What Is Complex vs. Proportional Damping?
Damping's two (the models' — the C's): the proportional (the Rayleigh's — the 1877; the diagonal) keeps (the modes' — the real; the decoupled), while the complex (the nonproportional's — the FVD's; the 20%) creates (the modes' — the complex; the coupled). The proportional's — the 5% diagonal; the complex's — the 20% coupled.
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Proportional damping
The Rayleigh (the 1877's — the C=αM+βK; the 2-mode), the modal (the 5%'s — the diagonal; the decoupled), the real (the modes' — the Phi's; the orthogonal), the 5% (the default's — the RSA's; the spectra's), and the 2-5% (the NRHA's — the 1st/2nd's; the anchored).
Complex damping
The nonproportional (the FVD's — the 20%'s; the localized), the complex (the modes' — the Phi's; the coupled), the 20% (the effective's — the Ch. 18's; the damped), the state-space (the 2N's — the formulation; the solved), and the 2-3x (the reduction's — the drift's; the force's).
In practice
The 5% (the RSA's — the proportional's; the spectra's), the 20% (the FVD's — the complex's; the Ch. 18's), the state-space (the 2N's — the NRHA's; the solved), the 2-mode (the Rayleigh's — the 1st/2nd's; the anchored), and the 1877 (the Lord's — the 150-year; the still used). The proportional's — the simple; the complex's — the damped.
The bottom line
Use proportional damping (Rayleigh/modal, 5% default, real decoupled modes) for RSA and undamped structures — switch to complex state-space (2N formulation) for nonproportional 20%+ FVD systems per Ch. 18.
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