Experimental Modal Testing: Are My Hammer Impact Results Valid?

When performing experimental modal testing of a structure or component using impact (or ping) testing, it is important to consider and verify the validity of any results. A modal analysis is valid if it satisfies several assumptions. Some basic checks include:

linearity,
reciprocity,
time invariance and
observability

A series of checks should be done to gain confidence that the experimental results satisfy the requirements inherent to this type of analysis.

We will deal with each of these checks over a series of articles. This article, Part 1, deals with Linearity.

Experimental Modal Testing – Linearity Check

Modal analysis is a process of calculating the transfer function between the responses and the excitation. The transfer function is generally expressed as
$H=X/F$
where H is the transfer function also called the frequency response function (FRF); X is the measured system response and F is the applied external force.

For a linear system, the larger the applied force to a structure, the stronger the response, therefore the transfer function will not be affected by the level of excitation force that is applied on the structure each time. Therefore, if the linearity assumption is true, the individual FRFs calculated from each time can be averaged to obtain a smoother FRF. In some cases when non-linear behaviour is inevitable but not overwhelm the main linear trend, averaging FRFs can smooth linear estimation.

Typically, the linearity can be checked in two ways:

Checking the consistency of the FRF by varying the excitation force level: For example, we can measure the response at one end of a free-free hanging steel bar with a excitation force applied at the other end of the bar. If the transfer function does not vary with the excitation force applied, the structure response is linear.

Impact, response & transfer function - experimental modal testing — Figure 1: Impact, response & transfer function

However, when the impact force exceeds a certain limit, non-linear modes could be excited and the FRF will be contaminated as shown in the following figures.

experimental modal testing - non-linear mode — Figure 2: Non-linear mode (1)

experimental modal testing - no linear mode - 2 — Figure 3: Non-linear mode (2)

Checking the coherence function during the impact test: The coherence indicates the percentage of energy transferred from the excitation to the response. It can be treated as an indicator of the system linearity. Good coherence is close to one over the frequency band concerned that indicates the vibration response is perfectly correlated to the excitation force. The figure below shows a comparison of a high (top) and low-quality (bottom) coherence graphs. The coherence values are too low over the regions circled and “messy”, the measurement should be repeated. It is worth noting the coherence is normally low at an anti-resonances.

coherence - experimental modal testing — Figure 4: Coherence

Strong non-linearities in the system can cause distortions in the FRFs that shall be avoided in impact testing. Many reasons can cause the non-linear behaviour, for example:

Excess impact force can excite non-linear modes of the structure and contaminate the transfer function matrix.
Transfer functions calculated often shows poor linearity when performing impact test on a highly damping complicated coupled structure.
Improper supporting method will introduce non-related system coupling issues.

Watch this space for the next article in this series on experimental modal testing which will describe reciprocity.

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Dr Cindy (Xin) Wang

Applications Engineer at Prosig

Cindy has a BSc from the Dept of Jet Propulsion at Beijing University of Aeronautics and Astronautics, a Masters from the University of Sheffield in Mechanical Engineering and an MPhil/PhD from the University of Southampton for her thesis “Computational aeroacoustics of slat track system”. Cindy has extensive experience working in Automotive and joined Prosig in 2019 as an Applications Engineer.