Effect of the Normal Transverse Stress on the Superharmonic Resonance Problem of Three Layered Sandwich Beams with Viscoelastic Core

Purpose: This paper focuses on the analysis of non-linear forced vibrations of a sandwich beam with a viscoelastic core layer. The analytical formulation considers normal, transverse, and shear deformations in the core layer by utilizing the refined higher-order zig-zag theory (HZZT). Method: The Ritz’s method coupled to the modal transformation was employed to derive the nonlinear differential equations of motion. In order to investigate superharmonic resonance cases, the perturbation technique was applied to the equation of motion, and analytical frequency-amplitude relationships were obtained using the multiple scale method. This model is commonly applied to describe materials exhibiting both elastic and viscous characteristics. Results: The frequency response curves, which depict superharmonic resonance behaviour were analyzed and commented upon by varying the material characteristics of the viscoelastic core layer and the geometric parameters of the sandwich beams. Particular attention was given to assessing the influence of the transverse stress on the response curves.