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2020•Journal of Mathematical and Computational ScienceOpen access

Investigation of plane longitudinal waves in a micro-isotropic, micro-elastic solid

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Abstract

In the frame work of plane harmonic wave solution, we investigate the phase velocities of longitudinal micro-rotational (MR), micro-isotropical (MI), and micro strain (MS) waves. Two sets of MR waves, one set of MI and MS waves are obtained. These waves are dispersive in nature. Micro non-rotational (MNR) waves are obtained as a particular case of MR waves. Micro-isotropical shear (MIS) and micro strain shear (MSS) waves are obtained as a particular case of MI and MS waves. MNR waves are dispersive in nature, while MIS and MSS waves are non-dispersive and they depend only on elastic constants. With the help of MATLAB programme, numerical example is considered, and speeds are plotted against frequency ratios and wave number.

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In the frame work of plane harmonic wave solution, we investigate the phase velocities of longitudinal micro-rotational (MR), micro-isotropical (MI), and micro strain (MS) waves. Two sets of MR waves, one set of MI and MS waves are obtained. These waves are dispersive in nature. Micro non-rotational (MNR) waves are obtained as a particular case of MR waves. Micro-isotropical shear (MIS) and micro strain shear (MSS) waves are obtained as a particular case of MI and MS waves. MNR waves are dispersive in nature, while MIS and MSS waves are non-dispersive and they depend only on elastic constants. With the help of MATLAB programme, numerical example is considered, and speeds are plotted against frequency ratios and wave number.

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Available abstract

In the frame work of plane harmonic wave solution, we investigate the phase velocities of longitudinal micro-rotational (MR), micro-isotropical (MI), and micro strain (MS) waves. Two sets of MR waves, one set of MI and MS waves are obtained. These waves are dispersive in nature. Micro non-rotational (MNR) waves are obtained as a particular case of MR waves. Micro-isotropical shear (MIS) and micro strain shear (MSS) waves are obtained as a particular case of MI and MS waves. MNR waves are dispersive in nature, while MIS and MSS waves are non-dispersive and they depend only on elastic constants. With the help of MATLAB programme, numerical example is considered, and speeds are plotted against frequency ratios and wave number.

Key concepts: Longitudinal wave, Shear waves, Love wave, Mechanical wave, Rectilinear propagation, Rayleigh wave, Plane wave, Isotropy

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