The disturbances in an infinite inhomogeneous medium due to transient forces and twists on the surface of a buried spherical source

Summary In this paper the disturbances in an inhomogeneous medium due to two types of forces (i) transient normal forces, (ii) transient twists in presence of a buried spherical source has been considered. The material of the inhomogeneous medium is assumed to be transversely isotropic. The results are in terms of modified Bessel functions. In a particular case, the equation reduces to an ordinary differential equation of second order.     

On the disturbances in an inhomogenous medium due to transient forces and twists on the surface of a burried spherical source

Summary In this paper the displacements and stresses are obtained due to two types of forces: (i) transient normal forces, (ii) transient twists on the surface of a burried spherical source. The material is assumed to be inhomogeneous and spherically aeolotropic. Laplace transform technique has been used here.     

Waves produced in an infinite elastic medium due to normal forces and twists on the surface of a burried spherical source

Summary In this paper, the waves propagated in an infinite medium has been considered by disturbances on the surface of a burried spherical source. The disturbances are produced by two types of forces viz. i) Transient normal force, ii) Transient twist applied on the surface of the source. The solutions are obtained in a very simple form. Graphical representations of some numerical solutions has been added at the end of each problem.     

On the disturbances in a viscoelastic medium due to blast inside a spherical cavity

Summary In this paper we have considered the disturbances in a viscoelastic medium due to a blast of intensityP and durationT sec inside a spherical cavity.     

On disturbances produced in an elastic medium by twists applied on the inner surface of a spherical cavity

Summary In this note, disturbances generated in an isotropic elastic medium by some simple types of twisting forces applied on the inner surface of a spherical cavity have been investigated. Prof.S. K. Chakraborty, Surendranath College, 24 Harrison Road,Calcutta (India).     

Disturbances in a viscoelastic medium due to impulsive forces on a spherical cavity

Summary The disturbances produced in a visco-elastic medium by impulsive forces on the surface of a spherical cavity inside the medium have been studied.     

Disturbances in a viscoelastic medium due to a twist of finite duration on the surface of a spherical cavity

Summary The disturbances in a viscoelastic medium by a twist of finite duration applied on the inner surface of a spherical cavity inside the medium have been considered.     

Waves and stresses produced in an elastic medium due to impulsive radial forces and twist on the surface of a spherical cavity

Summary Displacements and stresses produced by impulsive radial pressure and by impulsive twists have been determined. In the former case total flow of energy across a spherical boundary has been obtained.     

Disturbances in an infinite slab due to torsional forces applied on a cylindrical cavity

Summary The paper deals with the disturbances in an infinite slab of finite thickness, the medium being homogeneous, isotropic and perfectly elastic.     

OnSH type of motion due to body forces and due to stress-discontinuity in a semi-infinite viscoelastic medium

Summary In this paper, surface displacements of theSH type of motion due to time-dependent body forces and due to sudden introduction of a discontinuity in the shearing stress in a semi-infinite, homogeneous, isotropic, viscoelastic medium have been worked out by the use of Laplace and Fourier transforms. The displacements due to a point force and due to a stress discontinuity over a fixed region have been calculated numerically.     

On the disturbance due to a spherical distortional pulse in an elastic medium

Summary Theoretical expressions are derived for the displacement, velocity and stress in the time domain induced by an axially symmetric shearing stress applied at the inner surface of a spherical cavity in a hornogeneous, isotropic, elastic medium of infinite extent. Theoretical seismograms are computed for a step source and for three sources with exponential decay in time. A satisfactory time-dependence of the source can be obtained by combining the step source with one or more exponentially decaying sources.     

Note on the propagation of waves in infinite spherically-aeolotropic medium produced by a blast in a spherical cavity

Summary By using the Laplace transform method, solution has been obtained for the elastodynamic problem due to blast pulse on the inner surface of a spherical cavity in an infinite spherically aeolotropic elastic solid. Both types of blast producing radial and rotational waves have been considered.     

Note on the propagation of waves from a spherical cavity in an infinite solid

Summary The present note, as its title implies, is concerned with the investigation of disturbances in an infinite elastic medium containing an initial magnetic field in the axial direction. The equations ofMaxwell, those of elasticity have been effectively made use of to solve the problem.     

On the attenuation of transient spherical waves in a four-element viscoelastic model and its implications

Summary In a four-element model, which consists of two Voigt elements in series, the impulse responses of spherical waves for particle displacement, velocity, acceleration and strain are computed numerically. These impulse responses are shown to be useful in synthesis for the desired wave response through convolution, between the input of the source function and the impulse responses. The rate of decay of peak amplitude versus distance, as waves radiate out, is examined in the region close to the source which may be nuclear or dynamite explosives and found to be linear in log-log scale. The amplitude spectra of the unit impulse response are obtained through Fourier analysis, and the model is found to behave as a low pass filter. With the properly chosen elastic constants for springs in the model and damping coefficients for dashpot, it is seen that, like the earth materials, the attenuation exponent (in neper/1000 ft) versus frequency in the model is approximately linear. One of the results observed byCollins andLee [1] is fitted by the model. The model thus simulates more nearly the wave in earth materials close to the source than the Voigt solid.     

Thermo-elastic interactions in an infinite elastic solid due to a concentrated transient heat source

Summary The present paper is concerned with the determination of thermo-elastic stress and temperature distribution in an infinite elastic solid when it is subjected to a concentrated transient heat source taking into account the effect of coupling. The fundamental partial differential equation for the thermo-elastic potential is solved by means of the operational method. The solutions are obtained for small values of time in terms of known functions such as complementary error functions and associated complementary error functions and have the form of power series with respect to the parameter of coupling . Since this parameter is generally very small for most of the metals, the expressions for stress and temperature distribution have been obtained by considering terms upto linear .     

Motion in a non-homogeneous elastic medium by a twisting impulsive force on the surface of a spherical cavity

Summary In this paper, the propagation of disturbance due to a twisting impulsive force on the surface of a spherical cavity, in a non-homogeneous isotropic medium, in which the rigidity and density vary inversely as the distance from the centre is investigated. Numerical solution is done by the method suggested byKromm.     

On disturbances produced by a time-periodic twist on the surface of a spheroidal cavity

Summary The problem of disturbances in an elastic medium produced by a twist on the surface of a spheroidal cavity has been solved using spheroidal functions.     

On disturbances in an elastic medium in contact with a liquid medium and subjected to a magnetic field

Summary The present note makes use of electromagnetic equations of Maxwell and those of mechanical motions to work out the problem of disturbances in two perfectly conductive media—an ideal liquid and a perfectly elastic solid-acted upon by a magnetic field perpendicular to their plane of contact. The displacement suffered by solid medium has been determined when a tangential force, exponentially decaying with time, acts in the plane of contact of the two media. The solution of the problem is achieved by using the method of Laplace transform.     

On the stresses produced by impulsive displacemens applied to the inner surface of a spherical cavity

Summary In this note displacements and stresses produced in an infinite elastic solid by impulsive radial and twisting displacements applied to the inner surface of a spherical cavity have been determined.