We propose a multi-displacement continuum (MDC) model to characterize the local resonance presented in a lattice system. Dispersion curves in a mass-in-mass system are studied and compared to the single-displacement model. It is shown that the dispersive relations and the local resonant band gap structures can be adequately described. The acoustic mode can be accurately predicted, while the optical mode is correctly predicted for certain frequency range, where the wave length is large enough. The single-displacement model fails to describe the bang gap structure inherent in the system due to local resonance.
Aiping Liu 1 Guoliang Huang 2 Gengkai Hu 1 ( 1 School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, China) ( 2 Department of Systems Engineering, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA)
The electromechanical behavior of poly(vinylidene fluoride-trifluoroethylene)[P(VDF -TrFE)]ferroelectric thin film was investigated using the three dimensional(3D) phase-field method. Various energetic contributions,including elastic,electrostatic,and domain wall energy were taken into account in the variational functional of the phase field model.Evolution of the microscopic domain structures of P(VDF-TrFE) polymer film was simulated.Effects of the in-plane residual stress,the film thickness and externally applied electric bias field on the electromechanical properties of the film were explored.The obtained numerical results showed that the macroscopic responses of the electric hysteresis loops are sensitive to the residual stress and electric bias field.It was also found that thickness has a great effect on the electric hysteresis loops and remanent polarization.
Tao Li,~(1,a))Changqing Chen,~(2,b)) and Jinxiong Zhou~1 1)School of Aerospace,Xi’an Jiaotong University,Xi’an 710049,China 2)Department of Engineering Mechanics,AML & CNMM,Tsinghua University,Beijing 100084,China
