Influences of the temperature rise on the vibration energy flow in a dissipative elastic metamaterial plate based on the structural intensity approach

Abstract

The effects of the temperature rise on the vibration energy flow in a dissipative elastic metamaterial plate with a nonlinear membrane strain are investigated based on the structural intensity approach using the finite element method. The thermal field is assumed to be uniform throughout the entire metamaterial plate with local resonances and constituent viscoelastic materials. The dissipative plate elements are considered because analysis of the vibration energy flow is shown to depend on the loss factor. The stiffness matrix of the plate element can be regarded as a function of the temperature rise. In the numerical calculation, the band gaps of the finite metamaterial plate agree well with the band structures, which verifies the effectiveness of the method. The Influences of the temperature rise and mechanical load on the vibration energy flow path are analyzed. For a given mechanical load, the magnitude of the vibration energy flow increases with the increase in the temperature rise. The vibration energy flow magnitude increases with increasing mechanical load for a given temperature rise. Additionally, the divergence of the vibration energy flow is calculated to localize the energy sources and sinks, which validates the effectiveness of the streamline representation technique. It is also observed that the vibration energy flow direction 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 temperature rise region (TRR) can be found in which the temperature rise plays a more important role in controlling the direction of the vibration energy flow than the mechanical load.