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| The Coupling Mechanism Between Highly Nonlinear Solitary Waves with Large Plate |
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Abstract The stress waves can form and propagate stably when the one-dimensional granular chain is impacted by a particle with an initial velocity. These stress waves, called highly nonlinear solitary waves, have constant wavelength, speed, and amplitude, and do not reflect until encountering the boundary. Solitary wave is a superior carrier and is widely used in the nondestructive evaluation of plate. Based on the properties of solitary wave, we investigate the coupling mechanism between highly nonlinear solitary waves and large elastic plate. Basing on the Hertz’s law and Intrinsic Inelasticity of large plate, we can obtain the complete coupling differential equation system between the highly nonlinear solitary wave and the large elastic plate. By solving the equations with the fourth-order Runge-Kutta method, we attain the curves of displacement and velocity of each particle in the crystal chain. By analyzing the time when the reflected wave peak appears, the energy carried by the reflected wave, and the effects of gravity, Young’s modulus and thickness of the large plate on the solitary wave, we find that the primary and second reflected solitary waves are sensitive especially to Young’s modulus and thickness of the large plate. Besides, compared to the horizontal granular chains, the vertical granular chains have influence on the whole interaction process. These findings provide theoretical bases for the detection of highly nonlinear solitary wave on the structure; and this assessment method can be applied to the fast inspection of structure and the study of controllability.
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Received: 25 December 2015
Published: 15 February 2017
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2017, Vol. 38 
