Complex Exponential Method for Modal Parameter Identification

The Complex Exponential Method identifies modal parameters by representing free vibration responses or impulse response functions as sums of complex exponential terms, using linear estimation techniques. Based on modal superposition principles from vibration differential equations, it establishes relationships between dynamic responses and modal parameters. By fitting impulse response data, complete modal parameters (frequency, damping, mode shapes) can be extracted with excellent fitting accuracy. The core methodology involves constructing Prony polynomials whose zeros correspond to Z-transform factors containing frequency information, transforming parameter identification into solving polynomial coefficients. This approach provides efficient numerical implementation for experimental modal analysis.