Disturbance from a circularly symmetric load spreading over an acoustic half-space

1965 ◽  
Vol 55 (4) ◽  
pp. 673-691
Author(s):  
H. R. Aggarwal ◽  
C. M. Ablow
Keyword(s):  
Pressure Distribution ◽  
Closed Form ◽  
Wave Front ◽  
Half Space ◽  
Closed Form Solution ◽  
Surface Displacement ◽  
Form Solution ◽  
Displacement Fields ◽  
Axis Of Symmetry ◽  
Symmetric Load

abstract An exact closed form solution for the disturbance due to a circularly symmetric load spreading arbitrarily from a point on the surface of an acoustic half-space is presented using the Laplace and Hankel transforms. The pressure distribution inside the loaded area is assumed uniform at each time. Wave-front surfaces are discovered and analyzed. Explicit expressions for stress and surface displacement fields are obtained. Simple formulas for the stresses on the axis of symmetry and at the wave front are given.

scholarly journals A New Closed-Form Solution of the Side Abutment Pressure Distribution of Roadway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang Cheng ◽  
Yidong Zhang
Keyword(s):  
Plastic Zone ◽  
Pressure Distribution ◽  
Closed Form ◽  
Abutment Pressure ◽  
Closed Form Solution ◽  
Evaluation Process ◽  
Friction Angle ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Roadway Stability

Instability of coal wall is one of the hot-button and difficult issues in the study of coal mine ground control. The shallow side coal of roadway in the coal measures is usually weak and consequently easy to bring about failure. Hence, the side abutment pressure redistributes and dramatically influences the roadway stability. Since the previous closed-form solutions of the side abutment pressure do not take into account all the necessary parameters which include the properties of the coal and the interface between coal and roof/floor, the roadway height, and the support strength, a mechanical model is established based on the equilibrium of the plastic zone, and a new closed-form solution is derived in this paper. Moreover, a numerical investigation is conducted to validate the accuracy of the closed-form solution. The numerical results of the side abutment pressure distribution are in good agreement with the closed-form solution. Afterwards, a parametric analysis of the width of the plastic zone is carried out, and the results show that the width of the plastic zone is nearly negatively linearly correlated with the friction angle and the cohesion of the coal, the interfacial cohesion, and the support strength. By contrast, it is positively linearly correlated with the roadway height and negatively exponentially correlated with the interfacial friction angle. The results obtained in the present study could be useful for the evaluation process of roadway stability.

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

Exact closed-form solutions for Lamb’s problem—III: the case for buried source and receiver

2020 ◽  
Vol 224 (1) ◽  
pp. 517-532
Author(s):  
Xi Feng ◽  
Haiming Zhang
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Closed Form Solution ◽  
Time History ◽  
Natural Generalization ◽  
Elastic Half Space ◽  
Form Solution ◽  
Elementary Functions ◽  
Heaviside Step Function ◽  
Lamb’S Problem

SUMMARY In this paper, we derive the exact closed-form solution for the displacement in the interior of an elastic half-space due to a buried point force with Heaviside step function time history. It is referred to as the tensor Green’s function for the elastic wave equation in a uniform half-space, also a natural generalization of the classical 3-D Lamb’s problem, for which previous solutions have been restricted to the cases of either the source or the receiver or both are located on the free surface. Starting from the complex integral solutions of Johnson, we follow the similar procedures presented by Feng and Zhang to obtain the closed-form expressions in terms of elementary functions as well as elliptic integrals. Numerical results obtained from our closed-form expressions agree perfectly with those of Johnson, which validates our explicit formulae conclusively.

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