# Vibration analysis

Every device in nature has countless vibrational frequencies and mode shapes, which are called natural frequencies. The calculation of these frequencies and their modes is of particular importance in the vibrations of engineering problems. Its natural frequencies and modes for simple shapes are determined using analytical methods. But for complex shapes, it is only possible to determine it using numerical methods such as the finite element method.

Vibration analysis is divided into two main categories:

• Natural frequency extraction and mode mode
• Forced vibration analysis

## Modal Analysis

The collapse of the Tacoma Bridge is exacerbated by the phenomenon
Using natural frequency analysis, the natural frequencies of the structure are determined. The frequency of an alternating force acting on a structure can be close to one of the natural frequencies of the structure. If this happens, the frequency is excited and the structure begins to vibrate in normal frequency mode. If the excitation frequency is close to the natural frequency of the structure, the resonance or resonance phenomenon occurs. In many cases, the phenomenon of exacerbation is undesirable. Therefore, either the excitation frequency or the natural frequencies of the structure must change.

The collapse of the Tacoma Bridge is exacerbated by the phenomenon

## Forced vibration analysis

In some cases, especially in complex structures, the phenomenon of resonance is inevitable. In these cases, vibration levels must be determined. Forced vibration analysis can be used to calculate the vibrational response of the structure (displacement, velocity, and acceleration) to determine the vibrational frequencies of the structure relative to the excitation frequencies. Stress and displacement due to intensification in the structure can cause injury, fatigue, discomfort to the crew, residents, or passengers. In forced vibration analysis, the excitation forces, their frequencies, and the natural frequencies of the structure must be determined. Determining excitation frequencies is sometimes not easy. For example, the force and frequency of excitation due to wind current around the suspension bridge or fluctuations due to propeller drift force in rough seas can not be easily calculated. On the other hand, in order to obtain the desired results, the damping characteristics of the structure and material must be determined very carefully.