Effect of Loose Bonding and Corrugated Boundary Surface on Propagation of Rayleigh-Type Wave

Abstract

The problems concerns to the propagation of surface wave propagation through various anisotropic mediums with initial stress and irregular boundaries are of great interest to seismologists, due to their applications towards the stability of the medium. The present paper deals with the propagation of Rayleigh-type wave in a corrugated fibre-reinforced layer lying over an initially stressed orthotropic half-space under gravity. The upper free surface is assumed to be corrugated; while the interface of the layer and half-space is corrugated as well as loosely bonded. The frequency equation is deduced in closed form. Numerical computation has been carried out which aids to plot the dimensionless phase velocity against dimensionless wave number for sake of graphical demonstration. Numerical results analyze the influence of corrugation, loose bonding, initial stress and gravity on the phase velocity of Rayleigh-type wave. Moreover, the presence and absence of corrugation, loose bonding and initial stress is also discussed in comparative manner. , , u u u  The displacement components of fibre-reinforced layer along , ,x y z direction respectively. G  Biot's gravity parameter.  Bonding parameter. INTRODUCTIONThe problems of elastodynamics are not limited to the mechanics of those elastic materials which are simply isotropic, rather the problems take a more general and realistic form when the media considered are anisotropic. The presence of some effective physical factors namely initial stress, hydrostatic stress, cracks, fractures, etc. causes the mediums to behave anisotropically to the propagation of waves through it. These initial stresses tensile/compressive are the results of overburdened layer, atmospheric pressure, variation in temperature, slow process of creep and gravitational field. Tensile stress is said to responsible for more rigidity and compressive stress for less rigidity of a medium. On the other hand, presence of fibre-reinforced materials in earth's crust, in the form of hard or soft rocks may also affect the wave propagation. These composite materials adopt self-reinforced behavior under certain temperature and pressure. It finds numerous applications in construction, civil engineering, geophysics and geomechanics due to its low weight and high strength. The reinforcement of soil, both naturally and synthetically, enhances the strength and load bearing capacity of it. The mechanical behavior of composite materials could be well understood through the study of anisotropic elasticity. Carbon, nylon or conceivable metal whiskers, etc. are good models of fibre-reinforced materials. Prikazchikov and Rogerson 2003 studied the effect of pre-stress on the propagation of small amplitude waves in an incompressible, transversely isotropic elastic solid. Prosser and Green 1990 calculated some of the nonlinear third order moduli of T300/5208 graphite/ epoxy composite by measuring the normalized change in ultrasonic "natural" velocity as a function of stress and temperature. A lot of information abou...

Mathematical Analysis on Dispersion Relation of Rayleigh Wave for an Initially Stressed Magneto-Poroelastic Material with Corrugated and Impedance Boundary

“…Consequently, some authors have made contributions to this concepts of impedance and corrugated boundaries, and other related wave propagation phenomena (Singh et al, 2008(Singh et al, , 2015(Singh et al, , 2018Das et al, 1992;Abd-Alla et al 2016;Chattopadhyay et al, 1975;Roy et al, 2017;Singh et al, 2011;Gupta et al, 2014;Anya et al, 2018Anya et al, , 2020Sunita et al, 2019;Dey et al, 1977;Nunziato et al, 1979;and Puri et al, 1975), as an individual or part considerations of the interacting physical quantities rather than in combined effect as presented in this investigation. Also, Zghal et al (2021), dealt on free vibration analysis of porous beams with gradually varying mechanical properties.…”

Mathematical Modeling of Waves in a Porous Micropolar Fibrereinforced Structure and Liquid Interface

“…Grooved boundary surface could be visualized as a series of parallel furrows and ridges whose encounter in mechanical propagation of wave results to several effects especially across interfaces. Interestingly, some authors had worked on this concept of corrugated boundaries and other related wave propagation phenomena [21][22][23][24][25][26][27][28][29]. Also, certain discussions on materials [30][31][32][33] could aid understanding of material characterizations.…”