Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration

Abstract

Vibrations and stability responses are two mechanical characteristics of engineering materials that are highly important for designing new engineering structures. This numerical research deals with investigating the effects of reinforcing a hybrid nanocomposite viscoelastic rhombic plate with Carbon Nano-Tubes (CNTs) and Carbon Fibers (CFs) on the post-buckling behavior, free and forced vibration as well as energy absorption characteristics. The structure is located on a viscoelastic torsional fractional substrate. In addition, the influence of random distribution, waviness, and agglomeration of CNTs is analyzed using the Halpin-Tsai theory. The structural damping is based on the Kelvin-Voigt method and the structure model is created according to the first-order shear deformation theory. Four types of boundary conditions such as fixed, simply, and free-supported are considered for the structure model. To solve the governing equations, a novel approach known as the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) is applied. The numerical achievements revealed that by reducing the skewness angle to 30°, decreasing the aspect ratio to 1, and increasing the CNTs weight percentage up to 0.4, dimensionless frequency improved by 101%. Application of FFFF boundary conditions has dramatically effect since the amplitudes of the dynamic deflection sharply raised (about 91.78% higher than CCCC rhombic plate) and led to deteriorated energy absorption. The dynamic deflection of the structure is increased by nearly 29.36% when both waviness and random distribution (agglomeration) parameters are considered for CNTs. Besides, the random distribution factor is more effective than waviness on post-buckling behavior, energy absorption, and stability of the rhombic plate. It is also worth mentioning that the weight percent of the CNTs affects the number of oscillations and changes the vibration pattern so that with increasing the CNTs content, the number of oscillations is enhanced.