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Distributed-Parameter Based Treatment of Interaction Process between Elastic and Dielectric Energy in Piezoelectric Transducer

The interaction process between elastic and dielectric energy in a piezoelectric transducer, which has been treated on the basis of lumped parameters in the framework of electrical equivalent circuit, is treated on a distributed-parameter basis. The concept of coupling between elastic and dielectric energy modes is introduced, and the superposition of the energy mode after the coupling is considered, which allows us to determine the frequency characteristics of the transducer with an electromechanical coupling. Mathematically, the coupling effect is represented by the exponential of a matrix, and the superposition of the energy mode is calculated with the infinite geometric series of a matrix, Neumann series, which provides physically reasonable results.