The vibration reduction characteristics of the flexible blade with a dovetail joint and underplatform damper are studied in this paper. Considering the influence of the platform mass on the inherent characteristics of the blade, this paper regards the underplatform as a particle with mass. Moreover, two types of friction models are introduced on the contact interfaces of the blade. Meanwhile, the normal pressure of the contact interfaces will change with the rotating speed of the blade. Also, the dynamical equation for the rotating blade is established based on the finite element method. The nonlinear friction force on the contact interface is brought into the dynamical equation, and the vibration response of the blade is solved. The effects of the rotating speed, the initial preload, and the contact angle of the underplatform on the vibration reduction characteristic of the blade are investigated.

The vibration dissipation mechanism of the rotating blade with a dovetail joint is studied in this paper. Dry friction damping plays an indispensable role in the direction of vibration reduction. The vibration level is reduced by consuming the total energy of the turbine blade with the dry friction device on the blade-root in the paper. The mechanism of the vibration reduction is revealed by the variation of the friction force and the energy dissipation ratio of dry friction. In this paper, the flexible blade with a dovetail interface feature is discretized by using the spatial beam element based on the finite element theory. Then the classical Coulomb-spring friction model is introduced to obtain the dry friction model on the contact interfaces of the tenon-mortise structure. What is more, the effects of the system parameters (such as the rotating speed, the friction coefficient, the installation angle of the tenon) and the excitation level on blade damping characteristics are discussed, respectively. The results show that the variation of the system parameters leads to a significant change of damping characteristics of the blade. The variation of the tangential stiffness and the position of the external excitation will affect the nonlinear characteristics and vibration damping characteristics.

An improved principle is proposed in this paper to achieve a more efficient amplitude suppression of an oscillating pendulum by a controllable moving mass. By establishing the governing equation of the pendulum with a moving mass, several suppression rules are presented to stipulate the motion parameters of the moving mass. The damping ratio is introduced to quantify the suppression effects generated by the mass intermittent motion. With the verification of the accuracy of the present model, some simulation has been taken to get the maximum damping ratio and solve the problem of the nonsynchronous motion. The simulation results show that the new principle is a more powerful control method for the oscillation problem of a pendulum. It is suggested that the new method should carry out the relevant active control experiment in the future research.

Considering the large-deformation hypothesis, the modeling and nonlinear vibration characteristics of symmetrically 3-layer composite thin circular cylindrical shells with arbitrary boundary conditions are analyzed by applying four sets of artificial springs. Firstly, by employing a set of orthogonal polynomials and trigonometric functions, the energy equations of the shells are derived with Donnell's nonlinear thin-shell theory. Then, the arbitrary boundary conditions are simulated by imposing the equivalent elastic constraint to obtain the potential energy of the edges of the shell, which can be universally applicable to all classical boundary conditions. The vibration equation is obtained by using the Lagrange equation method. In order to obtain correct numerical results, several comparisons of linear and nonlinear results are carried out to validate the approach method in the present study; meanwhile, the calculation convergence is checked. At last, the influence of boundary conditions, geometric parameters, symmetrical lamination schemes and damping coefficients on the nonlinear amplitude-frequency characteristics of symmetrically 3-layer composite thin circular cylindrical shells are investigated. The numerical results indicate that the present method is powerful to calculate the nonlinear vibration response characteristics of symmetrically 3-layer composite circular cylindrical thin shells subjected to various boundary conditions.

A dynamic model is proposed in this paper for analyzing the nonlinear characteristics of a flexible blade. The dynamical equation of motion for a rotational flexible blade in a centrifugal force field is established based on the finite element method. A macro-stick-slip mechanical model of dry friction is established to simulate the constraint condition of the flexible blade. The combined motion of the external excitation and friction produces a piecewise linear vibration which is actually nonlinear. The numerical integration method is employed to calculate the vibration reduction characteristics of the nonlinear constrained rotating blade. The results show that the nonlinear dry friction force produced by the dovetail interface plays an important role in vibration reduction. And the effect of dry friction vibration reduction is significant when the rotating speed is slow or the friction coefficient is small. Besides, the magnitude of external excitation also has a great impact on the state of the friction. Therefore, some relevant experimental researches should be done in the future.