Large Amplitude Vibrations of Clamped Circular Plate of Variable Thickness

1984 ◽  
Vol 51 (1) ◽  
pp. 207-210 ◽  
Author(s):  
S. K. Chaudhuri
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Amplitude ◽  
Nonlinear Oscillations ◽  
Numerical Results ◽  
Varying Thickness ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Plate Of Variable Thickness ◽  
Large Amplitude Vibrations

In this paper nonlinear oscillations of a clamped circular plate of linearly varying thickness have been investigated using von Karman equations expressed in terms of displacement components. Numerical results obtained have been compared and discussed.

Large Deflections of Circular Plates of Variable Thickness

1982 ◽  
Vol 49 (1) ◽  
pp. 243-245 ◽  
Author(s):  
B. Banerjee
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Deflection ◽  
Numerical Results ◽  
Large Deflections ◽  
Circular Plates ◽  
Uniform Load ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.

Nonlinear Transverse Vibrations of a Spinning Disk

1964 ◽  
Vol 31 (1) ◽  
pp. 72-78 ◽  
Author(s):  
Jerzy L. Nowinski
Keyword(s):  
Large Amplitude ◽  
Close Agreement ◽  
Vibration Mode ◽  
Linear Case ◽  
Field Equations ◽  
Spinning Disk ◽  
Transverse Vibrations ◽  
Von Karman ◽  
Large Amplitude Vibrations ◽  
Von Kármán

Using the von Karman field equations, large amplitude vibrations of a spinning disk are analysed. For definiteness, the disk is assumed to be free, and its deflection is represented by a two-term polynomial. A vibration mode associated with two nodal diameters is studied in more detail. A familiar phenomenon of a decreasing period of vibration with an increasing amplitude is corroborated. The results specialized to the linear case show a close agreement with the classical results of Lamb and Southwell. The dependence of the membrane stresses on the amplitude of vibration and the velocity of spin is discussed.

scholarly journals Canonical polynomials in the problem about the bend of circular plate of variable thickness

2021 ◽  
pp. 105
Author(s):  
O.V. Bugrim ◽  
Ye.S. Sinaiskii
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Variable Thickness ◽  
Variable Coefficients ◽  
Tau Method ◽  
Canonical Polynomials ◽  
Plate Of Variable Thickness

The problem about the bend of circular plate of variable thickness under specifically selected laws of rigidity change is reduced to the ordinary differential equation with variable coefficients of polynomial kind. The construction of the approximate solution of equation that satisfies boundary conditions is realized by means of canonical polynomials and $\tau$-method of Lantzosh.

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