Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

Abstract

The present article aims essentially to present an analytical and numerical method which makes it possible to study the damped vibrations of viscoelastic FGM nanoplates resting on viscoelastic foundations. A new model for the higher-order shear deformation plate theory is coupled with the internal Kelvin - Voigt viscoelastic model and the three-parameter viscoelastic foundation model for the purpose of reducing and minimizing the vibration response of the system. It is widely admitted that the mechanical properties of these new functionally gradient materials (FGMs) vary according to the thickness of the plate and depend on its volume fraction. The use of FGM plates seems to be an ideal solution for the study of free vibrations because of their multifunctionality that is fully integrated with the nonlocal Eringen effect. The dynamic response of such a complex system has been investigated by varying the aspect ratio of the plate, the mechanical characteristics of the material used, the internal and external damping and the foundation rigidity. The results obtained, with and without the nonlocal effect, were compared with those of different models of higher-order theories and under various boundary conditions; they were found to be in good agreement with those reported in the literature.

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…A large variety of types of structural elements is considered, including beams [187,194,195,206,213,228,232], plates [193,202,203,214,218,220,227], shells [204], composite beams [186,198,201,207,211,215,224,225], composite plates [155,185,191,199,200,210,212,222,223,226], composite shells [190,216,219,221], nanobeams [184,189,196], FG nanoplates [192,197,208,[229][230][231], and FG nanoshells/nanopanels [188,209,217].…”

Viscoelastic Dynamic Response of Asphalt Pavement in Long Slope Sections

“…; it is typically a viscoelastic material. The researchers employed several constitutive laws and methods to simulate the behavior of viscoelastic materials [2][3][4][5], such as the Kelvin-Voigt viscoelastic model [6], Generalized Maxwell rheological model [7], Kelvin, Maxwell, Vanderpoel, and Burgers models are commonly used to present the performance of asphalt layers in analytical methods [8][9]. Some experts conducted excellent work in this field as well.…”