In linear static analysis, the loads are applied gradually and slowly until they reach their full magnitude. After reaching their full magnitude, the loads remain constant (time-invariant). The accelerations and velocities of the excited system are negligible, therefore, no inertial and damping forces are considered in the formulation:

When loads applied vary with time, inertial and damping effects cannot be ignored, static studies do not give accurate results. Linear dynamic studies use natural frequencies and mode shapes to evaluate the response of structures to dynamic loading environments. You can define:

**Modal time history**studies to define loads and evaluate response as functions of time.

A baseball bat undergoes a shock load when it hits the ball. To understand complete response in the bat this shock wave needs to be analyzed. Simply applying a static load will lead to over designing the bat and make it very heavy

**Harmonic**studies to define loads as functions of frequency and evaluate the peak response at various operating frequencies.

**Random vibration**studies to define random loads in terms of power spectral densities and evaluate the response in terms of the overall root mean square values or power spectral densities at various frequencies. Use a random vibration study to calculate the response due to non-deterministic loads. Examples of non-deterministic loads include:- Loads generated on a wheel of a car traveling on a rough road
- base accelerations generated by earthquakes
- pressure generated by air turbulence
- Pressure from sea waves or strong wind

In a random vibration study, loads ( as the image above) are described statistically by power spectral density functions. The solution of random vibration problems is formulated in the frequency domain. After running the study, you can plot root-mean-square (RMS) values, or psd results of stresses, displacements, velocities, etc. at a specific frequency or graph results at specific locations versus frequency values.

**Response Spectrum**studies to estimate peak responses over time for a system subjected to a particular base motion descibed in terms of a design spectrum.In a response spectrum analysis, the results of a modal analysis are used in terms of a known spectrum to calculate displacements and stresses in the model. For each mode, a response is read from a design spectrum based on the modal frequency and a given damping ratio. All modal responses are then combined to provide an estimate of the total response of the structure.

Rajat Trehan

Product Manager

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