The theory of forced oscillations of the piezoelectric resonator in the form of a rectangular parallelepiped is presented in article. This method based on representation of unknown components of mechanical displacements and electric potential in the resonator in the form of the linear combinations of orthogonal basic functions. The Legendre polynoms was chosed as basic functions for rectangular resonator. The unknown coefficients entering these linear combinations are defined from a condition of a stationarity of the Lagrangian of the system. Unlike the known RPR method (rectangular parallelepiped resonance) which allows to calculate natural frequencies for the free resonator the presented method defines distribution of mechanical and electric fields in the resonator for the given exciting frequency. Advantage of a method is the possibility of use of complex material constants that allows taking into account the viscosity and electrical conductance of material of the resonator.
$^1$Kotel’nikov Institute of Radio Engineering and Electronics of RAS, Saratov Branch
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