Wavelet transform for boundary control of smart thin-walled beam cantilever

摘要

Wavelets provide a new tool in vibration, identification and control. By their properties wavelets transform are stronger than FEM and FFT. We dispose to several wavelets family as Haar, Daubechies, Morlet, Mallat, etc. and use the filter banks for vibration analysis. This paper deals with the problem of controlling the bending oscillations of a thin walled cantilever beam with arbitrary cross section. The control is achieved via the action of a bending moment applied at a tip of structure. A possibility to generate the control bending moment at the wing tip is via the implementation into the structure of piezoactuators. The velocity feedback control allows the possibility to generate damping through the feedback gain coefficient. Feedback law where the bending moment at a tip is proportional to the velocity is included into matrix wavelet implementation. Numerical examples for PDE are computed and compared with other examples for particular cases included in earlier paper of Librescu, Na. The paper uses the Haar wavelet transform to algebrize PDE leading to a powerful and general method to study the nonlinear problems with more flexibility and localization of peak resonance in comparison with other procedures.