91 examined the vibration characteristics of a large expandable circular netting antenna ring truss construction with a fixed busbar using an Copyright 2007, Elsevier.(A) Dry fabric preform; (B) resin infusion in a mold; (C) curing; (D) resultant sandwich structure; (E) image of warp yarn; (F) image of weft yarn.XIONG ET AL.|215 evaluated the resistance of the sandwich structure to bullet penetration by filling the blank area of the pyramidal lattice F I G U R E 4 Impact failure of interlocked square lattice structure.Reproduced with permission. 38Copyright 2023, Elsevier.(A) Intersections of the ribs; (B) blank area of the grid.
XIONG ET AL.| 219 energy absorption capability of the structure significantly increased.
developed an equivalent elastic model for the foam-filled integrated hollow sandwich structure.The numerical simulations verified the feasibility of the equivalent model.The effects of foam and core topologies (triangular, trapezoidal, and square) on the free vibration performance were investigated.The triangular core has a smaller bending deflection due to its maximum stiffness.The frequency increase of foam-filled core F I G U R E 6 Impact response of composite lattice.Reproduced with permission. 57Copyright 2014, Elsevier.(A) Mechanical curve.(B) Visual damage of the surface.

A
variety of uncertainties can be caused by variable material properties, fabrication processes, and external excitations for all-composite sandwich structures.These uncertainties could significantly affect the structural mechanical performance.Using beam theory, Xu and Qiu 79 investigated the free vibration response of two types of lattice core structures, tetrahedral and pyramidal.First, the regulating partial differential equation of the sandwich structure's equivalent beam is constructed using Hamilton's principle to obtain the mathematical analysis model of the sandwich core structure's intrinsic frequency.The numerical model of the sandwich structure is then developed to examine the law of influence of the parent material characteristics and geometric dimensions of the structure on the vibration response.The structure's stiffness is shown to influence the inherent frequency of the sandwich structure, which increases as the core or panel thickness increases.As the inclination angle of the internal lattice strut gradually increases, the inherent frequency of the sandwich does not change monotonically but first increases and then decreases.This means that the entire structure's vibration performance may be modulated by varying the sandwich structure's core and panel in engineering applications with specific load scenarios.
analogous cylindrical shell model.The analogous cylindrical shell of the ring truss structure was created by reducing the cylindrical truss's three-dimensional framework to a two-dimensional "flat" layout.The equivalent process and homogenization approach are employed to calculate the membrane and bending rigidity, and the theoretical results are verified by numerical simulations.The simulation results are in good agreement with the natural frequency and modal vibration pattern of the theoretical model.To reduce the vibration F I G U R E 8 Vibration characteristics of lattice sandwich panels.Reproduced with permission. 80Copyright 2013, Elsevier.(A) Frequency response analysis; (B) dynamic properties of structures with different viscoelastic thickness; (C) the first six modes of the sandwich.ofthe cylindrical lattice truss shell, Li et al.92 derived the sheets' free and forced vibration solutions based on the variation and integral methods for the lattice truss material with a damping coating.Tests were carried out to ensure that the theoretical model was valid.In addition, the experimental results revealed that the thickness of the damping coating had a more significant effect on the resonance than on the natural frequency.A [45°/−45°] lay-up was suggested for better vibration suppression.To obtain a cylindrical thin-walled structure with improved static mechanical characteristics and dynamic responsiveness, Li et al.93

F I G U R E 9
Vibration characteristics of lattice sandwich constructions.Reproduced with permission. 87Copyright 2014, Elsevier.(A) Diagram of lattice structure; (B) active vibration control.F I G U R E 10 Vibration characteristics of lattice truss cylindrical shell structure.Reproduced with permission. 89Copyright 2014, Elsevier.(A) Pyramidal truss sandwich.(B) Mode shapes.(C) Natural frequencies.(D) Damping loss factors.