Tunable Vibration Absorption of a Cantilever Beam Utilizing Fluidic Flexible Matrix Composites

Bonding a fluidic flexible matrix composite (F2MC) tube to a cantilever beam can create a lightly damped tuned vibration absorber. The beam transverse vibration couples with the F2MC tube strain to generate flow into an external accumulator via a flow port. The fluid inertia is analogous to the vibration absorbing mass in a conventional tuned vibration absorber. The large F2MC tube pressure accelerates the fluid so that the developed inertia forces cancel most of the vibration loads. An analytical model is developed based on Euler-Bernoulli beam theory and Lekhnitskii’s solution for anisotropic layered tubes. The analysis results show that the cantilever beam vibration can be reduced by more than 99% by designing the F2MC fiber angle, the tube attachment points, and the flow port geometry.

Vibration Control of Nonlinear Rotating Beam Using Piezoelectric Actuator and Sliding Mode Approach

In this research, we develop a general methodology for the vibration control of nonlinear rotating beam. The dynamic model of a rotating Euler-Bernoulli beam integrated with piezoelectric actuator is formulated. An integral sliding mode control design is proposed for the vibration suppression of the system with nonlinear coupling effects between the hub rotation and the beam transverse vibration. The sliding surface is constructed using part of the system states, and the rotating hub dynamics is treated as the internal dynamics of the system under the condition that the states of the zero dynamics are bounded. The robust stability of the proposed controller is also guaranteed. A series of simulation studies demonstrate that the proposed control method can effectively suppress the beam vibrations induced by the hub rotation and the external disturbance.

Active Parametric Damping of Distributed Parameter Beam Transverse Vibration

An active vibration control for a modified, nonlinear, dynamic, simply supported, Bernoulli-Euler beam is introduced using one of the distributed, time-dependent parameters of the system. The control is carried out by observing the axial velocity of the end point of the beam and applying a modified bang-bang variation of beam tensile stress to control beam transverse stiffness. Numerical simulation of the closed-loop system of partial differential equations demonstrates the effectiveness of the control. Two cases representing initial value problems are given as examples. This active control applied to first mode vibration of an undamped system model yields an asymptotically stable system which loses its total system energy to a level that is 0.26 percent of its initial value in five and one half cycles.