Viscoelastic high-damping vibration attenuation of sandwich FG-GPLRC face sheets by incorporating full nonlinear effects

Abstract

This article deals with the study of geometrically and materially nonlinear free-damped vibration analysis of Sandwich beams incorporating flexible cores governed by various frequency-dependent viscoelastic models, surrounded with top and bottom face sheets reinforced through a functionally graded distribution of graphene platelets (GPLs) in large deformation. In fact, two types of nonlinearities are considered in the formulation: one arising from the nonlinear strain-displacement relationship, and the other due to the viscoelastic material behavior in the sandwich beam. To analyze the impact of including nonlinear terms in both geometric and material behavior—which has not been reported in the literature—the results are computed by adopting the geometrically nonlinear von Kármán assumptions for the core and the face sheets on one hand, and by employing a viscoelastic core material with complex frequency-dependent Young's/shear modulus that induces material nonlinearity on the other. Based on the Extended Higher-Order Sandwich Panel Theory (EHSAPT), a set of coupled nonlinear governing equations is derived using the Lagrangian technique. As a progressive step, this is the first time that a displacement control technique has been enhanced to simultaneously account for both geometric and material nonlinearities in order to obtain the vibrational characteristics of a system, making it valid for large vibration amplitudes and high damping. To validate the approach, the results obtained from EHSAPT are compared with available data in the literature. Additionally, the problem is also examined by applying Euler–Bernoulli and Timoshenko beam theories to the face sheets and core, respectively. The complex nonlinear eigenvalue problem is solved, and the natural frequencies and loss factors of the viscoelastically damped sandwich beam are calculated. Parametric studies are discussed in detail to investigate the effects of weight fraction, graphene platelet distribution pattern, core-to-face sheet thickness ratio, boundary conditions, viscoelastic core temperature, and vibration amplitude. The results provide valuable and practical insights, showing that considering appropriate ranges of geometry and material in large-amplitude nonlinear vibrations of frequency-dependent viscoelastic core sandwich beams leads to improved design and industrial optimization.