# Frequency Analysis

Every structure has the tendency to vibrate at certain frequencies, called natural or resonant frequencies. Each natural frequency is associated with a certain shape, called mode shape, that the model tends to assume when vibrating at that frequency.

When a structure is properly excited by a dynamic load with a frequency that coincides with one of its natural frequencies, the structure undergoes large displacements and stresses. This phenomenon is known as resonance. For undamped systems, resonance theoretically causes infinite motion. Damping, however, puts a limit on the response of the structures due to resonant loads.

If your design is subjected to dynamic environments, static studies cannot be used to evaluate the response. Frequency studies can help you avoid resonance and design vibration isolation systems. They also form the basis for evaluating the response of linear dynamic systems where the response of a system to a dynamic environment is assumed to be equal to the summation of the contributions of the modes considered in the analysis.

Resonance is desirable in the design of some devices.

A real model has an infinite number of natural frequencies. However, a finite element model has a finite number of natural frequencies that is equal to the number of degrees of freedom considered in the model. Only the first few modes are needed for most purposes.

The natural frequencies and corresponding mode shapes depend on the geometry, material properties, and support conditions. The computation of natural frequencies and mode shapes is known as modal, frequency, and normal mode analysis.

Video: Sample Mode Shapes (animation of the first few modes of a rectangular plate simply supported along its two short edges).

## Effect of Loads on Frequency Analysis

When building the geometry of a model, you usually create it based on the original (undeformed) shape of the model. Some loads, like the structure’s own weight, are always present and can cause considerable effects on the shape of the structure and its modal properties. In many cases, this effect can be ignored because the induced deflections are small.

Loads affect the modal characteristics of a body. In general, compressive loads decrease resonant frequencies and tensile loads increase them. This fact is easily demonstrated by changing the tension on a violin string. The higher the tension, the higher the frequency (tone).

You do not need to define any loads for a frequency study but if you do their effect will be considered.

To include the effect of loading on the resonant frequencies, you must use the Direct Sparse solver. If your Solver option is set to Automatic, the Direct Sparse solver will be used if loads are defined for a frequency study.

## Dynamic Loads

Use linear dynamic studies to compute the response due to dynamic loads and base excitations.

The effect of loads on frequencies and mode shapes is not considered when using linear dynamic studies, as their calculation is based on a stress-free model state. It is recommended to define a Nonlinear Dynamic study instead to account for any possible stress-stiffening or stress-softening effects that can alter the modal characteristics of the model.