Bending and torsional vibration control of composite beams through intelligent constrained-layer damping treatments

This paper is to develop a mathematical model to predict bending, twisting, and axial vibration response of a composite beam with intelligent constrained layer (ICL) or active constrained layer (ACL) damping treatments. In addition, preliminary experiments are conducted on composite beams to evaluate this new technique. The ICL composite beam model is obtained by integrating the existing ICL composite plate model proposed by Shen. When the plate width (along the x-axis) is much smaller than the plate length (along the y-axis), integration of the ICL composite plate equations and linearization of displacement fields with respect to x leads to a set of equations that couples bending, tosional, and axial vibrations of a composite beam. The equations of motion and associated boundary conditions are normalized and rearranged in a state-space matrix form, and the vibration response is predicted through the distributed transfer function method developed by Yang and Tan. A numerical example is illustrated on a composite beam with bending-torsion coupling stiffness. Numerical results show that ICL damping treatments may or may not reduce coupled bending and torsional vibrations of a composite beam simultaneously. When the deflection is fed back to actuate the ICL damping treatment, a sensitivity analysis shows that only those vibration modes with significant bending response are suppressed simultaneously with their torsional components. In the preliminary experiments, two different ICL setups are tested on a composite beam without bending-torsion coupling. Damping performance of both ICL setups agrees qualitatively with existing mathematical models and experimental results obtained from other researchers. The damping performance, however, is not optimized due to the availability of materials and their dimensions in the laboratory. An optimization strategy needs to be developed to facilitate design of ACL damping treatments with maximized damping performance.