Transverse vibration bandgaps in phononic‐crystal Euler beams on a Winkler foundation studied by a modified transfer matrix method. Issue 7 (25th February 2013) - Zhang, Yan; Han, Lin; Jiang, Lin‐hua
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. <boxed-text content-type="graphic" position="anchor" orientation="portrait"> </boxed-text> 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.