Elastodynamic response of an anisotropic medium due to a line-load

Abstract

Two-dimensional elastodynamic displacements and stresses for a monoclinic solid have been obtained in relatively simple form by the use of the eigenvalue method, following Laplace and Fourier transforms. The main aim of this paper is to present a straightforward analytical eigenvalue method for a monoclinic solid which avoids the cumbersome nature of the problem and is convenient for numerical computation. The use of matrix notation avoids unwieldy mathematical expressions. A particular case of normal line-load acting in an orthotropic solid is discussed in detail. The corresponding deformation in time-domain is obtained numerically. The variations of elastodynamic displacements and stresses for an anisotropic medium with the horizontal distance have been shown graphically. It has been found that anisotropy is affecting the trend of distribution curves significantly.

Evaluation of inverse Fourier transforms through romberg integration

“…I guess, it should be a breakthrough. It surprises more when a good numbers of studies (Sharma and Kumar, 1997;Ezzat et al, 2001;Garg et al, 2004;Kumar and Ailawalia, 2004, and many more) use the same technique in inverting the Fourier transforms even in the problems of wave propagation in elastic plates, where there are infinite number of singularities (waveguide modes). Whatever be the truth, but in no way, it can be possible to imagine that Maurice Ewing and co-workers were not aware of a standard procedure like Romberg integration.…”

“…I could collect only fifty of them, which are published in the international journals devoted to mechanics of solids. They are Kumar (1996, 1997), Deswal (2000, 2001), Kumar and Choudhary (2001, 2003, Kumar and Rani (2004,b,c, 2006, Kumar and Ailawalia (2004,b,c,d, 2006a, Choudhary and Deswal (2008), Choudhary (2008, 2009), Kumar et al ( , 2004aKumar et al ( , 2003b, Kumar and Devi (2008), Gupta (2008, 2009a,b,c), Kumar and Rupender (2009a,b,c), Garg et al (2004), Ezzat et al (2001), Othman (2003), Sharma and Chauhan (2001), Sharma and Chand (2005), Sharma et al (2000Sharma et al ( , 2004Sharma et al ( , 2005Sharma et al ( , 2006Sharma et al ( , 2008a, and Ram et al (2008). In most of these references, the same procedure (as explained in section 2) is mentioned to numerically evaluate the inverse Fourier transforms appearing in the theoretical derivations there.…”