Particle damping (PD) is a passive mean of vibration control in which small metallic or ceramic particles are placed inside a cavity that attached to the primary structure at the place of high vibration amplitudes. The kinetic energy of the primary structure is dissipated by non-elastic impact and friction between particles and walls. This paper represents a series of experimental investigations of the effects of multi-unit particle dampers (MUPD) attached to a bracket structure under harmonic excitation and random excitation. As a platform to investigate the particle damping characteristics under extreme acceleration environments, the bracket structure was featured by an extremely high response on the top, and its maximum acceleration exceeds 50 times gravity acceleration when the bracket structure was subjected to resonance. This broad range of acceleration conditions was far beyond the scope concerned in most previous work. The experimental results show that for a small weight penalty (no more than 8.8%), multi-unit particle damper can reduce the resonance of the primary structure by more than 50%, whether under sinusoidal excitation or random excitation. And the response of the primary structure depends on the type of cavities and filled coefficient. Layering the cavity in the direction of the main vibration can improve the damping capacity of the multi-unit particle damper. And the damper with small particle size and large number of features is suitable for vibration reduction under high acceleration conditions.

In turbomachinery applications, thin-walled gears are cyclic symmetric structures and often subject to dynamic meshing loading which may result in high cycle fatigue (HCF) of the thin-walled gear. To avoid HCF failure, ring dampers are designed for gears to increase damping and reduce resonance amplitude. Ring dampers are installed in the groove. They are held in contact with the groove by normal pressure generated by interference or centrifugal force. Vibration energy is attenuated (converted to heat) by frictional force on the contact interface when the relative motion between ring dampers and gears takes place. In this article, a numerical method for the prediction of friction damping in thin-walled gears with ring dampers is proposed. The nonlinear damping due to the friction is expressed as equivalent mechanical damping in the form of vibration stress dependence. This method avoids the forced response analysis of nonlinear structures, thereby significantly reducing the time required for calculation. The validity of this numerical method is examined by a comparison with literature data. The method is applied to a thin-walled gear with a ring damper and the effect of design parameters on friction damping is studied. It is shown that the rotating speed, geometric size of ring dampers and friction coefficient significantly influence the damping performance.

The gear is a cyclic symmetric structure, and each tooth is subjected to a periodic mesh force. These mesh forces have the same phase difference tooth by tooth, which can excite gear vibrations. The mechanism of additional axial force caused by gear bending is shown and examined, which can significantly affect the stability of a self-excited thin spur gears vibration. A mechanical model based on energy balance is then developed to predict the contribution of additional axial force, leading to the proposed numerical integration method for vibration stability analysis. By analyzing the change in the system energy, the occurrence of the self-excited vibration is validated. A numerical simulation is carried out to verify the theoretical analysis. The impacts of modal damping, contact ratio, and the number of nodal diameters on the stability boundaries of the self-excited vibration are revealed. The results prove that the backward traveling wave of the driven gear as well as the forward traveling wave of the driving gear encounter self-excited vibration in the absence of sufficient damping. The model can be used to predict the stability of the gear self-excited vibration.