• Advances in nano research
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• 제9권4호
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• pp.295-307
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• 2020

The vibrational characteristics of Multi-Phase Nanocomposite (MPC) reinforced annular/circular plate under initially stresses are presented using the state-space formulation based on three-dimensional elasticity theory (3D-elasticity theory) and Differential Quadrature Method (DQM). The MPC reinforced annular/circular plate is under initial lateral stress and composed of multilayers with Carbon Nanotubes (CNTs) uniformly dispersed in each layer, but its properties change layer-by-layer along the thickness direction. The State-Space based Differential Quadrature Method (SS-DQM) is presented to examine the frequency behavior of the current structure. Halpin-Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale composite. A singular point is investigated for modeling the circular plate. The CNTs are supposed to be randomly oriented and uniformly distributed through the matrix of epoxy resin. Afterward, a parametric study is done to present the effects of various types of sandwich circular/annular plates on frequency characteristics of the MPC reinforced annular/circular plate using 3D-elasticity theory.

• Advances in nano research
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• 제16권5호
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• pp.473-487
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• 2024

The current study employs the nonlocal Timoshenko beam (NTB) theory and von-Kármán's geometric nonlinearity to develop a non-classic beam model for evaluating the nonlinear free vibration of bi-directional functionally-graded (BFG) nanobeams. In order to avoid the stretching-bending coupling in the equations of motion, the problem is formulated based on the physical middle surface. The governing equations of motion and the relevant boundary conditions have been determined using Hamilton's principle, followed by discretization using the differential quadrature method (DQM). To determine the frequencies of nonlinear vibrations in the BFG nanobeams, a direct iterative algorithm is used for solving the discretized underlying equations. The model verification is conducted by making a comparison between the obtained results and benchmark results reported in prior studies. In the present work, the effects of amplitude ratio, nanobeam length, material distribution, nonlocality, and boundary conditions are examined on the nonlinear frequency of BFG nanobeams through a parametric study. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies for the same amplitude of the nonlinear oscillator. The study finds that the difference between the dimensionless linear frequency and the nonlinear frequency is smaller for CC nanobeams compared to SS nanobeams, particularly within the α range of 0 to 1.5, where the impact of geometric nonlinearity on CC nanobeams can be disregarded. Furthermore, the nonlinear frequency ratio exhibits an increasing trend as the parameter µ is incremented, with a diminishing dependency on nanobeam length (L). Additionally, it is established that as the nanobeam length increases, a critical point is reached at which a sharp rise in the nonlinear frequency ratio occurs, particularly within the nanobeam length range of 10 nm to 30 nm. These findings collectively contribute to a comprehensive understanding of the nonlinear vibration behavior of BFG nanobeams in relation to various parameters.