Vibration characteristics of functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports

Abstract

This paper presents the first known vibration characteristics of moderately thick functionally graded carbon nanotube reinforced composite rectangular plates on Pasternak foundation with arbitrary boundary conditions and internal line supports on the basis of the firstorder shear deformation theory. Different distributions of single walled carbon nanotubes (SWCNTs) along the thickness are considered. Uniform and other three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates are studied. The solutions carried out using an enhanced Ritz method mainly include the following three points: Firstly, create the Lagrange energy function by the energy principle; Secondly, as the main innovation point, the modified Fourier series are chosen as the basic functions of the admissible functions of the plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges; Lastly, solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. In this study, the influences of the volume fraction of CNTs, distribution type of CNTs, boundary restrain parameters, location of the internal line supports, foundation coefficients on the natural frequencies and mode shapes of the FG-CNT reinforced composite rectangular plates are presented.

The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations

“…Example 2. In the second comparison, the accuracy in terms of dimensionless linear frequency for single-layer square isotropic plates resting on the Pasternak elastic foundation for b = 100 h, a = b, K w /D 0(1) = 500 and K p /D 0(1) = 10 is ensured by comparing it with Wang et al [40] and Zhong et al [41]. In this example, relationship (21) is used for 2 reveals consistent agreement between our formulation and the findings presented in Wang et al [40] and Zhong et al [41], although based on different approaches.…”

Free Vibration Analysis of Single Walled Carbon Nanotube with Exponentially Varying Stiffness

“…Effect of length-to-height ratio (L/h) on the first four frequency parameters has been investigated. First four frequency parameters are given in Table 4 for different L/h (10,20,30,40,50). In this table, we have considered all the boundary conditions such as SS, CS, CC and CF with µ = 1 nm 2 and η = 0.2.…”

“…Various applica-tions concerning CNT reinforced structure like reinforced beam, plate etc. can be found in the literatures [4][5][6][7][8][9][10][11]. Ever since the discovery of the fullerene, the family of carbon nanostructures has been steadily expanded.…”

Influence of multi‐walled carbon nanotubes reinforced honeycomb core on vibration and damping responses of carbon fiber composite sandwich shell structures

“…The strength and moduli of the foam‐filled honeycomb structure increase than those of the carbon fiber braided honeycomb core without the reinforcement of polymer foam. Zhong et al [ 11 ] presented the dynamic characteristics of honeycomb sandwich plates with FG‐CNT reinforcement based on first‐order shear deformation theory (FSDT). Various functionally graded sandwich plates such as FGX‐CNT (CNTs are concentrated at top and bottom regions), FGV‐CNT (CNTs are concentrated at top regions), FGO‐CNT (CNTs are concentrated at top and bottom regions) and UT‐CNT (CNTs are uniformly distributed) were considered.…”