title: Variational Problem on Vibrations of Unequal-Thickness Rings and Its Application for Calculating Ultrasonic Vibration Concentrators
abstract: The paper considers a method for calculating the natural frequencies of vibrations of unequal-thickness rings, based on application of Hamilton’s variational principle and theories of vibrations of curved beams of the Euler-Bernoulli and Timoshenko type. Solutions of the problem are represented as Fourier series providing possibility of its reduction to the system of linear algebraic equations. The problem of determining natural frequencies is reduced to a generalized problem for the eigenvalues
journal: Science & Technique