Flutter analysis of rotating beams with elastic restraints

The aeroelastic stability of rotating beams with elastic restraints is investigated.The coupled bending-torsional Euler-Bernoulli beam and Timoshenko beam models are adopted for the structural modeling.The Greenberg aerodynamic model is used to describe the unsteady aerodynamic forces.The additional centrifugal stiffness effect and elastic boundary conditions are considered in the form of potential energy.A modified Fourier series method is used to assume the displacement field function and solve the governing equation.The convergence and accuracy of the method are verified by comparison of numerical results.Then,the flutter analysis of the rotating beam structure is carried out,and the critical rotational velocity of the flutter is predicted.The results show that the elastic boundary reduces the critical flutter velocity of the rotating beam,and the elastic range of torsional spring is larger than the elastic range of linear spring.

Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman＇s plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material （FGM） circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.

Vibration Characteristics and Power Transmission of Coupled Rectangular Plates with Elastic Coupling Edge and Boundary Restraints

Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increased mathematical complexity compared with the single plate structure.In order to study analytically the vibration characteristics and power transmission of the coupled-plate structure,an analytical model consisting of three coupled plates elastically restrained along boundary edges and elastically coupled with arbitrary angle is considered,in which four groups of springs are distributed consistently along each edge of the model to simulate the transverse shearing forces,bending moments,in-plane longitudinal forces and in-plane shearing forces separately.With elastic coupling condition and general boundary condition of both flexural and in-plane vibrations taken into account by setting the stiffness of corresponding springs,the double Fourier series solution to the dynamic response of the structure was obtained by employing the Rayleigh-Ritz method.In order to validate the model,the natural frequency and velocity response of the model are firstly checked against results published in literatures and the ANSYS data,and good agreement was observed.Then,numerical simulation of the effects of several relevant parameters on the vibration characteristics and power transmission of the coupled structure were performed,including boundary conditions,coupling conditions,coupling angle,and location of the external forces.Vibration and energy transmission behaviors were analyzed numerically.The results show that the power transmission can be significantly influenced by the boundary restraints and the location of excitation.When the excitation is located at the central symmetry point of the model,the energy flow shows a symmetrical distribution.Once the location deviates from the central symmetry point,the power circumfluence occurs and the vortex energy field is formed at high frequency.