By F. Ebrahimi
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Additional info for Advances in Piezoelectric Transducers
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3. The solution of the system’s characteristic equation approach to limit described by equation: 32 Advances in Piezoelectric Transducers kn 2n 1 , 2l n 1, 2, 3... (10) This solution is precise for n > 3. For the lower values of n solutions should be readout from the graphic solution (Fig. 3) and they are presented in table 4. Fig. 3. The graphic solution of the characteristic equation of the system (equation 7) Taking into account the system’s boundary and initial conditions, after transformations the sequence of eigenfunctions is described by the equation: Xn x An cos knl cosh knl cos knx cosh knx sin knx sinh kn x.