Engineering | Finite Element Analysis | Stress
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Transient Solutions: Modal & Direct
There are usually two approaches one can take when carrying out a transient analysis,
modal solutions or purely direct solutions.
The modal approach involves evaluating
the relevant natural frequencies of a structure first. Once this is carried out,
the response is converted to the time domain and is included in the evaluation of
transient response of the structure. Modal analyses are usually used where there
many natural frequencies within the operation range. It is important to evaluate
the natural frequencies above and below that of the analysis range. This is due to
the fact that, in practice, there is never just one distinct mode of vibration due
to an excitation, but one dominant mode with a range of additional harmonics from
the adjacent upper and lower modes.
Direct solutions are used to evaluate the response
of a structure within a very narrow frequency range of interest, and are usually
used for models that subject to high frequency impulses. The solution is purely transient,
no frequency extraction is carried out first.
The Solution Approach
As a transient load is applied, the solution must follow the response of the structure.
To achieve this, the overall time period being studied is divided into a number of
linear time pieces, each one being referred to as a time step. The successful implementation
of any time domain analysis is dependant on a suitable number of time steps being
selected. If the time step is too large, portions of the response (such as spikes)
could be missed or truncated. On the other hand, if the time step is too small, the
analysis will become excessively long or even prohibitive.
The progression of the
solution from one time step to the next is achieved by implementing time integration
techniques. Despite many packages providing automatic time stepping estimates, the
full response of the structure may not be captured, and manual intervention will
be required. If there is a discontinuity in your automatically time stepped results,
chances are there is a spike in the response that is not being fully captured.
Dynamic Impulse - transient
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