Vibration analysis
Vibration can occur in a component or assembly in operation as a result of time-varying loads. Such vibration can cause excessive stresses, potentially up to and including component failure. The vibration may be free (natural frequencies) or forced.
Whether critical vibration arises within the component's operating range can be checked in advance using dynamic finite element analysis. If the vibration behaviour proves excessive, the design can be optimised by changing mass and stiffness. In this way a component can be deliberately detuned to ensure safe operation.
Natural frequency analysis / modal analysis
For components subject to harmonic excitation in operation, knowing their natural frequencies and mode shapes is essential.
A modal analysis determines the component's natural frequencies and mode shapes.
To prevent resonance excitation, the natural frequency must not coincide with the excitation frequency. Depending on the damping, an adequate safety margin must be maintained.
Mode shape of a tank on a steel structure
Frequency response analysis (analysis in the frequency domain)
A frequency response analysis determines the response of a component to sinusoidal excitation, in order to assess its vibration behaviour. This can be used, for example, to determine how a component behaves under unbalance excitation. Unlike modal analysis, frequency response analysis requires a specific excitation (magnitude and direction) to be defined.
The calculated results (e.g. deformation, stress, phase shift) are obtained as a function of the excitation frequency. This type of analysis considers the steady state; the transient start-up is not taken into account.
Transient dynamics (analysis in the time domain)
If an arbitrary, time-varying load signal is to be considered in the simulation, the response of the component or assembly can be simulated by a transient analysis. The results are the response quantities (e.g. acceleration, deformation, stress) as a function of time. Time-transient analyses can become very demanding for long time signals, since the step size depends among other things on the vibrations to be captured.
Seismic simulation / response spectrum analysis
The response spectrum method is used to solve problems economically where a relatively long-lasting, time-varying load is present. A transient analysis would result in extremely long and therefore uneconomical computation times. The response spectrum defines the response of a component to a transient signal in the frequency domain. This method is typically applied to seismic verifications (earthquake simulations), for example.
Random vibration / PSD (power spectral density)
In some fields of application, components and assemblies are exposed to strong vibration, yet the load history over time is not known. Examples of such loads include waves, wind gusts, vibration during a rocket launch, and the loads from various driving routes. A PSD excitation spectrum is derived from a range of measured excitation signals in the time domain. This PSD spectrum is then used as the load in the PSD analysis. The results are probabilistic RMS values (stresses, strains, etc.).
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