A Somewhat Comprehensive Critique of Experimental Modal Analysis

Abstract

Over the past 70 years, the US aerospace community has maintained a standard for verification and validation of experimentally determined, real structural dynamic modes and mathematical models based on mass-weighted orthogonality criteria. This standard fundamentally contradicts observable physical aspects associated with the mechanical behavior of structures. Specifically, (a) energy dissipation (damping) forces are most often concentrated in joints, rather than nearly uniformly distributed throughout the structure; (b) structural modes are mathematically complex, yet often approximately real except when successive modal frequencies are closely spaced; and (c) complex structural modes, while often are approximately real, do not strictly satisfy mass-weighted orthogonality criteria. A bottom-up approach, based on the Simultaneous Frequency Domain Technique (SFD-2018), employs left-hand eigenvectors to (1) isolate individual complex measured modes and (2) guarantee mathematical orthogonality of complex measured modes (completely independent of a theoretical mass matrix and model expectations). In addition, (3) complex modes deduced from virtually all experimental modal analysis techniques are classified in terms of a complex mode index parameter that indicates each mode’s level of “complexity,” and (4) conventional experimental mode orthogonality and experimental-to-theoretical mode cross-orthogonality metrics are adapted via replacement of the transform operator with the Hermitian operator permitting direct employment of complex experimental modes. A welcome surprise, due to review of a specific real experimental mode approximation extends the useful life of established US aerospace community standards for verification and validation of modal test data and correlation and reconciliation of modal test results and mathematical model predictions.