Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet–Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Efficient numerical treatment of periodic systems with application to stability problems. [in linear systems and structural dynamics

Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate

Vibration damping of marine lifting surfaces with resonant piezoelectric shunts

Dynamic modeling for rotor-bearing system with electromechanically coupled boundary conditions

A novel method to fully suppress single and bi-modal excitations due to the support vibration by means of piezoelectric actuators

A novel ring-shaped vibration damper based on piezoelectric shunt damping: Theoretical analysis and experiments

The parametric instability of a rotor system with electromechanically coupled boundary conditions under periodic axial loads is studied Based on the current flowing piezoelectric shunt damping technique, the detailed rotor model is established by the finite element (FE) method In the matrix assembly procedure, a novel simple process is proposed to make the equations of shunt circuits more conveniently to be introduced into the global FE equations The discrete state transition matrix method which is used for determining the influence of circuit parameters on instability regions in this paper has also been presented The numerical simulation shows that only the combination instability regions exist when the shaft is rotating The mechanical damping has different effect on the simple and combined instability regions These two points are consistent with the previous references, which verifies the obtained FE model In addition, the simulated results also reveal that the introduction of shunt circuits has little influence on the rotor’s original whirling frequencies It gives rise to the appearance of new synchronous whirl modes The new whirling frequencies are combined with the original ones to form the new combination instability regions Furthermore, the resistance of shunt circuits has the same performance as the mechanical damping has That is, moving up the start points of instability regions and expanding its width

Stability analysis of a rotor system with electromechanically coupled boundary conditions under periodic axial load

The invention discloses a piezoelectric stack-based vibration reduction ring device, and belongs to the field of design for vibration reduction devices The vibration reduction ring device comprises an inner ring, an outer ring, an inner ring end cover, an outer ring end cover, piezoelectric stacks and butterfly-shaped connection elements, wherein one piezoelectric stack is connected to the longitudinal symmetry axis of each butterfly-shaped connection element; the butterfly-shaped connection elements are uniformly distributed in aligned grooves between the inner ring and the outer ring; and the inner ring end cover and the outer ring end cover are further arranged at the upper ends of the inner ring and the outer ring separately According to the novel vibration reduction ring design disclosed by the invention, the vibration reduction ring is capable of effectively reducing vibration transferred to supporting by a transmission system through a shaft and a bearing by virtue of a piezoelectric shunt damping technology, and capable of effectively preventing the piezoelectric stacks from bearing tangential stress and torque, thereby prolonging the service lives of the piezoelectric stacks

Piezoelectric stack-based vibration reduction ring device

It is known that piezoelectric material shunted with external circuits can convert mechanical energy to electrical energy, which is so called piezoelectric shunt damping technology. In this paper, a piezoelectric stacks ring (PSR) is designed for vibration control of beams and rotor systems. A relative simple electromechanical model of an Euler Bernoulli beam supported by two piezoelectric stacks shunted with resonant RL circuits is established. The equation of motion of such simplified system has been derived using Hamilton’s principle. A more realistic FEA model is developed. The numerical analysis is carried out using COMSOL® and the simulation results show a significant reduction of vibration amplitude at the specific natural frequencies. Using finite element method, the influence of circuit parameters on lateral vibration control is discussed. A preliminary experiment of a prototype PSR verifies the PSR’s vibration reduction effect.

Xing Tan

Papers

A novel ring-shaped vibration damper based on piezoelectric shunt damping: Theoretical analysis and experiments

Dynamic modeling for rotor-bearing system with electromechanically coupled boundary conditions

Stability analysis of a rotor system with electromechanically coupled boundary conditions under periodic axial load

Piezoelectric stack-based vibration reduction ring device

Reduction of structural vibrations with the piezoelectric stacks ring