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Free vibration analysis of a nonlinear beam using homotopy and modified lindstedt-poincare methods
, Article Journal of Solid Mechanics ; Volume 1, Issue 1 , Volume 1, Issue 1 , 2009 , Pages 29-36 ; 20083505 (ISSN) ; Mojahedi, M ; Moeenfard, H ; Sharif University of Technology
Abstract
In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions are valid for a wide range of...
Characterization of static behavior of a nonlinear doubly clamped microbeam under electrostatic actuation and detection
, Article Proceedings of the ASME Design Engineering Technical Conference ; Volume 1 , August , 2013 ; 9780791855843 (ISBN) ; Barari, A ; Mojahedi, M ; Firoozbakhsh, K ; Sharif University of Technology
American Society of Mechanical Engineers
2013
Abstract
In this study, the static deflection and pull-in instability of the doubly clamped microbeam with a mass attached to its midpoint are investigated. Nonlinear electrostatic forces, fringing fields, base rotation and mid-plane stretching of the beam in this model are considered. First, a system of two nonlinear integro-differential equations are expressed in partial derivatives which describe coupled flexural-flexural motion of electrostatically actuated microbeam gyroscopes under rotation. Then static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (direction and sensing) directions are studied. The equations of static motion are reduced by...
A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams
, Article Journal of Mechanical Science and Technology ; Volume 25, Issue 3 , 2011 , Pages 557-565 ; 1738494X (ISSN) ; Mojahedi, M ; Ahmadian, M. T ; Sharif University of Technology
Abstract
This paper uses Hes Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkins projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For...