The Response of a Plate on an Elastic Foundation

1968 ◽  
Vol 35 (1) ◽  
pp. 186-187 ◽  
Author(s):  
J. P. Jones
Keyword(s):  
Elastic Foundation ◽  
Elastic Plate ◽  
Pressure Pulse ◽  
Specific Problem ◽  
Underground Structure ◽  
Approximate Equation ◽  
Step Function ◽  
Simple Expression ◽  
Acoustic Medium ◽  
Recent Interest

There has been much recent interest in the possibility of hardening an underground structure by means of an elastic plate placed on the ground above the structure. To obtain a simple expression for the interaction pressure between the ground and the plate, the present analysis treats the problem of a plate on top of an acoustic medium subjected to a uniformly moving pressure pulse. It is found that an approximate equation suggested by S. B. Baldorf is quite valid in the superseismic range of load speed. The specific problem of a step function loading traveling with uniform velocity, superseismic to the foundation, is treated. The extension of this problem to an actual elastic foundation is straightforward and is not treated.

On the Vibration of an Elastic Plate on an Elastic Foundation

1967 ◽  
Vol 42 (5) ◽  
pp. 1202-1202
Author(s):  
David H. Y. Yen ◽  
S. C. Tang
Keyword(s):  
Elastic Foundation ◽  
Elastic Plate

On the Solution of Beam-on-elastic-foundation Problems by Means of a Mechanical Analogue

1950 ◽  
Vol 163 (1) ◽  
pp. 307-310 ◽  
Author(s):  
A. A. Wells
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Pressure Vessel ◽  
Finite Differences ◽  
Specific Problem ◽  
Elastic Shells ◽  
Elastic Foundations ◽  
Mechanical Analogue ◽  
Method Of Solution ◽  
Direct Use

The equation d4 y/ dx4- f(x)y + g(x) = 0 may be solved by means of the differential analyser, but only straightforwardly when the four boundary conditions are specified at one point. When the equation is associated with beams on elastic foundations, or elastic shells, the boundary conditions are more often specified at two points, and a quicker method of solution is desirable. In the analogue, direct use is made of the beam in the form of an elastic wire, supported at intervals in cradles on which weights may be made to simulate the terms f(x)y and g(x); the wire takes up a transversely deflected form which may be measured, and boundary conditions are imposed where they are required. A specific problem is examined and the results are shown to agree reasonably with the solution by calculation. A disadvantage when d2 y/dx2 is required is the inaccuracy inherent in differentiating by finite differences, but for engineering calculations the simplicity of the method may have its advantages. The solution of a typical pressure-vessel problem, by means of the analogue, is described.

Effect of an Acoustic Medium on the Dynamic Buckling of Plates

1956 ◽  
Vol 23 (2) ◽  
pp. 201-206
Author(s):  
F. L. DiMaggio
Keyword(s):  
Elastic Plate ◽  
Infinite Plate ◽  
Approximate Solutions ◽  
Dynamic Buckling ◽  
Steel Plates ◽  
Acoustic Medium ◽  
Middle Plane ◽  
Numerical Example ◽  
Compressive Stresses ◽  
Surrounding Fluid

Abstract The effect of a surrounding fluid on the dynamic buckling of an elastic plate under suddenly applied compressive stresses in its middle plane is studied. Assuming an infinite plate supported at regular intervals and a semi-infinite acoustic medium, exact and approximate solutions are obtained. By a numerical example, it is shown that for steel plates in water, with dimensions usually encountered in ship structures, the compressibility of water can be neglected.

scholarly journals Use of Ice Covers for Transportation

1971 ◽  
Vol 8 (2) ◽  
pp. 170-181 ◽  
Author(s):  
L. W. Gold
Keyword(s):  
Thermal Stress ◽  
Elastic Foundation ◽  
Elastic Plate ◽  
Maximum Stress ◽  
Theoretical Calculations ◽  
Strength Properties ◽  
Vehicle Speed ◽  
Vehicular Traffic ◽  
Total Load

Observations are reported on the failure and use of freshwater ice covers for vehicular traffic. The study showed that good quality ice covers can support loads of up to P = 250 h2, where P is the total load in pounds and h is the thickness of the ice in inches. Failures were reported, however, for loadings as low as P = 50 h2. Factors contributing to the failure of covers for loading less than P = 250 h2 were: vehicle speed, thermal stress due to drop in temperature, and fatigue and quality of the cover. The results are discussed with reference to Westergaard's equations for the maximum stress due to circular loads on an elastic plate resting on an elastic foundation. Information is presented on the elastic and strength properties of ice covers required for theoretical calculations. Experience in the construction and use of ice roads and parking areas is described.

The Green's function of an elastic plate

1953 ◽  
Vol 49 (2) ◽  
pp. 319-326 ◽  
Author(s):  
W. R. Dean
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Elastic Plate ◽  
Arbitrary Point ◽  
Normal Derivative ◽  
Simple Expression ◽  
Transverse Force ◽  
Transverse Displacement ◽  
Straight Lines

In this paper a simple expression in finite terms is found for the small transverse displacement of a thin plane elastic plate due to a transverse force applied at an arbitrary point of the plate. The plate is clamped along the semi-infinite straight lines represented by AB, CD in Fig. 1, these lines being the only boundaries of the plate. The transverse displacement w at any point (x, y) of the plate is a biharmonic function of the variables (x, y) which vanishes together with its normal derivative at all points of the boundary. Clearly w is also a function of the coordinates (x0, y0) of the point of application of the force, and it is known ((5), p. 173) that it is a symmetrical function of the coordinate pairs (z, y) and (x0, y0); it is the Green's function associated with the differential equation and the boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document