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*Modal analysis*, or the mode-superposition method, is a [linear dynamic-response|kb:Nonlinear] procedure wherewhich evaluates and superimposes free-vibration mode shapes are evaluated and superimposed to characterize structuraldisplacement displacementpatterns. Mode shapes describe the configurations into which a structure will naturally displace. LateralTypically, lateral displacement patterns are generally of primary concern. Mode shapes characterizedof by low-order mathematical expressionsexpression tend to provide the greatest contribution to structural response. As orders increase, mode shapes contribute less. Further, high-order modesand are predicted less reliably. ThereforeIt it is reasonable to truncate analysis oncewhen sufficientlythe accurate response is achieved. It is typical for only a few number of mode shapes to sufficiently describe deflected configuration.

Modal analysis may be conducted for single\- or multi-degree-of-freedom (MDOF) systems. is sufficient.

A structure with NDOF will have N corresponding mode shapes. Each mode shape is an independent and normalized displacement pattern which may be amplified and superimposed with the series of mode shapes to indicate structural behavior. The modal superposition of a three-translational-DOF cantilever-column system iscreate a resultant displacement pattern, as shown in Figure 1:

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!Mode shapes.png|align=center,border=1,width=600pxpxpxpxpxpxpxpx600px!

{center-text}Figure 1 - Resultant displacement and modal components{center-text}

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This visual indicates how
modal
contributions sum to create a resultant displacement pattern. [Numerical evaluation|Numerical-evaluation summary] proceeds by reducing the equations of motion (N simultaneous differential equations coupled by full mass and stiffness matrices) to a much smaller set of uncoupled second order differential equations (N independent normal-coordinate equations). This reduction is enabled by the The orthogonality of mode-shape relations. enables this reduction.


{list-of-resources2:label=modal-analysis|drafts-root=Modal analysis drafts}