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In this paper, a new method for determining the rheological parameters of viscoelastic liquids is presented. To this end, we used the perturbation method applied to shear vibrations of cylindrical piezoceramic resonators. The resonator was viscoelastically loaded on the outer cylindrical surface. Due to this loading, the resonant frequency and quality factor of the resonator changed. According to the perturbation method, the change in the complex resonant frequency /spl Delta/~/spl omega/ = /spl Delta/w/sup re/ + j/spl Delta//spl omega//sup im/ is directly proportional to the specific acoustic impedance for cylindrical waves Zc of a viscoelastic liquid surrounding the resonator, i.e., /spl Delta/~w /spl sim/ jZ/sub c/, where j = (-1)/sup 1/2/. Hence, the measurement of the real and imaginary parts of the complex resonant frequency determines the real part, R/sub c/, and imaginary part, X/sub c/, of the complex acoustic impedance for cylindrical waves Z/sub c/ of an investigated liquid. Further-more, the specific impedance Z/sub L/ for plane waves was related to the specific impedance Z/sub c/ for cylindrical waves. Using theoretical formulas established and the results of the experiments performed, the shear storage modulus /spl mu/ and the viscosity /spl eta/ for various liquids (e.g., epoxy resins) were determined. Moreover, the authors derived for cylindrical resonators a formula that relates the shift in resonant frequency to the viscosity of the liquid. This formula is analogous to the Kanazawa-Gordon formula that was derived for planar resonators and Newtonian liquids.