Modeling the mechanical vibrations of Rayleigh surface wave in a medium exhibiting heterogeneity as elementary transcendental functions of depth

Abstract

The present article develops mathematical modeling of Rayleigh wave propagation in a medium under the influence of inhomogeneity parameter associated with means of elementary transcendental functions. The equations of motion and constitutive relations have been taken forward to produce the frequency equation. With the help of suitable potential functions and appropriate mathematical treatment, displacement components have been derived. Furthermore, by means of intrinsic boundary conditions, the frequency equation has been achieved in terms of the inhomogeneity function and its derivative. The inhomogeneity function has been later considered as a hyperbolic, logarithmic, and exponential function. Variation of phase velocity for these fundamental functions, as well as their compositions, has been shown graphically. A comparison between various inhomogeneity parameters and their influences on phase velocity has been discussed and demonstrated through graphs. As an outcome, a significant effect of inhomogeneity parameters on Rayleigh wave propagation has been observed which finds its applications towards the synthesis of biomaterials, property enhancement, wave mechanics, civil engineering, and mechanical engineering.

Dynamic response of torsional waves in an anisotropic infinite cylinder with finite thickness

“…Dynamic response of torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium has been explored by Ozturk and Akbarov [12]. References may be given to [13][14][15] for there commendable work. There are several energy flow issues involving torsional waves through arbitrarily composite cylinders like pipe ducts, bars, hollow pillars etc., with various kinds of anisotropy.…”