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### Modal dynamic analysis

In a modal dynamic analysis, triggered by the *MODAL DYNAMIC key word, the response of the structure to dynamic loading is assumed to be a linear combination of the lowest eigenmodes. These eigenmodes are recovered from a file "problem.eig", where "problem" stands for the name of the structure. These eigenmodes must have been determined in a previous step, either in the same input deck, or in an input deck run previously. The dynamic loading can be defined as a piecewise linear function by means of the *AMPLITUDE key word. The displacement boundary conditions (only zero displacement boundary conditions are allowed) in a modal dynamic analysis should be the same as those used in the determination of the eigenmodes. Nonzero displacement boundary conditions, temperature loading or residual stresses are not allowed. If such loading arises, the direct integration dynamics procedure should be used.

Damping can be included by means of the *MODAL DAMPING key card. The damping model provided in CalculiX is the Rayleigh damping, which assumes the damping matrix to be a linear combination of the problem's stiffness matrix and mass matrix. This splits the problem according to its eigenmodes, and leads to ordinary differential equations. The results are exact for piecewise linear loading, apart from the inaccuracy due to the finite number of eigenmodes.

Next: Direct integration dynamic analysis Up: Types of analysis Previous: Buckling analysis Contents