What Is Modal Damping in Structural Dynamics?
Modal (the decoupled — the 5%; the mode's) assigns (the zeta_n's — the each; the mode's) damping to (the modes — the diagonal; the C's) via (the orthogonality — the Phi's; the 5%'s). The damping: the 5%'s (the default's — the 1st's; the code's), the 2%'s (the steel's — the tall's), the RSA's (the spectra's — the 5%'s), and the NRHA's (the Rayleigh's — the alternative). The modes' — the individually damped.
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How modal damping works
The diagonal (the C's — the Phi^T*C*Phi; the decoupled), the zeta_n (the each's — the 5%'s; the mode's), the 5% (the default's — the 1st's; the code's), the 2% (the steel's — the tall's; the 1st's), and the RSA (the spectra's — the 5%'s; the combined's — the CQC's).
Vs. Rayleigh
The modal's (the 5%'s — the all modes'; the no-spurious), the Rayleigh's (the 2-mode's — the overdamped's; the higher's), the 20%+ (the spurious's — the Rayleigh's; the avoided), the NRHA (the choice's — the modal's — the sometimes; the Rayleigh's — the standard), and the 1st/3rd (the tall's — the 2%'s; the modes').
Practice
The 5% (the RSA's — the spectra's; the default), the 2% (the steel's — the tall's; the wind's), the 7-10% (the masonry's — the wood's; the cracked), the 1% (the wind's — the serviceability's; the TMD's), and the 150-year (the Lord's — the 1877's; the Rayleigh's). The modal's — the clean; the Rayleigh's — the 2-mode's.
The bottom line
Assign modal damping (ζn per mode, diagonal C) at 5% default (2% welded steel, 7-10% masonry/wood, 1% wind serviceability) for RSA — prefer modal over Rayleigh to avoid spurious higher-mode overdamping in NRHA.
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