In design validation, modal analysis helps to identify a structure’s response to an input. A complex response is divided into a set of simple mode shapes, each with individual parameters that describe the structure’s output to a transient event. The overall structural response helps engineers to determine the natural vibration frequencies and validate the structure’s design.

#### Why Is This Important?

Modal analysis is necessary for the construction of complex structures. Engineers must understand the natural vibration frequencies of a system to make sure they do not coincide with excitation frequencies. If an external vibration matches a structure’s natural vibration, resonance will occur. If unaccounted for, the natural vibration will be amplified and can result in structural fatigue or damage.

If an external force excites a structure’s natural frequency, a structure can be modified to shift the natural frequency. To do so, an engineer may add an element to the structure to adjust the stiffness or mass or change the material to adjust the damping. Engineers can also use modal analysis for monitoring post-production to determine if there was a change or shift due to fatigue or other potential failure mechanisms.

### Modal Analysis Basics

When a structure is excited at its natural frequency, the resulting vibration creates different shapes (Figure 1). These mode shapes help to describe the vibration generated by the structure.

However, the vibration of complex structures generates a combination of many mode shapes. They may have multiple resonances that interact and then complement or negate one another. To simplify the analysis, the structure is parsed into a set of single-degree-of-freedom (SDOF) substructures. The mode shapes and corresponding parameters of the substructures are identified and then combined to describe the entire structure.

### Modal Test Setup

Modal analysis can be experimental or operational. Engineers most often use experimental analysis where a mechanical device is used to excite the structure, and the response is recorded. Operational analysis is more common for long-term observation.

A modal test setup includes a device to generate the excitation, transducer(s), and data recording hardware. The structure is subject to an impact, the transducers attached to the structure record the response, and the output signal is sent to a dynamic signal analyzer such as the ObserVR1000.

#### Impact Hammer Tool

The ObserVIEW Modal Testing module is compatible with a modal impact hammer for excitation. An impact hammer is a measurement tool that produces short-duration excitation upon impact with a structure. The ObserVR1000 records the impulse via the hammer’s force sensor and the structure’s output via the response accelerometers.

When using an impact hammer, the user can capture data using the roving hammer or roving accelerometer method. In modal testing, the term “roving” refers to the device being moved during the test. With the roving hammer method, the accelerometer stays in place and the hammer impacts the structure at different points. Alternatively, with the roving accelerometer method, the accelerometer is moved to different points and the hammer impacts the structure at the same location.

The excitation setup must be correct for accurate data/results as it is used as the reference measurement for later calculations. The ideal impact is rapid so that all modes of vibration are excited with equal energy. A hammer cannot strike for an infinitely brief duration but has a known contact time. A longer contact time equates to a smaller range of bandwidth.

Most modal hammers include a variety of tips. A softer tip will result in a smaller bandwidth of frequencies excited; a harder tip will excite a wider bandwidth of frequencies. A softer tip is easier to use and therefore results in fewer double hits.

A double hit occurs when there are multiple impulses after one hit due to structure rebound. The ObserVIEW software employs automatic double-hit detection. If there is a second peak in the input that is a certain percentage of the main peak value, it is considered a double hit and rejected automatically. The user defines the percentage value per their own requirements.

#### DOF in Modal Testing

During experimental modal analysis, a structure is excited at pre-determined points called degrees-of-freedom (DOF). It is important to note that the use of DOF in modal testing is not the same as DOF in other vibration analysis processes such as the power spectral density. In modal testing, the DOF value indicates a contact point on the structure in reference to the transducer. Figure 2 displays a basic structure labeled with contact points 1 through 9, where the transducer is positioned on the value of 5. The DOF is defined by two points: the contact point and the location of the transducer (1:5, 2:5, 3:5, etc.).

The impact hammer is used to strike each DOF location a defined number of times. The software accepts or rejects each hit until the pre-determined number of hits is reached. Then, the software averages the response for each DOF to generate the individual frequency response functions.

#### Adjusting the Response

The response signal is displayed in an exponential window. If the signal has low damping, it will fade out slowly and can introduce noise at low amplitudes as a result. In the force-exponential window, the length of the response can be adjusted to reduce potential noise after the impact. To do so, the noise level is defined to determine the window length. Defining the response length also reduces measurement time.

### Transfer Function

Once the data are acquired, the time response of the structure can be converted to the frequency domain by using a Fourier transform. The frequency response of all the modes of the system is known as the transfer function (also known as the frequency response function).

The transfer function is calculated from the input signal and its corresponding output. It operates in the frequency domain, and the fast Fourier transform is employed to move from the time to the frequency domain. For a linear and time-invariant system, the transfer function describes the ratio of the two signals over a defined frequency range.

The resulting value represents the magnitude and phase response over the defined frequency range. The transfer function is used to identify the frequencies most sensitive to excitation. These dominant frequencies are used as the individual modes of the structure.

The coherence plot can be used to validate the transfer function graph. Coherence is used as a measure of confidence that a peak observed in a transfer function is a resonant frequency of the device under test and not a spike due to measurement noise. Learn more about coherence mathematics.

### Modal Testing in ObserVIEW

In ObserVIEW, the Modal Testing software collects a set number of responses from each DOF. The average response is calculated for each DOF to generate a smooth transfer function or FRF. From there, the collection of FRFs can be exported to a modal analysis software such as MEscope.

Modal testing is the central feature of the ObserVIEW 2021.1 software release. Along with the ObserVR1000, ObserVIEW can perform dynamic signal analysis, which is essential to modal analysis.

ObserVIEW reads RPC^{®} and RSP time waveform files and supports pasted traces. Organized FRF data are exported to a UFF or another modal data format.

With Modal Testing in ObserVIEW, the user can:

- Manage table of hits per location and review hits
- Average multiple data recordings
- Calculate decay rate from transient ring-down events
- Manage the recording channel using a large, interactive display
- View transfer function as a Nyquist plot
- And more!

To learn more about the features of Modal Testing in ObserVIEW, please visit the software page.