Wavelets transform in oscillation and optimal feedback control of smart cantilever thin‐walled beams

Based on the recent results obtained by Na and Librescu concerning the dynamic response characteristics of thin‐walled cantilever beams made by smart materials subjected to transient loadings, this paper proposes to use the technique of wavelets transforms. As smart materials, the piezoelectric elements in the optimal feedback control of adaptive structures are considered and the oscillations are induced by the action of the blast loading. Wavelets provide a new tool for analysis, control, and identification of localized phenomena and vibrations. Instead of seeking to break down a signal into its harmonics, which are global functions that go forever, the signal is broken down into a series of local basis functions called wavelets. Each wavelet is located in a different place on the time axis. Several families of wavelet functions were studied. Haar, Meyer, Mallat, Daubechies, and Newland are in pattern recognition, image processing, turbulence, etc. This paper uses the Haar wavelets in order to perform the optimal control law with input voltage constraint and input power consumption. The influence of the inclusion of the excitations in the quadratic performance criterion of size and location of piezoactuator patches on the dynamic response of thin‐walled beams subjected to blast pulses are studied.