Vibrational Energy Flow Analysis Of Electro-thermal-elastic Coupled Metamaterials Based On Finite Element Method

Based on the structural intensity approach,the vibrational energy flow(VEF)of the electro-thermal-elastic coupled metamaterial structures is analyzed in this paper.The effects of temperature rise and input voltage on the energy flow in metamaterial structures are considered respectively.A finite element model is proposed to derive the motion equation of the electrothermal-elastic coupled metamaterial plate that the stiffness matrix depends on the temperature rise and input voltage.Bloch boundary conditions are introduced to analyze the band structure of metamaterial plates,In the numerical calculation,the band gaps of the finite metamaterial plate agree well with the band structures,which verifies the effectiveness of the finite element model.Then the band gaps under different input voltage and temperature rise is considered.The vibration characteristics of the electro-thermal-elastic coupled metamaterial structures are analyzed by establishing finite element mathematical model under temperature rise.The VEF-controlling regions in the electro-thermal-elastic coupled metamaterial structures are presented based on the structural intensity method.Firstly,a VEF analysis model is developed to investigate the influences of the temperature rise and the input voltage on the VEF magnitude and direction.In the present VEF analysis model,the structural intensity method is developed to investigate the influences of the temperature rise and the input voltage on the VEF magnitude and direction.Secondly,the divergence representation is proposed to obtain the positions of sinks and sources in some complex structures more clearly.The numerical simulation results show that the VEF magnitude increases with increasing temperature rise or input voltage.It can be also found that the influence of input voltage on VEF direction may be offset by the temperature rise,and the influence of the temperature rise on VEF paths also may be offset by the input voltage.To better analyze the influences of the temperature rise and input voltage,the temperature rise and input voltage controlling regions are given.