Vibration Attenuation Investigations on a Distributed Phononic Crystals Beam for Rubber Concrete Structures

Abstract

Locally resonant phononic crystals (LRPCs) beam is characterized by the band gaps; some frequency ranges within which flexural waves cannot propagate freely. So, the LRPCs beam can be used for noise or vibration isolation. In this paper, a LRPCs beam with distributed oscillators is proposed, and the general formula of band gaps and transmission spectrum are derived by the transfer matrix method (TMM) and spectrum element method (SEM). Subsequently, the parameter effects on band gaps are investigated in detail. Finally, a rubber concrete beam is designed to demonstrate the application of distributed LRPCs beam in civil engineering. Results reveal that the distributed LRPCs beam has multifrequency band gaps and the number of the band gaps is equal to that of the oscillators. Compared with others, the distributed LRPCs beam can reduce the stress concentration when subjected to vibration. The oscillator interval has no effect on the band gaps, which makes it more convenient to design structures. Individual changes of oscillator mass or stiffness affect the band gap location and width. When the resonance frequency of oscillator is fixed, the starting frequency of the band gap remains constant, and increasing oscillator mass of high-frequency band gap widens the high-frequency band gap, while increasing oscillator mass of low-frequency gap widens both high-frequency and low-frequency band gaps. External loads, such as the common uniform spring force provided by foundation in civil engineering, are conducive to the band gap, and when the spring force increases, all the band gaps are widened. Taken together, a configuration of LRPCs rubber concrete beam is designed, and it shows good isolation on the vibration induced by the railway. By the presented design flow chart, the research can serve as a reference for vibration isolation of LRPCs beams in civil engineering.

Topological Design of Two-Dimensional Phononic Crystals Based on Genetic Algorithm

“…However, despite the favorable sound-insulation performance exhibited by phononic crystals at different elastic wave frequencies, the currently designed phononic crystal structures tend to have relatively large dimensions, which are typically on the order of tens of millimeters. In the low-frequency range, particularly below 500 Hz, the optimization of sound-insulation performance for practical applications remains a challenge that has yet to be effectively addressed [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ]. For engineering applications, obtaining the widest possible bandgap within the desired frequency range is a key issue in the design of phononic crystal structures.…”

Vibration band gap characteristics of two-dimensional functionally graded grids using the spectral element method

“…The periodic structure can be used as a special vibration damping element, which can be introduced into the design of vibration damping and noise reduction of the structure. Researchers further studied the Bragg (Bordiga et al, 2019; Xiong et al, 2020) and local resonance band gap (Li et al, 2021b; Raghavan and Phani, 2013; Vadalá et al, 2021) characteristics of periodic structures with different topologies. In addition to using topology optimization to optimize the structure to change the wave propagation characteristics, researchers have also proposed several pioneering methods, such as using anisotropic materials (Wu et al, 2004), piezoelectric materials (Espo et al, 2020; Piliposian et al, 2012), thermosensitive materials (Bian et al, 2019), and inertial amplification mechanisms (Shoaib et al, 2021) to improve the band gap characteristics of the periodic structure.…”