Modeling and Solution of Large Amplitude Vibration Problem of Construction Elements Made of Nanocomposites Using Shear Deformation Theory

Abstract

The main purpose of the study is to investigate the vibration behaviors of carbon nanotube (CNT) patterned double-curved construction elements using the shear deformation theory (SDT). After the visual and mathematical models of CNT patterned double-curved construction elements are created, the large amplitude stress–strain relationships and basic dynamic equations are derived using the first order shear deformation theory (FSDT). Then, using the Galerkin method, the problem is reduced to the nonlinear vibration of nanocomposite continuous systems with quadratic and cubic nonlinearities. Applying the Grigolyuk method to the obtained nonlinear differential equation, large-amplitude frequency-amplitude dependence is obtained. The expressions for nonlinear frequencies of homogenous and inhomogeneous nanocomposite construction members such as plates, panels, spherical and hyperbolic-paraboloid (hypar) shells in the framework of FSDT are found in special cases. The accuracy of the results of the current study has been confirmed by comparing them with the reliable results reported in the literature. Original analyses are carried out to examine the effects of nonlinearity, CNT patterns and volume fraction changes on frequencies in the framework of shear deformation and classical shell theories.

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].…”

Radial Point Interpolation Method for Isotropic Nanoplates in Bending Using Strain Gradient Theory

“…These kind of structures, in fact, have proven to be extremely versatile, finding wide applications in Micro-Electro-Mechanical-Systems (MEMS) and Nano-Electro-Mechanical-Systems (NEMS) which require the employment of nanorods, nanobeams and nanoplates [Mariano and Trovalusci (1999); Barretta et al (2018); Mahmure et al (2021); ; Akgöz and Civalek (2015a); ; Numanglu et al (2018); ]. Nonlocal theories have been widely applied in the study of these structural components to investigate nonlocal effects in both static [Trovalusci and Augusti (1998); Tuna et al (2019); ; Tocci Monaco et al (2021b); Barretta and Marotti de Sciarra (2013)] and dynamic [Avey et al (2021); Deniz et al (2021); Tocci Monaco et al (2021a); Numanglu et al (2018); Barretta et al (2019); ] analysis.…”