## Experimental Modal Analysis

by Nikolay Donets – Feb. 2, 2012 · 4 min read

Experimental Modal Analysis **EMA** is the study of the dynamic properties of a structure by means of test data. The goal of experimental modal analysis is to determine the modal parameters of a structure. **EMA** requires a forced vibration testing of a structure or usage of impulse hammer to excite vibrations.

Modal parameters are the parameters that define the modal behaviour of a structure. Modal behaviour refers to the vibration pattern of a structure at a particular natural frequency. The modal parameters of a structure include natural frequencies, mode shapes, and damping ratios.

There are two basic methods of experimental modal analysis: the frequency domain method and the time domain method. The frequency domain method, also known as the Fourier transform method, is used to analyse data that is obtained from forced vibration testing. The time domain method, also known as the correlation method, is used to analyse data that is obtained from impact vibration testing.

## Modal Parameters

A structure will vibrate at a certain *natural frequency* when it is subjected to an excitation at that frequency. Natural frequency is the frequency at which a structure will vibrate when it is not subjected to damping.

*Damping* is the dissipation of energy that occurs when a structure is subjected to vibration. The amount of damping in a structure can be represented by the damping ratio.

*Mode shape* is a plot of the amplitude of vibration at each measurement point at a particular natural frequency. A mode shape is a plot of the vibration pattern of a structure at a particular natural frequency.

## Frequency Domain Method

The Frequency Domain Method, also known as the Fourier transform method, is used to analyse data that is obtained from forced vibration testing. Forced vibration testing is performed by exciting the structure with a known force and measuring the response of the structure. The excitation force is applied to the structure at one or more driving points. The response of the structure is measured at one or more response points. The excitation force and the response of the structure are then analysed in the frequency domain to determine the modal parameters of the structure.

A frequency response function is the relationship between the input force and the output response of a structure in the frequency domain. The frequency response function is calculated as the ratio of the Fourier transform of the output response to the Fourier transform of the input force. The excitation force must be applied to the structure at a single driving point or multiple driving points. The frequency and amplitude of the excitation force must be controlled. The response of the structure is measured at one or more response points. The response points can be the same as the driving points, or they can be different.

The frequency response function can be calculated by dividing the Fourier transform of the output response by the Fourier transform of the input force. The frequency response function is calculated for each response point. The natural frequencies of the structure can be determined from the frequency response function by looking for peaks in the magnitude of the frequency response function. The mode shapes of the structure can be determined from the frequency response function by looking at the relative amplitudes of the frequency response function at the natural frequencies. The damping ratio of the structure can be determined from the frequency response function by measuring the width of the peak in the frequency response function at half the maximum value of the peak.

## Time Domain Method

The time domain method, also known as the correlation method, is used to analyse data that is obtained from impact vibration testing. Impact vibration testing is performed by striking the structure with an impulse hammer and measuring the response of the structure. The impulse hammer is used to excite the structure at multiple driving points. The response of the structure is measured at one or more response points. The impulse force and the response of the structure are then analysed in the time domain to determine the modal parameters of the structure.

The impulse force must be applied to the structure at multiple driving points. The force applied by the impulse hammer is measured by a force transducer that is built into the impulse hammer. The response of the structure is measured at one or more response points. The response points can be the same as the driving points, or they can be different.

The impulse force and the response of the structure are analysed in the time domain to determine the modal parameters of the structure. The natural frequencies of the structure can be determined from the response by looking for peaks in the Fourier transform of the response. The mode shapes of the structure can be determined from the response by looking at the relative amplitudes of the response at the natural frequencies. The damping ratio of the structure can be determined from the response by measuring the width of the peak in the Fourier transform of the response at half the maximum value of the peak.