Exact Evaluation of Natural Frequency and Damping Ratio from a Frequency Response Curve

Several experimental modal analysis techniques fit resonance peaks to the response curves of a single degree of freedom system in order to identify the natural frequencies and modal damping ratios. The present study identifies a fundamental property of frequency response curves that allows the natural frequency to be identified from a simple characteristic of the curve, independently of the damping ratio. After the natural frequency has been determined, the damping ratio can be computed directly. The fundamental property holds for all values of damping, which eliminates the need to approximate either the natural frequency or damping ratio.