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Institute for Problems in Mechanical Engineering
of the Russian Academy of Sciences

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences

Fractional strain analysis on reflection of plane waves at an impedance boundary of non-local swelling porous thermoelastic medium

Autors:
S. Sharma, D. Batra, R. Kumar ,
Pages:
001–021
Annotation:

The current work focuses on developing a model to examine wave analysis in non-local swelling porous thermoelastic medium under fractional order strain. After converting the governing equations into two-dimensional and utilizing the dimensionless quantities for further simplification the Helmholtz decomposition theorem has been used to decompose the system into longitudinal and transverse components. The frequency dispersion relation is derived by assuming the plane wave solution in two-dimensional case for the given problem. It is found that there exist two dilatational waves, a thermal wave and two transversal waves travelling at distinct velocities. The amplitude ratios for the reflected waves are obtained with the aid of impedance boundary restrictions. The obtained amplitude ratios are used to obtain the energy ratios of different reflected waves. Influence of fractional order parameter on distinct types of wave speeds is illustrated graphically and it is observed that increase in fractional order parameter diminishes the magnitude of all existing waves except longitudinal wave in solid. Also impacts of swelling pores and fractional order on the attained energy ratios are displayed graphically versus angle of incidence. It is verified that during reflection phenomena, the sum of energy ratio is equal to unity at each angle of incidence and there is no dissipation on the boundary surface. Swelling porosity decrease the impact of energy ratios of reflected longitudinal wave and thermal wave for all values of fractional order parameter. Some unique cases are also presented. The results find application in geophysics, civil engineering and structure related issues.

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