A higher-order finite waveguide model for spectral analysis of composite structures

Abstract

A waveguide model for spectral analysis of finite composite structures based on higher-order shear deformation theory (HSDT) is reported in this paper. The advantages of using the proposed model are attributed to the following: (1) the displacement field interpolation is carried out using the basis vector from the null space of the characteristic system, and this numerical step is a bi-product of the usual wave dispersion analysis in frequency domain, (2) the standard finite element discretization procedure involving nodal variables is employed, (3) both the frequency response and the time domain response can be obtained with the help of fast Fourier transformation (FFT) algorithm and (4) no constraint in terms of low or high frequencies is imposed, except that for a prescribed frequency band of excitation the assumed field needs to be consistent with the geometric scales in the composite material system. A novel method of embedding functionally graded array of dissimilar material phases, periodic or aperiodic, in the finite element dynamic stiffness matrix is presented, where the homogenized properties of the material system in the smallest wavelength scale can be used. Numerical simulations under impact type loading are carried out to study the effect of frequency band of excitation on the velocity response of homogeneous and inhomogeneous beam type structures.