Interpreting piezoelectric oscillator dissipation effects in terms of the underlying materials viscoelastic relaxation phenomena

Equivalent circuit modeling has long been recognized as a valuable tool for describing transduction processes and the behavior of transducers. The formalism has been generalized to represent distributed properties, mode coupling, and the implications of structural complexity, mechanical loading, and electrical tuning. Dissipation or loss phenomena can also be accommodated by equivalent circuit methods. It is generally recognized that interpreting all relevant elastic, dielectric, and piezoelectric coefficients as complex numbers is an appropriate way to represent losses. All too often, the scope of this approach discourages the development of detailed results. This paper analyzes the dissipation modeling problem in terms of relaxation processes, a phenomenological approach that gives algebraic form to certain groupings of the electromechanical coefficients. The implication is that sound speed, coupling coefficients, materials moduli, etc., are frequency dependent. A mass-loaded longitudinal vibrator with a segmented piezoelectric cylinder is analyzed as an example of this model-parameter dispersion problem. Of particular interest is the effect of the adhesive joints on the oscillator admittance spectrum over a wide range of frequencies.