Journal ArticleDOI
Finite element displacement method for large amplitude free flexural vibrations of beams and plates
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TLDR
In this article, a finite element method to determine the nonlinear frequency of beams and plates for large amplitude free vibrations is presented, which is characterized by the basic stiffness, mass, geometrical stiffness and the associated inplane force matrices.About:
This article is published in Computers & Structures.The article was published on 1973-01-01. It has received 138 citations till now. The article focuses on the topics: Direct stiffness method & Finite element method.read more
Citations
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Journal ArticleDOI
Non-linear vibrations of orthotropic plates by a finite element method
Journal ArticleDOI
Analytical and Experimental Studies on the Large Amplitude Free Vibrations of Variable-Arc-Length Beams
TL;DR: In this article, the effect of large initial static sag deflections due to self-weight was investigated using the finite element method, and the large amplitude free vibration equation of motion was derived based on the variational formulation.
Journal ArticleDOI
Calculation of eigenvalue and eigenvector derivatives for nonlinear beam vibrations
J. W. Hou,J. Z. Yuan +1 more
TL;DR: In this article, a beam with immovable ends under large amplitude oscillations is axially subjected to an amplitudedependent stretching force which is induced by the geometrical nonlinearity.
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Adaptive Control of Nonlinear Free Vibrations of Composite Plates Using Piezoelectric Actuators
TL;DR: In this article, a coupled structural-electrical finite element modal formulation is employed for the control of nonlinear free vibrations of beams and composite plates in closed-loop simulations.
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Bifurcations and internal resonances in space-curved rods
TL;DR: In this article, a geometrically non-linear model of space-curved beams is discussed, which includes the shear effects and rotatory inertia, and the motion of the system is described by a nonlinear matrix equation, which accounts for nonlinearities up to the second order.
References
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Book
Theory of plates and shells
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Book
Vibration of plates
TL;DR: The fundamental equation of classical plate theory can be found in this article, where anisotropic and variable-thickness versions of the classical plates are considered, as well as other considerations.
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A new approach to the analysis of large deflections of plates
TL;DR: In this article, simplified equations for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions are derived and compared with available numerical solutions of the exact equations, and the deflections found by this approach are then used to obtain the stresses, and resulting stresses are compared with existing solutions.
Journal ArticleDOI
Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates
TL;DR: In this paper, approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified.