Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

Abstract

In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account for different distributions of CNTs (with uniform or nonuniform linear patterns), together with the presence of an elastic foundation, and von-Karman type nonlinearities. The basic equations of the problem are solved by using the Galerkin and Grigolyuk methods, in order to determine the frequencies associated with linear and nonlinear free vibrations. The reliability of the proposed methodology is verified against further predictions from the literature. Then, we examine the model for the sensitivity of the vibration response to different input parameters, such as the mechanical properties of the soil, or the nonlinearities and distributions of the reinforcing CNT phase, as useful for design purposes and benchmark solutions for more complicated computational studies on the topic.

Influences of Elastic Foundations and Material Gradient on the Dynamic Response of Polymer Cylindrical Pipes Patterned by Carbon Nanotube Subjected to Moving Pressures

“…where w CN is the mass fraction of the nanotube. It was assumed that V CN is defined as a function of the thickness coordinate as follows [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] (see Figure 2): [24]:…”

“…For these reasons, the researchers have begun to study the static and dynamic responses of cylindrical shape structures originating from CNT. The first studies of the static and dynamic behavior of CNT-based cylindrical shells, without considering the influence of soils, were carried out, and there are many significant studies on this topic [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

“…The first attempt to study the effect of EFs on the dynamic behavior of cylindrical shells originating from CNTs was carried out in the study by Shen and Xiang [48]. After this study, starting in 2015, several studies on the dynamic and static problems of cylindrical shells originating from CNTs resting on the EFs were carried out, and their relevance and importance in applications are still being studied [42,[49][50][51][52][53][54]. Despite the rapid increase in the number of studies devoted to the free vibration behavior of CNT-based cylindrical shells, panels, and pipes, the investigation on the forced vibration of such elements under moving pressures is scarce and has been conducted without considering the elastic foundations effect [55][56][57][58][59][60].…”

Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance

“…Such as many structures that are influenced by the time [ 9 , 10 , 11 , 12 ], the operation of AFMs may be time-dependent and, consequently, under dynamic conditions. Thus, most previous studies in this field have focused on the dynamic performance of AFMs.…”

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

“…For many decades, vibration analysis of mechanical structures was a major topic among scientists [1][2][3][4][5][6][7][8][9][10]. Over recent decades, a surge of interest in studying hyperelastic materials was shown.…”