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• An effective method is developed for dynamic modelling of hemispherical shells with fillets. • Effects of fillets on thermoelastic quality factors of hemispherical shells are deeply explored. • The lower fillet has larger influence on the natural frequencies than the upper fillet does. • For the lower fillet, there exists size interval where hemispherical shell has higher energy losses. In engineering applications, hemispherical shell resonators are typically machined with fillets to reduce stress concentration and enhance structure strength. The fillets will inevitably affect the dynamic properties and the mechanical quality factor of hemispherical shell resonators, which has been seldom investigated before. In this paper, an effective analytical method is developed to explore the free vibration and thermoelastic damping (TED) characteristics of the hemispherical shell with fillets. The fillets are characterized by the variation in the thickness of the hemispherical shell during modelling. The first-order shear deformation theory (FSDT) is used to describe the theoretical formulas of the hemispherical shell with fillets. By employing the unified Jacobi polynomials and Fourier series as the assumed mode shape functions, the equation of motion of the structure is established by Hamilton's principle and the assumed mode method. The analytical model for thermoelastic quality factor (Q TED) which is determined by TED is obtained by computing the dissipated energy and the maximum elastic potential energy of the hemispherical shell with fillets. The validity and accuracy of the present method are confirmed by comparing the present solutions with the published results and those obtained from the finite element method (FEM). The influences of fillets on the vibration behaviors and Q TED characteristics of the hemispherical shells are analyzed in detail. The present model can be used to optimize the design of the fillets of the hemispherical shell resonators with high quality factors. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to evaluate thermoelastic damping in laminated microring. • More items are needed to converge when values of ∆ E for the layers are quite different. • The temperature gradient in the circumferential direction has little effect on the TED. • Increasing thickness of metallic coating will increase TED of laminated microring resonators. Predicting thermoelastic damping (TED) is crucial in the design of micro-resonators with high quality factors. Until now, some analytical models have been developed to evaluate the TED effect on microrings which are widely used in many micro-resonators. However, most previous works are limited to microrings with single homogeneous material. This paper develops an analytical model for investigating the TED in the laminated microrings. The temperature fields along the thickness and circumferential directions in the laminated microring are presented using the generalized orthogonal expansion technique. The analytical model for the TED is obtained by computing the dissipated energy and the maximum elastic energy in each layer. The present analytical model for evaluating the TED is validated by comparing with the previously published result and the finite element method (FEM). The effects of the thickness and the property of the metallic layer on the TED characteristics of two- and three-layered microrings are analyzed. The present model can be used to optimize the design of the microring resonators with high quality factors. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to evaluate thermoelastic damping in cylindrical shells. • Cylindrical shell with clamped-clamped edges dissipates the minimum thermal energy. • Increasing circumferential and radial spring stiffnesses reduces thermoelastic damping. • Decreasing ratios of length to radius and radius to thickness reduces thermoelastic damping. An effective method is proposed for the dynamic modelling and thermoelastic damping (TED) evaluation of the cylindrical shells with arbitrary boundaries. The arbitrary boundary conditions of the cylindrical shell are simulated by a set of springs, and the degree of the boundary condition is achieved by adjusting the spring stiffnesses. Hamilton's principle with the Rayleigh-Ritz method is employed to establish the equation of motion of the cylindrical shell, and the natural frequencies of the cylindrical shell with arbitrary boundaries are obtained by solving the eigenvalue problem of the equation of motion. An analytical model for the TED in the cylindrical shell is obtained by computing the dissipated energy and the maximum elastic potential energy in the cylindrical shell. The correctness and feasibility of the present theoretical model are verified by comparing the natural frequencies and TED obtained by this analytical method with those from the published literature and the finite element method (FEM). The convergence analysis of the analytical expression of TED is carried out. The influences of geometrical parameters and different types of spring stiffnesses on the TED are studied. In addition, the effects of the boundary conditions and the vibration modes of the structure on the TED characteristics of the cylindrical shells with arbitrary boundaries are analyzed. The present model provides theoretical reference for optimizing the cylindrical shell resonators with high quality factors. [ABSTRACT FROM AUTHOR]

• A novel strategy is proposed for the dynamic modelling of hemispherical shell resonator. • An analytical model is developed to evaluate quality factors of hemispherical shell resonators. • Properly decreasing the radius of support rod reduces thermoelastic damping and anchor loss. • Frequency parameter is sensitive to geometric sizes of support rod for lower order modes. A novel strategy is proposed for the dynamic modelling and quality factor evaluation of the hemispherical shell resonators (HSR) considering the coupling of hemispherical shell and support rod. The artificial spring technique is introduced to realize the coupling connection of substructures and simulate the arbitrary boundary conditions. Hamilton's principle with the Rayleigh-Ritz method is employed to establish the equation of motion of the HSR, and the natural frequencies of the HSR are obtained by solving the eigenvalue problem of the equation of motion. The thermal energy method is applied to evaluate the thermoelastic damping (TED) of the HSR. The model of anchor loss is based on a separation and transfer method, in which the HSR and its substrate are first separated for analysis and then the stress from the clamped region of the support rod is transferred to the substrate for determining the vibration displacement across the clamped region. The energy losses to the substrate are formulated as the integral of the product of the stress and the vibration displacement across the clamped region per cycle of vibration. The results calculated from the present theoretical method are compared with those from the published literature and the finite element method (FEM), which validates the correctness and feasibility of the present theoretical model. The effects of the boundary conditions and geometrical parameters on the vibration behaviors of the HSR are analyzed, and the influences of the boundary conditions, geometrical parameters and material properties of the HSR on the quality factors related to the TED and anchor loss are investigated. The present model can be used to optimize the design of the HSR with a high quality factor. [ABSTRACT FROM AUTHOR]