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A structure with N degrees of freedom will have N corresponding mode shapes. Each mode shape is an independent and normalized displacement pattern which may be amplified and superimposed to create a resultant displacement pattern, as shown in Figure 1:

Figure 1 - Resultant displacement and modal components

Numerical evaluation 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). The orthogonality of mode-shape relations enables this reduction.

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