Lumped Element Modelling for 1-D and 2-D Periodic Lattice Structure

Abstract

In general, the lattices of phononic crystals are made with two or more materials with same or different mechanical properties. The waves unable to propagate within the Brag gap frequency range due to its periodic structure. Present research work endeavors computation of lumped element model of periodic spring-mass system. To start with, a 1-D model has been analyzed followed by a 2-D crystal using simple spring-mass arrangements. In order to reduce the complexity, initially the finite lattices have been analyzed. Subsequently, infinite series of lattices have been analyzed in 1D and 2D domain. Next, the complexity of damping has been incorporated in the analytical model. The analytical computational model has been verified with reported literature. For 1-Dlattice structure using phononic composite material of ends 50% aluminum & middle 50% PPMA(Poly Methyl Methacry late). For 2-D lattice structure using phononic composite material of epoxy with aluminium inclusion having finite or infinite number of unit cell in x and y direction. For this work, analysis on phononic band gap theory using lumped element method for 1-D and 2-D lattice structure. The main aim of work is to investigation of band gap phenomena and optimization of band gap structures and validated the analytical result of dispersion and acceleration response curve for 1-D and 2-D with the literature experimental results for infinite and finite number of unit cell with or without damping. The important parameters are number of unit cell, damping factor, damping coefficient(zeta), frequency, acceleration response and wave number (gamma)which responsible for analysis of band gap phenomenon.