Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative

doi:10.1088/1674-1056/22/7/074601

中国物理B ›› 2013, Vol. 22 ›› Issue (7): 74601-074601.doi: 10.1088/1674-1056/22/7/074601

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative

Rajneesh Kumar, Vandana Gupta

Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana, India

收稿日期:2012-12-13 修回日期:2013-01-18 出版日期:2013-06-01 发布日期:2013-06-01
基金资助:
Project supported by the Council of Scientific and Industrial Research (CSIR), India.

Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative

Rajneesh Kumar, Vandana Gupta

Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana, India

Received:2012-12-13 Revised:2013-01-18 Online:2013-06-01 Published:2013-06-01
Contact: Rajneesh Kumar E-mail:rajneesh_kuk@rediffmail.com
Supported by:
Project supported by the Council of Scientific and Industrial Research (CSIR), India.

摘要/Abstract

摘要： In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.

关键词: thermoelastic diffusion, fractional calculus, uniqueness theorem, reciprocity theorem

Abstract: In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.

Key words: thermoelastic diffusion, fractional calculus, uniqueness theorem, reciprocity theorem

中图分类号: (Application of continuum mechanics to structures)

46.70.-p

46.15.-x (Computational methods in continuum mechanics) 46.05.+b (General theory of continuum mechanics of solids)

Rajneesh Kumar, Vandana Gupta. Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative[J]. 中国物理B, 2013, 22(7): 74601-074601.

Rajneesh Kumar, Vandana Gupta. Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative[J]. Chin. Phys. B, 2013, 22(7): 74601-074601.

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Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative

Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative

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