Journal ArticleDOI
Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method
Jinhee Lee,William W. Schultz +1 more
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TLDR
In this paper, the free vibration of Timoshenko beams and axisymmetric Mindlin plates with clamped, simply supported, free and sliding boundary conditions was analyzed using the Chebyshev pseudospectral method.About:
This article is published in Journal of Sound and Vibration.The article was published on 2004-01-22. It has received 106 citations till now. The article focuses on the topics: Timoshenko beam theory & Chebyshev pseudospectral method.read more
Citations
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Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories
TL;DR: In this article, the fundamental frequency analysis of functionally graded (FG) beams having different boundary conditions is analyzed within the framework of the classical, the first-order and different higher-order shear deformation beam theories.
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Analytical modeling of spindle-tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF
TL;DR: In this paper, an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods is presented.
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Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method
TL;DR: In this paper, the authors used the modified rule of mixture to approximate material properties of the FGM beams including the porosity volume fraction and the Timoshenko beam theory is used to form the coupled equations of motion for describing dynamic behavior of the beams.
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Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method
TL;DR: In this paper, a study of free vibration of Timoshenko beams and Mindlin plates is presented based on a new numerical scheme, where collocation by radial basis functions and pseudospectral methods are combined to produce highly accurate results.
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Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory
TL;DR: In this paper, the frequency of the flap-wise bending vibrations of a non-uniform rotating nanocantilever was calculated considering the true spatial variation of the axial force due to the rotation.
References
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Book
A practical guide to pseudospectral methods
TL;DR: In this article, the authors introduce spectral methods via orthogonal functions and finite differences, and compare computational cost of spectral methods with FD and PS methods in polar and spherical geometries.
Journal ArticleDOI
Differential Quadrature Method in Computational Mechanics: A Review
Charles W. Bert,Moinuddin Malik +1 more
TL;DR: The differential quadrature method (DQM) as discussed by the authors is a numerical solution technique for initial and/or boundary problems, which was developed by the late Richard Bellman and his associates in the early 70s.
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Vibration analysis of circular mindlin plates using the differential quadrature method
TL;DR: In this article, the first fifteen natural frequencies of vibration are calculated for uniform circular plates with free, simply-supported and clamped edges, and the capability and simplicity of the differential quadrature method for moderately thick plate eigenvalue analysis is demonstrated.