Transverse vibration bandgaps in phononic-crystal Euler beams on a Winkler foundation studied by a modified transfer matrix method

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Abstract

In this paper, a modified transfer matrix method is proposed to solve the transverse vibration bandgaps (BGs) in phononic crystal (PC) Euler beams on a Winkler foundation. An equivalent critical frequency is introduced to facilitate the calculation of the end frequency of the first BG. The band structures of a lead–steel PC Euler beam either on a Winkler foundation or not show that the existence of a foundation has a significant influence on the distribution of BGs. A new BG that starts at 0 Hz appears. Additional results demonstrate that a very narrow passband could exist between the first two BGs. This study is aimed at searching for large BGs, especially at low frequencies.

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Band structures for the lead–steel PC Euler beam on a Winkler foundation (continuous line) or not (dash line). A new BG that starts at 0 Hz appears in the case of having a foundation.

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