Modeling and Dynamics of Sandwich Beams with a Viscoelastic Soft Core

摘要

The dynamic behavior of sandwich beams with a viscoelastic soft core is analytically studied. The analysis combines the concepts of viscoelasticity with those of the high-order sandwich beam theory and accounts for the shear and transverse (through the thickness) deformability and the viscoelastic effects through the constitutive laws of the core material. The beam model assumes no variation through the width. The viscoelastic response is introduced through the Kelvin-Voigt and Maxwell models, which characterize different materials and provide some of the fundamental building blocks for more refined viscoelastic theories. The governing equations that correspond to the two models and the solution procedures that combine time integration through Newmark's method with a numerical solution in space are derived. The formulation of a refined viscoelastic model based on the building blocks developed in the paper is analytically demonstrated. The capabilities of the model are studied numerically with emphasis on the time variation of the deflections and the interfacial shear and vertical normal stresses under step, impulse, and harmonic loads. A comparison between the theoretical results and experimental results available in the literature is also presented. The analytical models and the numerical study highlight some unique aspects of the dynamic response of sandwich beams with viscoelastic soft cores and provide fundamental analytical tools for their modeling.