Experimental Study on Parametric Anti-resonances of an Axially Forced Beam

Abstract

Long and flexible beam structures are in use in various fields of engineering. Vibration problems are common with such structures due to high flexibility and low damping. Therefore, new ideas to enhance the damping of lateral vibrations are of interest. In this experimental study, a slender non-metallic cantilever beam is subject to periodic forcing along the beam axis. The force is generated by a wire, which is attached to the free end and runs to the clamped end of the beam, where it is connected to a piezoelectric stack actuator. Operating in an uncontrolled mode, the actuator extends proportionally to an input signal that results in a force according to the total axial stiffness of the structure. By applying a pre-tension to the beam, the axial force at the tip of the beam can be modulated in time by the actuator and the system becomes parametrically excited. For modulation frequencies near non-resonant parametric resonances it is known from theoretical studies that such a system will exhibit increased damping properties. This study presents measurement results on such a system, verifying theoretical predictions and confirming first measurements. It is shown that the attenuation of free vibrations can be increased significantly by the proposed method. While the appropriate frequency must be met within rather narrow limits to achieve best results, the method is relatively insensitive to a distortion of the harmonic input signal and also quite tolerant regarding amplitude fluctuations.