Journal ArticleDOI
Effect of boundary condition nonlinearities on free large-amplitude vibrations of rectangular plates
TLDR
In this paper, the effect of boundary condition nonlinearities on free nonlinear vibrations of thin rectangular plates is analyzed and the results of the calculations with nonlinear boundary conditions differ essentially from the data obtained without these boundary conditions.Abstract:
The effect of boundary condition nonlinearities on free nonlinear vibrations of thin rectangular plates is analyzed. The method for analysis of the plate vibrations with geometrical nonlinearity and the boundary condition nonlinearity is suggested. The nonlinear boundary conditions for membrane forces are transformed into linear ones using the in-plane stress function. Additional boundary conditions for the in-plane displacements vanishing on the clamped edge of the plate are imposed on the stress function. Simply supported and cantilever plates are analyzed. The backbone curves obtained by satisfying linear and nonlinear boundary conditions are compared. It is shown that the results of the calculations with nonlinear boundary conditions differ essentially from the data obtained without these boundary conditions.read more
Citations
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Journal ArticleDOI
Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid
TL;DR: In this paper, a nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate was presented using the classical plate theory (CPT).
Journal ArticleDOI
Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane
TL;DR: In this paper, the nonlinear vibration characteristics of a moving membrane with variable velocity have been examined, and the velocity is assumed as harmonic change that takes place over uniform average speed.
Journal ArticleDOI
Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow:
K. V. Avramov,K. V. Avramov +1 more
TL;DR: In this paper, a method for analysis of stability and bifurcations of the plate self-sustained vibrations is suggested, based on the solution of the singular integral equations with respect to aerodynamic derivatives of plate pressure drop.
Journal ArticleDOI
Analysis and modeling of a flexible rectangular cantilever plate
TL;DR: In this article, a general nonlinear flexible rectangular cantilever plate considering large deflection and rotation angle is modeled, solved and analyzed, and the nonlinear differential dynamic equations and boundary conditions are obtained by introducing a coordinate transformation between the Cartesian coordinate system and the deformed local coordinate system.
Journal ArticleDOI
The effect of material and geometry on the non-linear vibrations of orthotropic circular cylindrical shells
TL;DR: In this article, the influence of both material properties and geometry on the nonlinear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied.
References
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Book
Practical Numerical Algorithms for Chaotic Systems
Thomas S. Parker,Leon O. Chua +1 more
TL;DR: The goal of this book is to present an elementary introduction on chaotic systems for the non-specialist, and to present and extensive package of computer algorithms for simulating and characterizing chaotic phenomena.
Book
Elements of vibration analysis
TL;DR: In this article, the authors provide contemporary coverage of the primary concepts and techniques in vibration analysis, and more elementary material has been added to the first four chapters of this second edition for an updated and expanded introduction to vibration analysis.
Book
Nonlinear Vibrations and Stability of Shells and Plates
TL;DR: In this article, a comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells is presented. But the authors do not consider the effect of boundary conditions on the large-amplitude vibrations of circular cylinders.
Journal ArticleDOI
Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments
TL;DR: In this article, the von Karman nonlinear strain-displacement relationship is used for large-amplitude (geometrically nonlinear) vibrations of rectangular plates subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances.
Journal ArticleDOI
Nonlinear free vibration behavior of functionally graded plates
TL;DR: In this article, an analytical solution for the nonlinear free vibration behavior of plates made of functionally graded materials is provided, where the material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents.