Determination of vibration energy flow-controlling regions in a piezoelectric metamaterial plate with temperature rise

Abstract

In this study, vibration energy flow (VEF)-controlling regions in a piezoelectric metamaterial plate were determined using the structural intensity method. A finite element model was developed to derive the motion equation of a piezoelectric metamaterial plate in which the stiffness matrix depends on the temperature rise and input voltage. A VEF analysis model was developed to investigate the influence of temperature rise and input voltage on the VEF magnitude and direction based on the structural intensity method. In the numerical calculations, the bandgaps of the finite piezoelectric metamaterial plate agreed well with the band structures, which verified the effectiveness of the finite element model. In the present VEF analysis model, the structural intensity method was developed to investigate the influences of temperature rise and input voltage on the VEF magnitude and direction, and a new representation, called the divergence representation, was proposed to obtain the specific locations of sinks and sources in some complex structures. The numerical results showed that the magnitude of VEF increased with temperature rise or input voltage. The influence of the input voltage on the VEF direction may be offset by the temperature rise, and vice versa. To better analyze the influence of these two parameters, temperature-rise and input voltage-controlling regions were first analyzed. The input voltage played a more important role in controlling the direction of VEF than the temperature rise in the input voltage-controlling region and vice versa.