The measurement of the loss factors of beams and plates with constrained and unconstrained damping layers: A critical assessment

Methods of measuring the loss factors of heavily damped beams and plates damped by uniform layers of visco-elastic damping are reviewed and compared. Deducing loss factors from measured spatial decay rates of free flexural waves in long beams is shown to be valid only for wave motion governed by the fourth-order flexural wave equation, so the method can only be used for unconstrained layer configurations. The usual approximation made in this method limits its accuracy and is examined. The flexural wave equation for three-layered sandwich beams and plates with constrained damping layers is of sixth order, so the spatial decay rate method is inapplicable for deducing loss factors. This is shown by both analysis and computer experiment. Reliable methods of damping measurement on finite damped sandwich beams are then investigated by computer experiment. Frequency-response functions for three-layered sandwich beams are computed for free–free and encastré beams, centrally excited. Loss factors of the fundamental symmetric modes are deduced from this computed response data as though it were experimental data. They are deduced by established methods such as the ‘half-power-point’ method, detailed analysis of Nyquist diagrams and the energy input method. Most of the deduced loss factors agree closely with the loss factors of the theoretical damped normal modes.