Many experts working in the field of vibration analysis will agree that resonance is a very common cause of excessive machine vibration.

Resonance is the result of an external force vibrating at the same frequency as the natural frequency of a system. Natural frequency is a characteristic of every machine, structure and even animals. Often, resonance can be confused with the natural frequency or critical frequency. If equipment is operating in a state of resonance, the vibration levels will be amplified significantly, which can cause equipment failure and plant downtime. It is, therefore, important that the running speed of equipment be out of the resonance range.

How to identify a resonance frequency

Many techniques can be used to identify and/or confirm a high vibration level caused by a resonance frequency. It is very important to confirm a resonance phenomenon by at least two different types of tests before trying to correct it. We will look at a few techniques commonly used in the industry.

Techniques used to confirm a resonance

Impact test:One of the most commonly used methods for measuring a system’s natural frequency is to strike it with a mass and measure the response. This method is effective because the impact inputs a small amount of force in the equipment over a large frequency range. When performing this technique, it is important to try impacting different locations on the structure since all of a structure’s resonant frequencies will always be measurable by impacting at one location and measuring at the same location. Both drive point and transfer point measurements should be taken when attempting to identify machine resonances.

This type of test must be performed with the equipment off. This way you can easily identify the natural frequencies of the equipment (see Figure 1).

Figure 1. Impact Test, Equipment Off

Impact test using an instrumented hammer:This test is basically the same as a regular impact test, except that an instrumented hammer is used to excite the system. This hammer, equipped with an accelerometer at one end, is used in tandem with the sensor used to measure the vibration. A two-channel vibration analyzer is needed, in which one channel is connected to the instrumented hammer and the other to the vibration sensor.

Using this technique, you can effectively measure the force induced to the system by the instrumented hammer and the response at different frequencies. When the phase shifts by 90 degrees, the frequency at which it occurs is a natural frequency (Figure 2). The advantage in using this method is that it allows you to monitor phase shifts and coherence. With this information, you can create operating deflection shapes to visualize the vibrating body.

Figure 2. Impact Test with Force Hammer

Coast down peak hold:Another method used is to monitor the vibration level using a peak hold function, while shutting down the equipment, as performed normally. The vibration level should drop at a steady rate. If the vibration levels start rising at any time while the equipment is being shut down, the speed at which the amplitudes increase is a possible natural frequency (Figure 3).

Figure 3. Coast Down Peak Hold

Coast down peak phase:Like the coast down peak hold, this test is to be conducted while the equipment is being shut down. By installing a photo tack and a piece of reflective tape on the rotating shaft of the equipment, you can monitor the vibration and its phase. This will allow you to see the amplitude and phase shift at all running speeds of the equipment. If there is no resonance excited by the turning speed, the vibration levels should drop at a steady rate. If the vibration peaks at a certain speed and the phase shifts by 180 degrees, this indicates a natural frequency of the equipment or structure. The actual natural frequency is the frequency situated in the middle of the phase shift (90 degrees) (Figure 4).


Figure 4. Coast Down Peak Phase

Formula for natural frequency

The natural frequency is the frequency of free vibration of a system, in which a system vibrates to dissipate its energy. The natural frequency (ωn) of an equipment, expressed in radian per second, is a function of its stiffness (k) and its mass (m), as shown by the following equation:

If any of these two parameters are altered, the natural frequency will change.

How do you modify a natural frequency?

If we want to modify the natural frequency of a body, we have to either change the stiffness or the mass. Increasing the mass or lowering the stiffness will lower the natural frequency while reducing mass or increasing stiffness will increase natural frequency.

How can we operate critical equipment if we can’t change the natural frequency?

If we cannot change the stiffness or the mass of the equipment, two possible choices are offered to us. One easy solution is to change the operating speed of the equipment by 20 to 30 percent, but this is not usually an option. Another solution is to install a dynamic absorber on the equipment to significantly reduce the vibration levels of the equipment. The dynamic absorber is a spring-mass system that is installed in series with the resonant system to create an out-of-phase exciting force to effectively counteract the initial exciting force.


Resonance is probably one of the five common causes of excessive machine vibration. Identifying a resonance frequency effectively can be challenging. We need to positively identify the natural frequency by performing at least two different tests such as impact test, coast down peak hold, coast down peak phase or impact test using a force hammer.

Once the resonance is confirmed, either change the mass or the stiffness of the equipment to change its natural frequency. If it cannot be accomplished try to change the operating speed of the equipment. If that fails, consider installing a dynamic absorber to counteract the initial exciting force.


Fox, Randy. “Dynamic absorbers for solving resonance problems”.

About the author:
Alain Pellegrino is a predictive maintenance technician for Laurentide Controls Ltd. As the local business partner for Emerson Process Management, Laurentide Controls is the largest supplier of automation solutions in eastern Canada. For more information, visit