Frequency response of beams with passively constrained damping layers and piezo-actuators

We present and review methods of frequency response analysis for cantilevered sandwich beams consisting of aluminum face plates and passively constrained damping layers at the mid-plane. These analysis methods include: (1) progressive wave method, (2) assumed modes method, and (3) finite element method. The progressive wave method accounts for the frequency dependent complex modulus in analyzing the frequency response function. In the assumed made and FEM analyses, the frequency dependent complex modulus is assumed to be a constant over the frequency range of interest (i.e. the first three modes). By selecting the value of complex modulus to nominally correspond to the second modal frequency, the error in predicted natural frequency can be minimized. However, this comes at the cost of increased error in the damping ratio predictions, which are minimized by selecting the value of complex modulus corresponding to the first mode.