Hybrid wave/mode active control of bending vibrations in beams based on the advanced Timoshenko theory

A hybrid approach to active control of bending vibrations in beams based on the advanced Timoshenko theory is described in this paper. It combines elements of both wave and mode approaches to active control and is an attempt to improve on the performance of these approaches individually. As is well known that the classical Euler–Bernoulli beam model considers only the lateral inertia and the elastic forces caused by bending deflections, and the effects of rotary inertia and shear distortion are neglected. As a result, the theory is not valid for higher frequencies, typically when the transverse dimensions are not negligible with respect to the wavelength. In the proposed hybrid approach based on the advanced Timoshenko model, wave control is first applied at one or more points in the structure. It is designed on the basis of the local behavior of the structure and is intended to either absorb vibrational energy or add damping, especially at higher frequencies. Then modal control is applied, being designed on the basis of the modified global equations of motion of the structure-plus-wave-controller. Because the higher order modes are relatively well damped, hybrid control improves the model accuracy and the robustness of the system and gives better broadband vibration attenuation performance. Numerical results are presented.