ارتعاشات غيرخطي ميكروتيرهاي مدرج تابعي بر اساس گراديان الاستيسيتهي اصلاحي و تئوري تير تيموشنكو غيركلاسيك

Nonlinear vibration of functionally graded microbeams based on modified gradient elasticity an‎d non-classical Timoshenko beam theory

مهندسي مكانيك

In recent years, microstructures have been widely utilized across many engineering domains, with microbeams playing a pivotal role in the fabrication an‎d design of microelectromechanical systems (MEMS). With the advent of micro-scale fabrication technology, functionally graded materials are now utilized in the production of MEMS due to their unique properties. Given the aforementioned factors, an accurate eva‎luation of the dynamic behavior of functionally graded microbeams is essential. This paper presents a non-classical Timoshenko beam model to investigate free nonlinear vibration in functionally graded microbeams. The new model is developed based on the modified gradient elasticity (MGE) an‎d von Kármán geometric nonlinearity. The material properties of the functionally graded (FG) beam are assumed to be graded in the thickness direction, an‎d they are determined by using the Mori-Tanaka homogenization technique. In this model, two length scale parameters are employed to capture the size effect. Governing equations an‎d corresponding boundary conditions are derived using the Hamilton principle. Then, a numerical method that makes use of the Ritz-Galerkin technique an‎d the differential quadrature method is employed to solve the equations. The effect of the length scale parameters, material property gradient index, length-to-thickness ratio, amplitude of the vibration, Poisson’s ratio, an‎d different end supports on the nonlinear an‎d linear frequencies of the microbeam are discussed later. The findings indicate that the difference between the predictions of this non-classical model an‎d those of the classical one becomes more significant for very thin microbeams. Moreover, it is found that the MGE model can properly predict the nonlinear behavior of the FG microbeam as well as previous theories.

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