Forward and inverse analysis of transient responses for a cantilevered rectangular plate under normal and oblique impact loadings

Abstract

This study investigates the transient responses of a cantilevered rectangular aluminum plate under normal and oblique impact loadings. The transient displacement and strain histories of the aluminum plate are forward calculated as a superposition of the normal modes using first-order shear deformation plate theory and the spectral collocation method considering both in-plane and out-of-plane dominant vibrations. A laser displacement meter and strain gauges are used to measure the displacement and strain histories of the same aluminum plate when subjected to normal and oblique loadings. Subsequently, frequency-dependent damping ratios are obtained from the associated wavelet spectrograms. The measured histories correlate well with those estimated using the theoretical analysis considering the damping ratios. Additionally, the inverse problem of determining the impact force history from the transient response is investigated. First, the transfer function between the impact force and measured response is derived using a theoretical analysis developed in the time domain. Subsequently, a wavelet deconvolution method is applied to reconstruct the impact force using a discrete wavelet transform with different scale and shift components. Thus, the impact force is obtained by reconstructing the wavelet expansion coefficients using these components, thereby demonstrating the validity of the wavelet deconvolution technique utilizing the theoretical transfer function.