Derivation of a force factor equation for a langevin-type flexural mode transducer

We propose a calculation method for the force factor of a Langevin-type flexural mode transducer. In this proposed method, after calculating the flexural vibration mode and the resonance frequency using the analytical solution given by Miklowitz for the Timoshenko beam theory, the force factor is calculated by substituting the obtained vibration distribution into the piezoelectric equation. In the calculation of vibration distribution, piezoelectric elements bound by metal blocks are considered using the matrix expression of the Miklowitz solutions. Differences between calculation results and measurements are within 35% for several bonded transducers. Therefore, this calculation method is useful for the design of Langevin-type flexural mode transducers.