Active control of nonlinear forced vibration in a flexible beam using piezoelectric material

ABSTRACT

Geometric nonlinearities of the beam and piezoelectric patch are considered. Velocity feedback control algorithm is implemented applying piezoelectric materials. The equation of motion of the system is established using Hamilton's principle. The effects of control gains on primary resonance properties of the beam are studied. It is observed that, with the amplitude of external excitation increasing, the amplitude of resonance curve increases. The velocity feedback control can improve unstable resonance of the beam. When the control gain is increased to a certain value, the unstable regions in the resonance and amplitude-frequency curves disappear.

KEYWORDS:

• beam
• piezoelectric material
• nonlinear vibration
• active control
• multiple-scales method

Funding

This research is supported by the National Basic Research Program of China (No. 2011CB711100) and the National Natural Science Foundation of China (Nos. 11172084 and 10672017).