Geometrically Nonlinear Electromechanical Instability of FG Nanobeams by Nonlocal Strain Gradient Theory
| Autor: | Jalal Torabi, S. M. J. Hosseini, A. Zabihi, Reza Ansari |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Geometrically nonlinear Applied Mathematics Mechanical Engineering Mathematical analysis Aerospace Engineering Ocean Engineering 02 engineering and technology Building and Construction 021001 nanoscience & nanotechnology Strain gradient Instability Functionally graded material Vibration Nonlinear system 020303 mechanical engineering & transports 0203 mechanical engineering 0210 nano-technology Homotopy analysis method Civil and Structural Engineering |
| Zdroj: | International Journal of Structural Stability and Dynamics. 21:2150051 |
| ISSN: | 1793-6764 0219-4554 |
| DOI: | 10.1142/s0219455421500516 |
| Popis: | This paper is concerned with studying the size-dependent nonlinear dynamic pull-in instability and vibration of functionally graded Euler–Bernoulli nanobeams (FG-EBNs) with the von Kármán hypothesis based on the nonlocal strain gradient theory (NLSGT). To this end, the partial differential equation (PDE) is developed by Hamilton’s principle considering the intermolecular, fringing field and electrostatic nonlinear forces. Then, the Galerkin method (GM) is utilized to acquire the ordinary differential equation (ODE) and the results are obtained with the help of an analytical approach called the homotopy analysis method (HAM). To verify the outcome of this study, the nonlinear and linear frequencies obtained are compared with those of the literature. Consequently, the pull-in voltage of the FG nanobeam is obtained and the variations of nonlinear and linear frequencies are discussed in detail. Also, the effects of initial amplitude, electrostatic force, length scale, nonlocal parameter, material gradient index and boundary condition (BC) on the electromechanical behavior of FG-EBNs are analyzed with the results commented. |
| Databáze: | OpenAIRE |
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