Method of collocation by derivatives in the study of axisymmetric vibrations of circular plates

Gupta, Utkarsh; Jain, S. K.; Jain, Dheeraj

doi:10.1016/0045-7949(95)00085-u

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…Roque et al (2007) used the multi-quadratic method to determine the natural frequency of plates. Gupta et al (1995) investigated the natural frequencies of circular plates by using the collocation method by derivatives. The first three vibration modes were then calculated.…”

Section: Introductionmentioning

confidence: 99%

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Shum¹,

Tsang²

2008

Bridge Structures

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A proposal for a numerical method based on the complete solution collocation method is presented to solve the cable-stayed bridge engineering structural problem. This complete function collocation method is presented from the viewpoint of calculating the pretension forces required for the final completed bridge structure, which is one of the most important and practical considerations in cable-stayed bridge design. The complete function collocation method is used to calculate stay cable forces by solving a set of partial differential equations. The study shows that this mesh-free collocation method can be used to solve practical structural engineering problems and provides an alternative to traditional finite element methods. A simple two-dimensional cable-stayed bridge is presented and is solved to illustrate this numerical method. Governing equations of deformation for a bridge structure are formulated in either Eulerian or Lagrangian coordinate systems according to the situation. Point loads due to stay cables on bridge pylons and bridge deck are modelled by Fourier or Gaussian representations. Transverse natural frequencies of stay cables subject to no body forces and caused by flow-induced vibration due to blowing wind are proposed. The preliminary computational procedure presented in this paper provides the basis for further analysis toward more realistic cable-stayed bridges, which would include nonlinear effects, live loadings and construction stage loadings.

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Section: Introductionmentioning

confidence: 99%

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Shum¹,

Tsang²

2008

Bridge Structures

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Moving least square Ritz method for vibration analysis of plates

Zhou

Zheng

2006

Journal of Sound and Vibration

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Effect of Foundation and Non-Homogeneity on the Vibrations of Polar Orthotropic Parabolically Tapered Circular Plates

Srivastava¹,

Sharma²,

Lal³

2015

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The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on fundamental, second and third mode of vibration have been studied for clamped and simply-supported boundary conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence and comparison studies have been carried out for specified plates.

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Method of collocation by derivatives in the study of axisymmetric vibrations of circular plates

Cited by 3 publications

References 16 publications

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Moving least square Ritz method for vibration analysis of plates

Effect of Foundation and Non-Homogeneity on the Vibrations of Polar Orthotropic Parabolically Tapered Circular Plates

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