Study of pure transverse motion in free cylinders and plates in flexural vibration by Ritz’s method

Bayón, A.; Gascón, F.; Ferro, Rafael Medina; Nieves, F. J. de las; Salazar, F.

doi:10.1016/j.euromechsol.2010.12.006

Cited by 6 publications

(2 citation statements)

References 18 publications

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“…Dirichlet or Neumann), various approximate methods of solutions have been developed. There exists on one hand analytical solutions based on expansion in terms of Bessel functions [8,9] where part of the boundary conditions are satisfied approximately, and on the other hand numerical solutions such as the Ritz method [10,11,12,13] or the finite element method [14]. These works using approximate methods concentrate mainly on eigenfrequency analyzes.…”

Section: Introductionmentioning

confidence: 99%

A hierarchy of dynamic equations for solid isotropic circular cylinders

Abadikhah

Folkow

2014

Wave Motion

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This work considers homogeneous isotropic circular cylinders adopting a power series expansion method in the radial coordinate. Equations of motion together with consistent sets of end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton's principle. Time domain partial differential equations are obtained for longitudinal, torsional, and flexural modes, where these equations are asymptotically correct to all studied orders. Numerical examples are presented for different sorts of problems, using exact theory, the present series expansion theories of different order, and various classical theories. These results cover dispersion curves, eigenfrequencies and the corresponding displacement and stress distributions, as well as fix frequency motion due to prescribed end displacement or lateral distributed forces. The results illustrate that the present approach may render benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.

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Section: Introductionmentioning

confidence: 99%

A hierarchy of dynamic equations for solid isotropic circular cylinders

Abadikhah

Folkow

2014

Wave Motion

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“…Hua et al [2] investigated axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound. Hasheminejad and Mirzaei [3] studied exact 3D elasticity solution for free vibrations of an eccentric hollow sphere. Buchanan and Liu [4] investigated analysis of the free vibration of thick walled isotropic toroidal shells.…”

Section: Introductionmentioning

confidence: 99%

Effect of Initial Stress on Wave Frequencies of Elastic Solid with Rotation

Yahya¹,

Elhag²,

Sanaa³

et al. 2014

JMP

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In this paper, the effect of initial stress on the radial vibrations of elastic hollow cylinder with rotation is discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free; fixed and mixed boundary condition is examined numerically. The determination is concerned with the eigenvalues of the natural frequency of the radial vibrations in the case of harmonic vibrations. The effect of rotation and initial stress on the natural frequencies was examined. It was shown that the dispersion curves of guided waves were significantly influenced by the rotation and initial stress of the elastic cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation and initial stress are very pronounced.

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