Modal analysis is the process of determining a structure's natural frequencies, mode shapes, and damping ratios — collectively called its modal properties. It is the foundation of dynamic analysis in earthquake engineering and is performed analytically, numerically, or experimentally.
Modal analysis is the study of the dynamic properties of a structure in terms of its natural frequencies, mode shapes, and modal damping ratios. In analytical and numerical modal analysis, these properties are obtained by solving the eigenvalue problem for the structure's mass and stiffness matrices: (K − ω²M)φ = 0. Each eigenvalue (ω²) yields a natural frequency, and each eigenvector (φ) yields the corresponding mode shape. For an N-degree-of-freedom system, this produces N natural frequencies and N mode shapes, ordered from lowest (fundamental) to highest. In practice, only the lowest modes — typically the first 3 to 10 — contribute significantly to the response under earthquake loading, though the number required depends on the structure's regularity and the frequency content of the excitation.
Modal analysis is central to earthquake engineering practice. In response spectrum analysis, the design response spectrum is applied to each significant mode individually, and the modal responses are combined using rules such as SRSS (Square Root of Sum of Squares) or CQC (Complete Quadratic Combination) to estimate the total maximum response. This approach is codified in all major design standards and is the workhorse method for seismic analysis of buildings and bridges. Modal analysis is also essential for understanding phenomena such as resonance, where the dominant frequency of the ground motion matches one of the structure's modal frequencies, producing amplified response. For structures with irregular geometry, large plan or vertical discontinuities, or significant higher-mode contributions, more sophisticated analysis — such as response history analysis with a full suite of ground motions — may be required.
Experimental modal analysis (EMA) is the empirical counterpart to analytical modal analysis, used to validate models and to characterize existing structures. It involves measuring the structural response to a known or unknown input and identifying modal properties from the resulting data. Experimental modal analysis (EMA) uses controlled input (impact hammer, shaker) and measures both input and output, making it suitable for laboratory specimens and small structures. Operational modal analysis (OMA) uses ambient or operational input (wind, traffic, microtremors) and relies only on output measurements, making it suitable for full-scale structures in service. Methods include peak picking, frequency domain decomposition (FDD), stochastic subspace identification (SSI), and eigensystem realization algorithm (ERA). In structural health monitoring, modal analysis is performed continuously to track changes in modal properties over time, providing an early indicator of damage, stiffness degradation, or changing boundary conditions. The same modal properties also feed into model updating, where the finite element model is calibrated to match the identified modal properties, improving its predictive accuracy for future load scenarios.