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Free vibration of two coupled nonlinear oscillators
Nonlinear Dynamics, 1994An analytical investigation is carried out on the free vibration of a two degree of freedom weakly nonlinear oscillator. Namely, the method of multiple time scales is first applied in deriving modulation equations for a van der Pol oscillator coupled with a Duffing oscillator.
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Finite Element Method for Nonlinear Free Vibrations of Composite Plates
AIAA Journal, 1997A multimode time-domain modal formulation based on the finite element method for large-amplitude free vibration of thin composite plates is presented. Accurate frequency-maximum deflection relations can be predicted for the fundamental and the higher nonlinear modes.
Shi, Yucheng +2 more
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Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells
International Journal of Structural Stability and Dynamics, 2019This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary ...
Kamaloo, Abbas +3 more
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Nonlinear Free Vibration of Laminated Composite Plates
Journal of Engineering Mechanics, 1992In this paper the nonlinear vibration of composite plates has been presented. Usually in the nonlinear analysis of plates, the von Karman‐type formulation is followed because it is possible to obtain the complete solution once the solution for lateral displacement is assumed.
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Nonlinear Free Vibration of Nanobeams With Surface Effects Considerations
Volume 7: 5th International Conference on Micro- and Nanosystems; 8th International Conference on Design and Design Education; 21st Reliability, Stress Analysis, and Failure Prevention Conference, 2011In this paper, simple analytical expressions are presented for geometrically non-linear vibration analysis of thin nanobeams with both simply supported and clamped boundary conditions. Gurtin-Murdoch surface elasticity together with Euler-Bernoulli beam theory is used to obtain the governing equations of motions of the nanobeam with surface effects ...
Ali Fallah +3 more
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Periodic geometrically nonlinear free vibrations of circular plates
Journal of Sound and Vibration, 2008Abstract The geometrically nonlinear free vibrations of thin isotropic circular plates are investigated using a multi-degree-of-freedom model, which is based on thin plate theory and on Von Karman's nonlinear strain–displacement relations. The middle plane in-plane displacements are included in the formulation and the common axisymmetry restriction ...
S. Stoykov, P. Ribeiro
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Nonlinear Free and Forced Vibrations of Symmetric Laminated Panels
Key Engineering Materials, 2011In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.
Alireza Shooshtari +3 more
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Nonlinear free vibration of piezoelectric laminated composite plate
Finite Elements in Analysis and Design, 2009This paper addresses the nonlinear free vibration characteristic of laminated composite plate with embedded and/or surface bonded piezoelectric layer. Nonlinear governing equations are derived in Green-Lagrange sense in the framework of a higher order shear deformation theory.
Padmanav Dash, B.N. Singh
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Nonlinear forced and free vibrations in acoustic waveguides
The Journal of the Acoustical Society of America, 1974Nonlinear acoustic theory is used to show that the cutoff frequencies and the resonant frequencies of modes in acoustic waveguides of finite length depend upon the mode amplitude. The amplitude εn, of mode n > 0, produced by a periodic piston motion of amplitude δn, is also determined.
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Nonlinear Free Vibration Analysis of a Fluid-Conveying Microtube
Volume 4A: Dynamics, Vibration, and Control, 2014Nonlinear free vibration of a microstructure has been analyzed in this study. A fluid-conveying microtube is mathematically modeled using non-classical beam theory. Partial differential equation of the model is considered in non-dimensional form. Simply-supported boundaries are taken into account and assuming three vibrating modes, an analytical method
Shamim Mashrouteh +3 more
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