Uncertainty propagation and experimental verification of nonlinear viscoelastic sandwich beams

Abstract

Abstract The nonlinear dynamic analysis of viscoelastic systems is not an easy task. In some cases, it is due to the difficulty in dealing with the temperature- and frequency-dependent properties of the viscoelastic substructure. Also, since the real-life viscoelastic treatments are characterized by inherent uncertainties affecting their efficiency, their handling in the nonlinear modeling is essential from an engineering point of view. In this contribution, a stochastic modeling based on the Karhunen-Loeve expansion is proposed for a three-layer sandwich beam having nonlinear behavior using the concept of complex modulus and shift factor. The nonlinear frequency responses were obtained by using an approximated harmonic balance method with the Galerkin bases. Due to the difficulty in solving the resulting complex nonlinear eigenproblem with a frequency-dependent stiffness, making the stochastic nonlinear analyses very costly, it is proposed an iterative reduction method to approximate the complex eigenmodes. The influence of the forcing amplitude and temperature on the computed nonlinear frequency responses has been confirmed by performing laboratory experiments with a three-layer sandwich beam specimen placed inside an environmental chamber. Also, a curve-fitting has been performed to calibrate the deterministic nonlinear model using optimization tools. The envelopes of nonlinear responses demonstrate the relevance of considering the uncertainties in design variables.