Effect of fractional temporal variation on the vibration of waves on elastic substrates with spatial non-homogeneity

Abstract

<abstract><p>The current manuscript examines the effect of the fractional temporal variation on the vibration of waves on non-homogeneous elastic substrates by applying the Laplace integral transform and the asymptotic approach. Four different non-homogeneities, including linear and exponential forms, are considered and scrutinized. In the end, it is reported that the fractional temporal variation significantly affects the respective vibrational fields greatly as the vibrations increase with a decrease in the fractional-order $ \mu. $ Besides, the two approaches employed for the cylindrical substrates are also shown to be in good agreement for very small non-homogeneity parameter $ \alpha. $ More so, the present study is set to play a vital role in the fields of material science, and non-homogenization processes to state a few.</p></abstract>

Closed-form asymptotic solution for the transport of chlorine concentration in composite pipes

“…In particular, since the acquired closed-form asymptotic solutions are difficult to evaluate analytically, the reliable computational algorithm for the inversion of the Laplace transform back to its original domain by Abate and Valko [11] will be deployed for the numerical simulation. In fact, the said inversion procedure for Laplace transform is highly accurate and reveals minimal error; read more about its applications in elasticity [8][9][10] as well as in solving some thermodynamical problems [36,37].…”

“…Furthermore, the mixture of the Laplace transform method [5] and the asymptotic approximations for the resultant modified Bessel functions [6,7] will be adopted, for the quest of closed-form analytical solutions, which serve as benchmark solutions for numerical investigations. Further, in line with this study concerning the cylindrical media, the literature is full of various studies of different phenomena in cylindrical coordinate systems, including, for instance, the study of wave transport in thermoelastic cylindrical pipe [8], and dispersion of waves in bi-material cylindrical media [9], and the fractional-order relevance on the transport temporal of waves in rectangular and circular elastic plates [10], just to mention a few.…”

Surface Wave Propagation in a Rotating Doubly Coated Nonhomogeneous Half Space with Application

“…where c = 1, 2 and all quantities with an asterisk are assumed to have the same asymptotic order. Therefore, the equation of motion given in Equation (1) and the constitutive relations in Equation (2) are rewritten for c = 1 as ∂τ ( * ,1) 23…”

“…The propagation of surface waves in various structural configurations has been a topic of much concern in different areas of real-life applications, such as geology, aerospace, seismology, mechanical and civil engineering, and non-destructive analysis, among others [1][2][3][4][5]. Thus, with recent technological advancements, considerable attention has been invested by many scientists in the examination and analysis of the propagation of waves in multilayered elastic structures [6][7][8][9].…”

Surface Waves on a Coated Homogeneous Half-Space under the Effects of External Forces

“…However, several investigations have recently been conducted on the impact of external factors that infiltrate or otherwise influence the propagation of surface waves in assorted media. The internal and external forces such as the gravitational force, magnetic field force, and damping force, to name a few, are known to influence the propagation of waves; one can also consider other well-known factors that significantly distort the propagation of elastic waves such as the external loads, e.g., elastic foundations, initial stress, rotational effects, porosity presence, material inhomogeneity, and cracks, among others, see [17][18][19][20][21][22][23][24] and the references listed therein for a quick review of such phenomena. Additionally, the thermal heating effect is equally a vital phenomenon with vast relevance in the field of elasticity, which later metamorphosed to the theory of thermo-elasticity [25][26][27][28][29][30][31].…”