Spectral finite element analysis of coupled wave propagation in composite beams with multiple delaminations and strip inclusions

Abstract

A spectral finite element model (SFEM) is developed to study the effect of wave scattering and power flow through multiple delaminations and strip inclusions in composite beams with general ply stacking sequence. The model uses three dimensional beam waveguides to represent the dynamics of the base-laminates and the sub-laminates or strip inclusions with distributed friction at the interlaminar region. A compact matrix methodology based on finite element discretization in wavenumber space (k-space) and fast Fourier transform (FFT) to obtain frequency domain as well as time domain response is developed. This model has exact shape function and dynamic stiffness matrices, and dynamically consistent load vector, which can be used to analyze broadband coupled wave propagation in composite beam waveguide. In the present paper, a sub-laminate-wise constant shear kinematics with multi-point constraints (MPC) in frequency domain is used to model the interface between multiple delaminations or strip inclusions and the base-laminate. The strip inclusion, which can be a passive or active device or integrated electronics embedded inside laminated composite, are considered to be in the form of rectangular sub-laminates with different material properties compared to the host structure. Performance of the model is validated by comparing the response from 2D plane stress finite element solution. Effect of length-wise and depth-wise multiple delaminations and strip inclusion on the scattered power flow is studied. The analysis may find its suitability and superiority to capture the dynamics of delaminated composite structure over broad frequency band in vibrating environment and in structural health monitoring applications using diagnostic waves.