Time-history analysis provides for linear or nonlinear evaluation of dynamic structural response under loading which may vary according to the specified time function. Dynamic equilibrium equations, given by K u(t) + C ^d/_dt u(t) + M d²/_dt u(t) = r(t), are solved using either modal or direct-integration methods. Initial conditions may be set by continuing the structural state from the end of the previous analysis. Additional notes include:

• Step Size – Direct-integration methods are sensitive to time-step size, which should be decreased until results are not affected.

• HHT Value – A slightly negative Hilber-Hughes-Taylor alpha value is also advised to damp out higher frequency modes, and to encourage convergence of nonlinear direct-integration solutions.

• Nonlinearity – Material and geometric nonlinearity, including P-delta and large-displacement effects, may be simulated during nonlinear direct-integration time-history analysis.

• Links – Link objects capture nonlinear behavior during modal (FNA) applications.

Related Content

Articles

Tutorials

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  Time-history analysis first steps
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  Vibrating-machinery steel skid on piles

Test Problems

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  Human-induced vibrations
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  Multi-pendulum model (Newton's cradle)
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  Steady-state vs. time-history analysis

See Also

• Multi-support excitation article