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If the excitation applied to a structure is impulsive rather than harmonic, many modes contribute to the response and it becomes more appropriate to use direct integration methods rather than modal analysis. There are a large number of applications where transient analyses are necessary. Many structures are subject to time varying loads such as impulse, blast, impact & seismic loadings. Transient dynamic analysis determines the time-response history of a structure subjected to a forced displacement function. The structure may behave linearly, or in some cases, friction, plasticity, large deflections or gaps may produce nonlinear behaviour. Once the time response history is known, complete deflection and stress information can be obtained for specific times.

The first step in any dynamic analysis should be the determination of the frequencies and shapes of the natural vibration modes. In a 3-D structure there are three dynamic degrees of freedom (DDOF) for every unrestrained node with non-zero mass and there is potentially a natural vibration mode for each DDOF. Thus, there are usually many potential vibration modes in a typical structure, but usually only a small number of vibration modes with the lowest frequencies that are of interest. In a multi-storey building, for example, it might be only a few in each of two horizontal directions, plus one or two torsional modes that have to be considered.

Frequency & Transient Analysis Differences

While frequency analyses take place in the frequency domain, transient analyses are studies in the time domain. It is always possible to go from the time domain to the frequency domain via a fourier transform. Correspondingly, a change from the frequency domain to the time domain may be achieved by implementing an inverse fourier transform.

Due to mathematical difficulties, solutions in the frequency domain can only be linear in nature. Therefore if the application requires a solution that is a non-linear function of time, then a time domain analysis must be carried out. The solution can subsequently be projected to the frequency domain if required. Frequency analyses can be solved using no boundary conditions, while transient analyses must be fully constrained.