Vibration analysis and active control for frame structures with piezoelectric rods using spectral element method

摘要

The dynamic responses and vibration suppression of frame structures considering the shear deformation are investigated using the spectral element method (SEM). Vibration suppression of the frame structures is studied through the active control technique using the piezoelectric rods. The local dynamic stiffness matrices of the spectral elements for the Timoshenko beams and longitudinal vibration of the rods are obtained in the Fourier phase space and that for the axial-bending-shear coupled vibration of the piezoelectric rod is also gotten. From the transformation between the local and global coordinates, the global dynamic stiffness matrix for the whole frame structures containing the piezoelectric rods is obtained. From the numerical simulation, the dynamic responses of the frame structures can be effectively and exactly calculated by the SEM comparing with the finite element method. It can be found that the dynamic responses of the frame structures can be effectively suppressed by the active control technique based on the piezoelectric rods. The influences of the structural parameters on the dynamic responses and active control effect are also analyzed.