Asymmetric Vibrations and Elastic Stability of Polar Orthotropic Circular Plates of Linearly Varying Profile

Gupta, Utkarsh; Ansari, A.H.

doi:10.1006/jsvi.1998.1589

Cited by 29 publications

(12 citation statements)

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“…They came to the conclusion that a travelling wave component is possible only if an internal resonance exists between modes of frequency well apart from the excitation frequency [15]. Asymmetric linear vibrations of circular plates of linearly varying thickness have also been considered recently in references [16,17]. Finally, recent development in computer simulations leads to numerical studies, which generally use a finite element method combined with the harmonic balance method, see for example references [18,19].…”

Section: Introductionmentioning

confidence: 96%

Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates. Part 1: Theory

Touzé¹,

Thomas²,

Chaigne³

2002

Journal of Sound and Vibration

103

100

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In this article, a detailed study of the forced asymmetric non-linear vibrations of circular plates with a free edge is presented. The dynamic analogue of the von K" a arm" a an equations is used to establish the governing equations. The plate displacement at a given point is expanded on the linear natural modes. The forcing is harmonic, with a frequency close to the natural frequency o kn of one asymmetric mode of the plate. Thus, the vibration is governed by the two degenerated modes corresponding to o kn ; which are one-to-one internally resonant. An approximate analytical solution, using the method of multiple scales, is presented. Attention is focused on the case where one configuration which is not directly excited by the load gets energy through non-linear coupling with the other configuration. Slight imperfections of the plate are taken into account. Experimental validations are presented in the second part of this paper. #

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Section: Introductionmentioning

confidence: 96%

Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates. Part 1: Theory

Touzé¹,

Thomas²,

Chaigne³

2002

Journal of Sound and Vibration

103

100

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“…However, for the centroidal deflection equal to 0.2 h, the thermal load for the simply supported plate is nearly 5% more than that for the clamped plate. In Table 2, a comparison is made of the presently found fundamental frequency, 1 , of a polar orthotropic circular plate with that computed by the Ritz method in [27]. For both simply supported and clamped circular plates with three values 0.75, 1.0 and 10.0 of the rigidity ratio k, the presently computed fundamental frequency agrees well with that computed by the Ritz method.…”

Section: Numerical Results and Discussionmentioning

confidence: 58%

Vibration of Thermally Post-Buckled Orthotropic Circular Plates

Liu

Batra

2006

Journal of Thermal Stresses

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Axisymmetric vibrations of a statically buckled polar orthotropic circular plate due to uniform temperature rise have been studied numerically. Effects of geometric nonlinearities have been incorporated into the problem formulation. The problem is challenging because the buckled configuration is unknown a priori. By assuming that the amplitude of plate's vibration and the additional strains induced in it are infinitesimal, and its response harmonic, the non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations; one for the thermal post-buckling, and the other for linear vibrations of the plate superimposed upon the post-buckled configuration. The plate's boundary is taken to be either clamped or simply supported but restrained from moving in the radial direction. The two sets of coupled boundary value problems are solved numerically by a shooting method. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and postbuckled plates, have been computed, and characteristic curves of the frequency versus temperature rise for different values of material anisotropy parameters are plotted. It is found that the three lowest frequencies of the pre-buckled plate decrease with an increase in the temperature, but those of a buckled plate increase monotonically with the temperature rise. The fundamental frequency of the deformed plate approaches zero at the onset of buckling.

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“…A relative error limit, "10\, was taken to warrant that both the numerical integration of equation (35) and the successive correction of equation (36) were carried out until the error norm became less than . For an unheated ( "0) circular plate (c"0)0001) without rigid mass ( "0), a comparison of the values of linear fundamental frequency in this paper with those obtained by Ritz's method in reference [5] is presented below. For prescribed values of the rigidity ratio k"0)75, 1)0, 10)0, the corresponding fundamental frequencies in this paper are "4)5421, 4)9351, 11)286 and those in reference [5] are "4)5418, 4)9351, 11)286, which shows an excellent agreement with the published results.…”

Section: Numerical Results and Discussionmentioning

confidence: 95%

“…[1}11]. Di!erent researchers have used di!erent analytical or numerical methods; Laura et al [1}3], Gupta et al [4,5], Gunaratnam [6] and others analyzed linear free vibration and buckling of polar orthotropic circular and annular plates. On considering the geometric non-linearity of the plates, large-amplitude axisymmetric vibrations of this kind of plates were presented in many literatures.…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Vibration and Thermal Buckling of an Orthotropic Annular Plate With a Centric Rigid Mass

Zhou

Song

2002

Journal of Sound and Vibration

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Asymmetric Vibrations and Elastic Stability of Polar Orthotropic Circular Plates of Linearly Varying Profile

Cited by 29 publications

References 0 publications

Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates. Part 1: Theory

Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates. Part 1: Theory

Vibration of Thermally Post-Buckled Orthotropic Circular Plates

Non-Linear Vibration and Thermal Buckling of an Orthotropic Annular Plate With a Centric Rigid Mass

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