Maximum Stresses in Beams and Plates Vibrating at Resonance

1962 ◽  
Vol 84 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Eric E. Ungar
Keyword(s):  
Simple Formula ◽  
Maximum Stress ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Simply Supported ◽  
At Resonance ◽  
Design Calculations ◽  
Maximum Stresses

Expressions are derived which relate the maximum stresses encountered in simply supported beams and rectangular plates and in clamped circular plates vibrating at resonance to modal displacements and modal loadings. Computation of modal loadings from time-wise harmonic or random pressures is discussed. It is shown that the resonant maximum stress may be reasonably approximated by a simple formula suitable for conservative design calculations for all types of beams and plates.

Bending of Rectangular Plates Subjected to a Uniformly Distributed Lateral Load and to Tensile or Compressive Forces in the Plane of the Plate

1949 ◽  
Vol 16 (3) ◽  
pp. 301-309
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Maximum Stress ◽  
Lateral Load ◽  
Rectangular Plates ◽  
Simply Supported

Abstract This paper presents a method of determining the distribution of deflection and stress in simply supported rectangular plates subjected simultaneously to a uniform lateral load and to uniform tensile or compressive forces in the plane of the plate. The problems are of particular importance in the design of a ship’s bottom plating and, for this reason, graphs are given whereby the maximum stress and deflection may easily be calculated. Illustrative examples are included to demonstrate the use of these graphs. An example is also given to illustrate how the method may be extended to include the case of hydrostatic pressure.

Response of Beams and Plates to Random Loads

1957 ◽  
Vol 24 (1) ◽  
pp. 46-52
Author(s):  
A. C. Eringen
Keyword(s):  
Cross Correlation ◽  
External Pressure ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Probable Number ◽  
Simply Supported ◽  
Random Loads ◽  
Stochastic Loading ◽  
Special Cases ◽  
The Cross

Abstract With the use of generalized harmonic analysis the problem of vibrating damped beams and plates under stochastic loading is solved. The resulting equations give the cross-correlation functions for displacements, stresses, moments, and so on, in terms of the cross-correlation function of external pressure. Mean square values of these functions are special cases of these results. Using a method due to Rice, we also calculate the probable number of times per unit time the random displacements or stresses will exceed a given value. The case of simply supported bars, cantilever bars, clamped circular plates, and simply supported rectangular plates are worked out in detail.

Deformation of Rectangular Slender Webplates with Boundary Members Flexible in the Webplate Plane

1966 ◽  
Vol 17 (4) ◽  
pp. 371-394 ◽  
Author(s):  
J. Djubek
Keyword(s):  
Linear Problem ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Non Linear

SummaryThe paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

scholarly journals VIBRATION OF CRACKED CIRCULAR PLATES AT RESONANCE FREQUENCIES

2000 ◽  
Vol 236 (4) ◽  
pp. 637-656 ◽  
Author(s):  
CHI-HUNG HUANG ◽  
CHIEN-CHING MA
Keyword(s):  
Circular Plates ◽  
At Resonance ◽  
Resonance Frequencies
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