Chinese Journal of Theoretical and Applied Mechanics ›› 2019, Vol. 51 ›› Issue (6): 1872-1881.DOI: 10.6052/0459-1879-19-211

• Dynamics, Vibration and Control • Previous Articles     Next Articles

STABILITY ANALYSIS ON PARAMETRIC VIBRATION OF PIEZOELECTRIC ROTATING CANTILEVER BEAM WITH ACTIVE CONTROL 1)

Tang Ye*,Wang Tao*,Ding Qian*2)()   

  1. * School of Mechanical Engineering, Tianjin University,Tianjin 300072,China
    School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000,Anhui, China
  • Received:2019-08-02 Accepted:2019-10-21 Online:2019-11-18 Published:2019-12-26
  • Contact: Ding Qian

Abstract:

In engineering application, rotating machines tend to be pulsating operation due to the errors of manufacturing and processing as well as the non-uniformity of assembly, which may cause parametric vibration of the system. Furthermore, if the pulsation parameters satisfy a certain relationship, the parametric vibration will cause the system to lose stability, which furtherly affects the normal operation of mechanical structures. In view of this problem, the piezoelectric material is introduced to suppress vibration of rotating cantilever beam subjected to parametric exciting. The problem about the parametric optimization and design of rotating cantilever beam with active control is studied in this paper. The first order approximate linear equation governing the piezoelectric rotating cantilever beam controlled by velocity feedback sensor is established based on the Hamilton' principle combining with the first-order Galerkin discretization method. Then, the multi-scale method is applied to obtain the governing equation of stability boundary of the piezoelectric rotating cantilever system with the 1/2 sub-harmonic parametric resonance. The correctness of the perturbation solution is verified by the direct analysis method. The critical damping ratio and the dimensionless parameter of pulsating amplitude of hub angular velocity in the perturbation solution are regarded as the indicators to evaluate the system stability. Numerical examples are presented to illustrate the effects of the hub radius, the average value and pulsating amplitude of hub angular velocity, the beam length and the feedback gain coefficient of velocity sensor on the dynamic stability. The results show that the stable region can be increased with the decrease of the beam length, the hub radius and pulsating amplitude of hub angular velocity, but the raise of the feedback gain coefficient, moreover, the relation between the average value of hub angular velocity and the stability is not monotonous. It provides a reference for the further design of piezoelectric rotating machinery structure.

Key words: piezoelectric rotating cantilever beam, active control, parametric vibration, stability, multi-scale method

CLC Number: