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In this paper, based on the theory of elastic structure analysis, considering the rotational softening and centrifugal stiffening of the blade, the dynamic model of the fir-tree rotating blade and the macroslip hysteresis model of the dry friction on the contact surface of fir-tree tenon are established. Based on elastic mechanics, the pressure distribution model of fir-tree tenon is innovatively established and the relationship between fit clearance and contact pressure has been derived. After the blade is discretized by the finite element method, the dynamic equation of the blade is solved iteratively by the Newmark-β numerical integration method. According to the dynamic equation of the blade, the influence of the change of the tenon angle on the forced response and contact stress of the blade is derived. Finally, some novel conclusions are obtained by analyzing the influence of pressure distribution, tenon angle, friction coefficient, rotational speed, and aerodynamic excitation on blade vibration characteristics. It provides a scheme and relevant basis for the design and development of tenon blades with the most damping effect at different speeds in industrial practice.

In this work, a continuum model is proposed to simulate and interpret the coupling vibration characteristics of a rotating disk-beam system with the dovetail interfaces. The dovetail interface feature is represented by a macroslip dry friction model. The present study also derives a new mode function to simulate the vibration of a rotating beam with loosely assembled dovetail attachment. The new proposed mode function is validated by comparing the natural characteristics and vibration response with those obtained from a finite element (FE) model. At last, based on the nonlinear response results obtained by the Newmark-β method, the effects of different parameters on the nonlinear dynamics of the coupling system are discussed. The following interesting phenomena have been revealed: the flexible disk can impose different influences on the response characteristics of the rotating beam. The effects of dry friction on the beam’s energy dissipation are significant, especially at a low rotational speed. Further analysis yields that the excitation level and friction coefficient also exhibit a significant impact on the damping effect of dry friction. Consequently, it should be noted that the optimal values of the contact surface’s parameters allow achieving a better damping effect in the engineering practice.

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.

A dynamic model of the rotating shrouded blade is established, considering the shroud mass, the Coriolis force, and the centrifugal stiffening effect. And a macroslip model of dry friction with variable normal load is established to simulate the separation-contact-stick-slip state of the shroud. The Lagrangian equation is utilized to solve the differential motion equation, and the Galerkin method is used for discretization. The influence of shroud structure’s parameters such as rotational speed, contact angle, friction coefficient, clearance, and shroud position on the damping effect of the shroud is reviewed by means of amplitude-frequency response and energy through the Newmark-β numerical method. The results demonstrate that the damping effect of the shroud by contact is more obvious than by friction and the amplitude-frequency curve of the shrouded blade shows a strong hard nonlinear phenomenon.

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.

Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.