An Influence Analysis of Second-Order Effect to the Vibration Control of Piezoelectric Beam by the Spline Finite Point Method

The field functions of the spline finite point (SFP) method were constructed by the linear combination of B-spline basis function, and the higher-precision results would be obtained with less discrete nodes by the SFP method. In this paper, based on Reddy's third order beam theory, a motion equation was developed by the SFP method to analyze the first five natural frequencies of piezoelectric laminated beam under different axial forces. The influence of second-order effect caused by the axial force on vibration control was discussed based on the modal control theory and the Linear Quadratic Regulator (LQR) optimal control method. It can be concluded that the SFP method is suitable for the dynamic analysis of piezoelectric beam which needs less computational cost and has high accuracy. The vibration of the structure can be effectively inhibited by the LQR method and modal control theory. And the axial force has significant impact on the natural frequencies and control voltage of piezoelectric beam.