Effective mass spectrum and dissipation power of granular material under the horizontal and vertical excitation

Abstract

In this paper, in order to explore the movement characteristics of granular system under the horizontal and vertical excitation, the effective mass spectrum and dissipation power of granular material are studied by numerical simulation. We use LIGGGHTS software to simulate a granular system consisting of 13340 dispersed particles in a cubic container. For the two different vibration directions of granular system (horizontal and vertical), we carry out a pressure unloading experiment in a pressure range from 1012.10 kPa to 8.66 kPa. It is found that under the horizontal and vertical excitation, the resonance frequency fg and volume modulus k of granular system satisfy piecewise power-law with the change of pressure P applied to the top surface. It follows the laws, that is, fg∝P1/6 and k∝P1/3 at low pressure and fg∝P1/4 and k∝P1/2 at high pressure. At the same time, according to the effective mass of the imaginary part, we can obtain the dissipative characteristics of the granular system. Under the horizontal and vertical excitation, the reciprocal of quality factor of granular matter, 1/Q, decreases exponentially with the change of pressure P. In the relaxation dynamics of the granular system, both the acceleration and the stress play a role similar to the role of temperature in the thermal system. In order to further study the influence of acceleration on solid-fluid-like transition of granular system, we measure the relationships between the dissipation power and the vibration intensity (1g-30g) under different pressures (8.66-1012.10 kPa), in the horizontal vibration (500 Hz). At the fixed frequency and pressure, there is a characteristic vibration intensity Γ* in the curve of the average power dissipation of granular system with vibration intensity Γ. When ΓΓ*, the granular system exhibits a solid-like behavior, and the variation of the average power dissipation with the change of vibration intensity Γ shows a power-law scaling, p∝Γα (2αΓ > Γ*, the granular system exhibits a liquid-like behavior, and the variation of the average power dissipation of granular system with the vibration intensity Γ changes into a linear fashion. Then, the phase diagram of transition from the solid-like phase to fluid-like phase, i.e., Γ-P phase diagram, in granular system under the horizontal excitation, is obtained in this paper.