Determination of System Damping From the Response Amplitude at Resonance

A method for estimating the damping of a vibratory system from the frequency of resonance and the response amplitude at that resonant peak alone is reviewed and applied to the determination of the system loss or quality factors of uniform, rectangular cantilever bare titanium beams and beams with damping enhancing hard coatings. Using results from experiments with several different nonlinear coating systems vibrating in several modes and temperatures, comparisons are given for the damping measures obtained by this method with those obtained by the traditional method for determining system damping from the bandwidth (BW) of the frequency response functions (FRFs). These comparisons, made for strains of engineering interest (to strains over 1000 ppm), show that the BW method generally leads to inflated measures of system energy dissipation and that the inflation (10-70%) depends generally on the degree of nonlinearity, i.e., the extent to which the system loss factor varies with strain amplitude. While developed for the ideal uniform, rectangular, cantilever beam for which the mode shapes are well known, the method may be applied to more complex geometries through the use of a finite element analysis (FEA).