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Large Amplitude Free Vibration Analysis of Isotropic Curved Nano/Microbeams Using a Nonlocal Sinusoidal Shear Deformation Theory-Based Finite Element Method
International Journal of Structural Stability and Dynamics ( IF 3.6 ) Pub Date : 2021-03-19 , DOI: 10.1142/s0219455421500747
G. Prateek 1 , De Sarthak 1 , R. Vasudevan 1 , M. Haboussi 2 , M. Ganapathi 1
Affiliation  

In this investigation, the nonlinear flexural free vibration characteristics of size dependent curved isotropic nano/microbeams are studied using the nonlocal elasticity theory along with the sinusoidal shear deformation theory (SSDT). Based on Hamilton’s principle, the governing equations are derived in terms of generalized displacements using finite element approach. The formulation by extending the von-Karman model accounts for both large deflections and rotations in the strain displacement definition. Direct iterative procedure is used to solve the nonlinear problem through eigenvalue procedure. This investigation aims to study the effect of various design parameters like slenderness ratio of the beam, curved beam included angle, nonlocal parameter, and boundary conditions on the amplitude–frequency response obtained from the free vibration behavior of curved nano/microbeams. This study is very useful to designers for optimal design of nano/microsystem involving structural elements of the beam type.

中文翻译:

基于非局部正弦剪切变形理论的各向同性弯曲纳米/微梁的大振幅自由振动分析

在这项研究中,使用非局部弹性理论和正弦剪切变形理论(SSDT)研究了尺寸相关的弯曲各向同性纳米/微梁的非线性弯曲自由振动特性。基于汉密尔顿原理,控制方程是使用有限元方法根据广义位移导出的。通过扩展 von-Karman 模型的公式说明了应变位移定义中的大变形和旋转。直接迭代过程用于通过特征值过程来解决非线性问题。本研究旨在研究梁的长细比、弯曲梁夹角、非局部参数、从弯曲纳米/微梁的自由振动行为获得的幅频响应和边界条件。这项研究对于设计人员对涉及梁型结构元素的纳米/微系统的优化设计非常有用。
更新日期:2021-03-19
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