Based on the theory of homogeneous elasticity,the traditional method for analyzing the structural characteristics of a ring-shaped resonators cannot accurately describe the influence of the mechanical properties of heterogeneous materials on the static and dynamic performance of resonators.According to the Euler beam theory of circular curved structures,a method for analyzing the structural properties of ring-shaped resonators with heterogeneous materials is established,utilizing the constitutive relationships of heterogeneous materials and Hamilton principle.With the theory above and Bubnov-Galerkin method,theoretical solutions are derived for the static bending and dynamic rotating problems.Then,the influence of heterogeneous mechanical properties is analyzed for the bending deflection,second-order bending angular frequency and precession coefficient.The performance analysis results of typical heterogeneous materials show that the traditional method has an error of over 59%in calculating the second-order bending angular frequency,while the proposed method can accurately predict the static and dynamic responses of structures of heterogeneous resonators and calculate the second-order bending angular frequency.
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