Abstract
A novel metrics termed the ‘wave electromechanical coupling factor’ (WEMCF) is proposed in this paper, to quantify the coupling strength between the mechanical and electric fields during the passage of a wave in piezoelectric composites. Two definitions of WEMCF are proposed, leading to a frequency formula and two energy formulas for the calculation of such a factor. The frequency formula is naturally consistent with the conventional modal electromechanical coupling factor (MEMCF) but the implementation is difficult. The energy formulas do not need the complicated wave matching required in the frequency formula, therefore are suitable for computing. We demonstrated that the WEMCF based on the energy formula is consistent with the MEMCF, provided that an appropriate indicator is chosen for the electric energy. In this way, both the theoretical closure and the computational feasibility are achieved. A numerical tool based on the wave and finite element method (WFEM) is developed to implement the energy formulas, and it allows the calculation of WEMCF for complex one-dimensional piezoelectric composites. A reduced model is proposed to accelerate the computing of the wave modes and the energies. The analytical findings and the reduced model are numerically validated against two piezoelectric composites with different complexity. Eventually an application is given, concerning the use of the shunted piezoelectric composite for vibration isolation. A strong correlation among the WEMCF, the geometric parameters and the energy transmission loss are observed. These results confirm that the proposed WEMCF captures the physics of the electromechanical coupling phenomenon associated with the guided waves, and can be used to understand, evaluate and design the piezoelectric composites for a variety of applications.
Highlights
The concept of smart structures provides another promising possibility of solving a variety of engineering issues, such as vibration control, noise reduction, fault diagnose, wireless sensing, self powering and so on
We study the factor that allows to quantify the coupling strength between the mechanical and electric fields during the passage of a wave in piezoelectric composites, termed the wave electromechanical coupling factor (WEMCF)
We show that to maintain the consistency with the classical modal electromechanical coupling factor (MEMCF), the WEMCF should be defined by the frequency difference of the open circuit (OC) and short circuit (SC) statues
Summary
The concept of smart structures provides another promising possibility of solving a variety of engineering issues, such as vibration control, noise reduction, fault diagnose, wireless sensing, self powering and so on. Speaking, arbitrary deformation of a finite structure can be expressed as the superposition of the modal deformations, and the modes whose natural frequencies are close to the considered excitation frequency range will have dominant contribution In this regard, it is reasonable to define the EMCF in terms of modes. Thomas et al [9] found, via closed-form expressions, that the best modal damping induced by the resistor and resistor-inductor shunts depend only on the MEMCF once the structural parameters remain constant This indicates that MEMCF can be used as a criterion to optimize the geometrics of the piezoelectric materials [11,12]. The EMCF should quantify the coupling strength between the mechanical and electric fields during the passage of a wave in piezoelectric composites, and in this paper it is termed the ‘wave electromechanical coupling factor’ (WEMCF) to distinguish itself from the aforementioned coupling factors. An application concerning the control of energy flow using shunted piezoelectric composite is presented in Section 6, in order to illustrate the usage of WEMCF
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