Visualization Analysis Of Vibration Energy Flow In A Metamaterial Plate Under The Temperature Rise

Based on the structural intensity approach,the vibrational energy flow in metamaterial plate structure is analyzed in this paper.The effects of structural damping,temperature rise and mechanical load on the energy flow in metamaterial structures are considered respectively.The thermal field is assumed to be uniform throughout the entire metamaterial plate.The stiffness matrix of the plate element can be regarded as a function of the temperature rise due to the nonlinear membrane strain.Firstly,periodic boundary conditions are introduced to analyze the band structure of metamaterial plates,then the band gaps under different damping and temperature rise are considered.The vibration characteristics of metamaterial plate are analyzed by establishing finite element mathematical model under temperature rise.The focus of the work is to analyze the vibration energy flow of the metamaterial structure under different temperature rise and mechanical load.The increase of damping can effectively suppress the vibration dissipation.For a given mechanical load,the magnitude of the vibration energy flow increase with the increase of temperature rise,but the increase amplitude decreases gradually;the angular deflection of energy flow decreases gradually and finally stabilizes at a fixed value.The vibration energy flow magnitude increase with increasing mechanical load for a given temperature rise and the direction deflection will increase to a fixed value.The influences of temperature rise and mechanical load on the amplitude and direction of the energy flow can be suppressed mutually.It is also observed that the vibration energy flow dirction can be controlled by the temperature rise provided that the temperature rise is sufficiently large,and the direction can be controlled by the mechanical load provided that the mechanical load is sufficiently large.Therefore,a transition regioncan be found,which divide the scope of mechanical load and thermal load to control the energy flow.In order to accurately describe the vibration energy flow,the divergence of the vibration energy flow is caculated to localiza the energy sources,local resonance mechanism of generating energy flow source was found.