Open AccessNonlinear Vibration of Microbeams Based on The Elastics Foundation Using High-Order Energy Balance Method and Global Error Minimization Method
Author(s) -
Dang Van Hieu
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i2.23.11882
Subject(s) - galerkin method , nonlinear system , vibration , harmonic balance , partial differential equation , mathematical analysis , mathematics , equations of motion , classical mechanics , physics , acoustics , quantum mechanics
In this paper, nonlinear vibration of microbeams based on the nonlinear elastic foundation is investigated. The equation of motion of microbeams based on three-layered nonlinear elastic medium (shear, linear and nonlinear layers) is described by the partial differential equation by using the modified couple stress theory. The equation of motion of microbeams is transformed into the ordinary differential equation by using Galerkin method. The high-order Energy Balance method and the high-order Global Error Minimization method are used to get the frequency – amplitude relationships for the nonlinear vibration of microbeams with pinned-pinned and clamped-clamped end conditions. Comparisons between the present solutions and the privious solutions show the accuracy of the obtained results.