Waves in Nonlocal Elastic Solid with Voids

• Published in: Journal of elasticity Vol. 128; no. 1; pp. 85 - 114
• Main Authors: Singh, Dilbag, Kaur, Gurwinderpal, Tomar, S. K.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2017; Springer Nature B.V
• Subjects: Attenuation coefficients; Automotive Engineering; Boundary conditions; Classical Mechanics; Critical frequencies; Free boundaries; Half spaces; Longitudinal waves; Parameters; Phase velocity; Physics; Physics and Astronomy; Plane waves; Stress propagation; Transverse waves; Voids; Wave dispersion; Wave propagation; Wave reflection; Voids; 73B18; 74J10; 73D15; Attenuation; Nonlocality; Reflection; Elastic wave; 35Q74; Phase speed
• ISSN: 0374-3535; 1573-2681
• DOI: 10.1007/s10659-016-9618-x

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter ( τ ) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.