Comment on "Lateral Vibration and Stability Relationship of Elastically Restrained Circular Plates"

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

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Optimum Elastic Restraint for Pressurised Circular Plates

Journal of the Royal Aeronautical Society ◽

10.1017/s0001924000062606 ◽

1963 ◽

Vol 67 (632) ◽

pp. 525-526

Author(s):

Charles W. Bert

Keyword(s):

Effective Stress ◽

Elastic Material ◽

Unit Volume ◽

List Type ◽

Maximum Deflection ◽

Type Number ◽

Circular Plates ◽

Uniform Thickness ◽

Isotropic Elastic Material ◽

Elastically Restrained

SummaryFor uniform-thickness, solid circular plates made of isotropic elastic material and elastically restrained at the edge, expressions are derived for the optimum support stiffness to minimise the following quantities: 1.The largest effective stress based on several different strength theories.2.The largest effective stress per unit of maximum deflection or per unit volume displaced.

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The flexural vibration of thin isotropic and polar orthotropic annular and circular plates with elastically restrained peripheries

Journal of Sound and Vibration ◽

10.1016/0022-460x(90)90576-l ◽

1990 ◽

Vol 143 (1) ◽

pp. 171-179 ◽

Cited By ~ 20

Author(s):

C.S. Kim ◽

S.M. Dickinson

Keyword(s):

Flexural Vibration ◽

Circular Plates ◽

Elastically Restrained ◽

Polar Orthotropic

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Thermal Stress and Deflection Analysis of a Glass Window (Circular Plate) Elastically Restrained Along its Edge in a Photonic Device

Journal of Electronic Packaging ◽

10.1115/1.1604807 ◽

2003 ◽

Vol 125 (4) ◽

pp. 602-608

Author(s):

John H. Lau ◽

Steve Erasmus ◽

Yida Zou

Keyword(s):

Thermal Stress ◽

Circular Plate ◽

Spring Constant ◽

Engineering Practice ◽

Thermal Coefficient ◽

Circular Plates ◽

Optical Coefficient ◽

Deflection Analysis ◽

Linear Spring ◽

Elastically Restrained

An exact analysis is presented for the stresses and deflections of circular plates (glass windows) elastically restrained along its edge in a photonic device’s housing subjected to the pressure and temperature loadings. Dimensionless curves and charts are also provided for engineering practice convenience. These charts show the interactions of the deflection, stress, temperature, pressure, linear spring constant, rotational spring constant, geometry of the glass windows, and the Young’s modulus, Poisson’s ratio, thermal coefficient of expansion, geometry, stress-optical coefficient, and birefringence of glass materials. The results presented herein should be useful for designing glass windows for shipping, storing, handling, functioning, and reliability.

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