Effective modal mass and modal participation factors provide a quantitative basis for identifying dynamically significant vibration modes and for guiding modal truncation in structural dynamic analyses. This paper presents a unified formulation for both base-excited systems and grounded systems subjected to externally applied forces.
For base excitation, modal participation is governed by rigid-body consistency through influence vectors, whereas for applied-force excitation it depends on the spatial correlation between mode shapes and the force distribution matrix. Clear definitions are given using mass-normalized eigenvectors, along with practical guidelines for selecting the number of modes based on effective mass, frequency range, and convergence. Worked examples are provided for lumped-parameter systems, isolated components, continuous beams and rods, and finite-element models, demonstrating practical application in structural dynamics, NVH, seismic, and vibration qualification problems.
See also: Natural Frequencies of Bernoulli-Euler Beams
– Tom Irvine
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