Wave Vibration Control of L-Shaped and Portal Planar Frames

This paper discusses the control of coupled bending and axial vibrations in L-shaped and portal planar frame structures. The controller is designed based on a wave standpoint, in which vibrations are described as waves traveling along uniform structural waveguides, and being reflected and transmitted at structural discontinuities. Active discontinuities are created using active control forces/moments both along structural elements and at structural joints to control vibration waves. The classical Euler–Bernoulli as well as the advanced Timoshenko bending theories are applied in modeling and controlling the flexural vibrations in planar frames. The axial vibrations are modeled using the elementary theory as it is typically valid for frequencies up to twice the cutoff frequency of Timoshenko bending waves. Results are compared between the two bending vibration theories. It is concluded that for relatively higher frequencies, typically when the transverse dimensions are not negligible with respect to the wavelength, the effects of rotary inertia and shear distortion must be taken into account for both vibration analysis and control design.