Natural frequencies of heated annular and circular plates

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

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Natural frequencies of monoclinic circular plates

The Journal of the Acoustical Society of America ◽

10.1121/1.1914616 ◽

1974 ◽

Vol 55 (4) ◽

pp. 874-876

Author(s):

J. Padovan ◽

J. Lestingi

Keyword(s):

Natural Frequencies ◽

Circular Plates

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The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part II: iterative and explicit analytical solution for non-linear coupled transverse and in-plane vibrations

Journal of Sound and Vibration ◽

10.1016/j.jsv.2003.08.039 ◽

2004 ◽

Vol 277 (1-2) ◽

pp. 1-30 ◽

Cited By ~ 26

Author(s):

M. Haterbouch ◽

R. Benamar

Keyword(s):

Analytical Solution ◽

Natural Frequencies ◽

Mode Shapes ◽

Circular Plates ◽

Axisymmetric Mode ◽

Explicit Analytical Solution ◽

Non Linear

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Comments on “bounds on natural frequencies of composite circular plates: Integral equation method” by W. B. Bickford and S. Y. Wu

Journal of Sound and Vibration ◽

10.1016/0022-460x(91)90740-b ◽

1991 ◽

Vol 144 (1) ◽

pp. 173-178

Author(s):

P.A.A. Laura ◽

E.A. Bambill

Keyword(s):

Integral Equation ◽

Natural Frequencies ◽

Integral Equation Method ◽

Equation Method ◽

Circular Plates

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Vibration of Circular Plates in Contact With Water

Journal of Applied Mechanics ◽

10.1115/1.2897209 ◽

1991 ◽

Vol 58 (2) ◽

pp. 480-483 ◽

Cited By ~ 69

Author(s):

M. K. Kwak

Keyword(s):

Natural Frequencies ◽

Integral Transformation ◽

Integral Equation Method ◽

Mass Effect ◽

Dual Integral Equation ◽

Practical Reasons ◽

Virtual Mass ◽

Circular Plates ◽

Transformation Technique ◽

Simply Supported

This paper is concerned with the virtual mass effect on vibrating circular plates due to the presence of water. Natural frequencies in water can be estimated from natural frequencies in air by using the approximate formula, which mainly depends upon the so-called added virtual mass incremental factor. The added virtual mass incremental factor is a function of geometry, material properties of the plates and mostly boundary conditions of the plates, and water domain. For practical reasons, the added virtual mass incremental factor is likely to be nondimensionalized. In this paper, the nondimensionalized added virtual mass incremental factors for circular plates having simply-supported, clamped, and free edges are obtained by employing the integral transformation technique in conjunction with the dual integral equation method. It is found that the effect of water on the natural frequencies decreases with order.

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