Design and analysis of three-dimensional phononic band gap structures with embedded intertial amplification mechanisms

Abstract

In this study, three-dimensional (3D) phononic band gap structures are investigated. First, in nite and nite periodic simple cubic, body centered cubic and face centered cubic lattices with and without inertial ampli cation mechanisms are considered. These 3D lattices are modeled with mass and spring elements that are parametrically varied to observe their e ects on band gap (stop band) limits. When inertial ampli cation mechanisms are used in the in nite periodic lattices, wide low frequency band gaps are generated. Moreover, wide and deep phononic gaps are obtained by using moderate amount of unit cells in the case of nite periodic lattices. Then, 3D phononic band gap structures are formed using distributed parameter inertial ampli cation mechanisms. The resonance and antiresonance frequencies that characterize the rst vibration stop band of the building block mechanism are obtained analytically and by nite element method. The mechanism is optimized to yield wide vibration stop bands in an octahedron and a 2 3 array of octahedrons. Furthermore, these structures are manufactured using a 3D polymer printer and their experimental frequency responses are obtained. Structural damping is added to the nite element model in order to match the resonant peak magnitudes of the numerical and experimental frequency response results. Moreover, a new inertial ampli cation mechanism is designed by adding constraining beams that reduce the degree of freedom of the initial mechanism. Consequently, ultra wide band gaps at low frequencies are attained. To sum up, it is demonstrated that the 3D structures built with inertial ampli cation mechanisms are capable of isolating excitations in longitudinal and two transverse directions in a very wide frequency range.