Nonlinear Dynamic Modeling and Vibration Analysis of Smart Composite Structures Using Multiscale Techniques

Abstract

Engineered smart composite structures are being utilized in the fields of aerospace, automotive and civil engineering due to adaptive capabilities that would be obtained through incorporation of functional materials such as piezoelectric fibrous or shape memory alloy materials within a heterogeneous matrix. As such, these materials lead to complex nonlinear dynamic responses as a result of the coupling of mechanical, electrical and thermal fields at a range of scales. A complete nonlinear dynamic modeling framework which uses the multiscale techniques to accurately model the interaction between microstructural constituents and their effect on the macroscopic vibration characteristics is developed in this paper. The proposed approach combines asymptotic homogenization theory and nonlinear finite element methods to incorporate both material nonlinearity (e.g. strain dependent stiffness) that results from a nonlinear relationship between the variables of a stress strain law and the associated geometric nonlinearity that arises due to large deformations. Finally, the dynamic response is studied under harmonic and transient excitations through the use of advanced analysis method including the nonlinear modal decomposition, Hilbert-Huang Transform (HHT), and continuous wavelet transform (CWT). The framework is applied to piezoelectric fibre reinforced laminates and it is found that microscale phase distribution variation significantly affects both damping capacity, modulated stiffness and intermodal energy transfer. Nonlinear phenomena including the resonance frequency shifts and internal resonances are predicted by the model, and these phenomena are often overlooked in single scale or linear models. Studies conducted in comparison confirm that the multiscale nonlinear approach improves the fidelity of vibration analysis, and revealed design and optimization important for the smart composite structures in dynamic environment.