scholarly journals Thermal Memory Response in Magneto-thermoelastic Medium Having Long Cylindrical Cavity

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Cylindrical Cavity ◽  
Integral Transform ◽  
Elastic Solid ◽  
Radial Symmetry ◽  
Inverse Laplace Transform ◽  
Polar Coordinate System ◽  
Inverse Transformation ◽  
Transform Method ◽  
Memory Response ◽  
Numerical Inverse Laplace Transform

The present paper deals with the memory response on thermal disturbances emanating from a cylindrical cavity in an unbounded thermoelastic solid. Here we have theoretically demonstrated the memory response of thermal disturbances in the generalized magneto-thermo-elastic materials. Firstly, the characteristics of thermoelastic disturbances originated from the cavity in an unbounded elastic solid under the light of generalized magnetothermoelasticity theory with memory dependent derivatives (MDD). For numerical computation, cylindrical-polar coordinate system with radial symmetry subjected to two different types of heat sources into the cavity are considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic NILT (Numerical Inverse Laplace Transform) is adopted. Finally, parameter studies are performed to evaluate the effect of the kernel function and time delay. For thermal wave the results show appreciable differences with those in the usual magneto-thermoelasticity theory.

scholarly journals Numerical evaluation of inverse integral transforms: Dynamic response of elastic materials

2020 ◽  
Vol 12 (2) ◽  
pp. 29-34
Author(s):  
M.D. Sharma ◽  
S. Nain
Keyword(s):  
Numerical Integration ◽  
Elastic Waves ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Integral Transforms ◽  
Inverse Laplace Transform ◽  
Branch Points ◽  
Transform Method ◽  
Improper Integral ◽  
Romberg Integration

This study discusses the use of numerical integration in evaluating the improper integrals appearing as inverse integral transforms of non-analytic functions. These transforms appear while studying the response of various sources in an elastic medium through integral transform method. In these studies, the inverse Fourier transforms are solved numerically without bothering about the singularities and branch points in the corresponding integrands. References on numerical integration cited in relevant papers do not support such an evaluation but suggest contrary. Approximation of inverse Laplace transform integral into a series is used without following the essential restrictions and assumptions. Volume of the published papers using these dubious procedures has reached to an alarming level. The discussion presented aims to draw the attention of researchers as well as journals so as to stop this menace at the earliest possible.Keywords: Inverse Fourier transforms, inverse Laplace transforms, Romberg integration, improper integral, elastic waves

Forced Vibration of Cylindrical Helical Rods Subjected to Impulsive Loads

2003 ◽  
Vol 70 (2) ◽  
pp. 281-291 ◽  
Author(s):  
B. Temel ◽  
F. F. C¸alim
Keyword(s):  
Forced Vibration ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Real Space ◽  
Inverse Laplace Transform ◽  
Transform Method ◽  
Scalar Form ◽  
Laplace Domain ◽  
Numerical Inverse Laplace Transform ◽  
Impulsive Loads

In this study, the forced vibration of cylindrical helical rods subjected to impulsive loads is theoretically investigated in the Laplace domain. The free vibration is then taken into account as a special case of forced vibration. The governing equations for naturally twisted and curved space rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The material of the rod is assumed to be homogeneous, linear elastic, and isotropic. The axial and shear deformations are also taken into account in the formulation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The desired accuracy is obtained by taking only a few elements. The solutions obtained are transformed to the real space using the Durbin’s numerical inverse Laplace transform method. The free and forced vibrations of cylindrical helical rods are analyzed through various example. The results obtained in this study are found to be in a good agreement with those available in the literature.

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

ELASTODYNAMIC STRESS INTENSITY FACTOR FOR A FINITE CRACK IN ELASTIC SOLID UNDER 3D TRANSIENT LOADING OF MODE I

2013 ◽  
Vol 05 (04) ◽  
pp. 1350044
Author(s):  
XIANHONG MENG ◽  
ZHAOYU BAI ◽  
MING LI
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Transform ◽  
Elastic Solid ◽  
Scattered Wave ◽  
Mode I ◽  
Finite Width ◽  
Infinite Length ◽  
Distance Ratio

In this paper, the three-dimensional dynamic problem for an infinite elastic medium weakened by a crack of infinite length and finite width is analyzed, while the crack surfaces are subjected to mode I transient linear tractions. The integral transform approach is applied to reduce the governing differential equations to a pair of coupled singular integral equations, whose solutions can be obtained with the typical iteration method. The analytical solution of the stress intensity factor when the first wave and the first scattered wave reach the investigated crack tip is obtained. Numerical results are presented for different values of the width-to-longitudinal distance ratio z/l. It is found that the stress intensity factor decreases with the arrival of the first scattered longitudinal wave and increases with the arrival of the first scattered Rayleigh wave and tends to be stable. The static value considering both the first scattered wave and the first wave is about 50% greater than that considering only the first wave, and then the effect of the reflected wave is remarkable and deserves further study.

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