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Effect of Impedance Boundary on Reflection of Plane Waves from Free Surface of a Rotating Thermoelastic Solid Half Space


Affiliations
1 Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
2 Department of Mathematics, School of Chemical Engineering and Physical Science, Lovely Professional University, Phagwara-Punjab, India
     

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The coupled partial differential equations governing a rotating thermoelastic medium in context of Lord and Shulman theory are solved for plane wave solutions. A cubic velocity equation is obtained, which correspond to the speeds of propagation of three coupled plane waves. A reflection phenomenon is considered in a rotating thermoelastic solid half-space for incidence of a coupled plane wave. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement components time frequency, respectively. The expressions for energy ratios of all reflected waves are obtained and computed numerically for a particular material representing the medium. The dependence of energy ratios on rotation parameter, impedance parameters and angle of incidence is shown graphically.

Keywords

Generalized Thermoelasticity, Impedance Boundary, Reflection, Energy Ratios, Rotation.
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  • Effect of Impedance Boundary on Reflection of Plane Waves from Free Surface of a Rotating Thermoelastic Solid Half Space

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Authors

Baljeet Singh
Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
Anand Kumar Yadav
Department of Mathematics, School of Chemical Engineering and Physical Science, Lovely Professional University, Phagwara-Punjab, India
Sachin Kaushal
Department of Mathematics, School of Chemical Engineering and Physical Science, Lovely Professional University, Phagwara-Punjab, India

Abstract


The coupled partial differential equations governing a rotating thermoelastic medium in context of Lord and Shulman theory are solved for plane wave solutions. A cubic velocity equation is obtained, which correspond to the speeds of propagation of three coupled plane waves. A reflection phenomenon is considered in a rotating thermoelastic solid half-space for incidence of a coupled plane wave. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement components time frequency, respectively. The expressions for energy ratios of all reflected waves are obtained and computed numerically for a particular material representing the medium. The dependence of energy ratios on rotation parameter, impedance parameters and angle of incidence is shown graphically.

Keywords


Generalized Thermoelasticity, Impedance Boundary, Reflection, Energy Ratios, Rotation.

References