What is resonance?

Understanding resonance is essential for solving problems of increased vibration

Resonance is a condition that can occur in mechanical structures and can be described as sensitivity to a certain vibration frequency. Resonance occurs when a natural frequency is at or close to a forcing frequency, such as rotor speed.

For machinery—such as pumps, turbines and electric motors—resonance can amplify the small vibratory forces from machine operation, and severe vibration levels can result.

Such problems often develop after a speed change has been implemented, as with retrofitting a machine with an adjustable-speed drive (ASD) or operating a 50-hertz motor on 60 hertz of power.

The solution to these problems frequently depends on distinguishing between structural resonance and a rotor critical speed.

Structural resonance refers to excessive vibrations of non-rotating components, usually machine components or supporting structures.

Rotor critical speed refers to a condition in which the speed of the rotating element of the machine matches the rotor’s natural frequency. 

Structural Resonance or Rotor Critical Speed?

Structural resonance is the more common resonant condition because of the complex design of the casing and supporting members. Most often the structure supporting a machine or a non-rotating machine component is resonant at or near the rotating speed of the machine.

Even slight vibratory forces from residual unbalance and misalignment effects of the machine can excite the resonant base structure, resulting in severe vibration. A good example of structural resonance is the reed frequency vibration that often occurs with vertical turbine pumps that have a motor mounted on top of the discharge elbow. The machine components can also be resonant.

There are many examples of two-pole electric motors where a resonant end bracket caused very high axial vibration at 1 x rpm or 2 x rpm. 

A rotor critical speed exists when the resonant component is the rotating element of the machine. This is common with centrifugal pumps; gas and steam turbines; and large, two-pole electric motors.

While the result is similar to structural resonance (high vibration when a certain operating speed is reached), rotor critical speed is a more complex phenomenon because of speed sensitive components, such as bearings.

When the operating speed reaches the resonant frequency of the rotating element, the rotating element distorts, and the vibratory forces increase significantly. 

It is important to properly distinguish between structural resonance and rotor critical speed. The term “critical speed” (without the word “rotor”) is somewhat ambiguous.

Technically, a critical speed could be either a structural resonance or a rotor critical speed. For the sake of clarity it is best to avoid using that term.

The simple term “resonance” can be applied to both conditions to avoid confusion. 

The Characteristics of Resonance 

As described above, the most notable characteristic of resonance is increased vibration when a certain operating speed is reached.

Also, as the operating speed is increased beyond the resonant frequency, the vibration amplitude will decrease somewhat. The Bode plot in Figure 1 shows the operating speed versus the amplitude.

For the sake of illustration, assume that the exciting force is residual unbalance of the rotor at the rotating speed. 

The formula for calculating the natural frequency is:

What Is Resonance?

Where “K” is the stiffness of the resonant structure or component, and “W” is the weight (mass). Note that at the core of this formula is: 

What Is Resonance?

Increased stiffness will, therefore, raise the natural frequency, and increased mass will lower it. That is logical since stiffness creates a force that is always directed against motion, while mass has inertia, which is a force always directed with motion. Resonance is what happens when these two opposing forces are equal. They cancel each other out, allowing vibration to increase.

What Is Resonance?
Figure 1. Bode plot of resonance

The Damping Factor 

A third force, damping, is at work throughout the speed range. Damping absorbs vibratory energy, converting it to heat. In doing so, damping reduces the maximum amplitude of the vibration at resonance and increases the width of the amplification zone (see Figure 2). A common example of damping is shock absorbers on a vehicle.

Machines with sleeve bearings may have significant damping that can even mask critical speeds. On machinery bases, concrete and grouting add significant damping to a base structure.

These forces (stiffness, mass and damping) determine the characteristics of resonance and are important to the distinction between structural resonance and rotor critical speeds. 

What Is Resonance?
Figure 2. The effect of damping on resonance

With structural resonance, the machine operates close to a resonant frequency. It is most noticeable when damping is low, since high vibration amplitude results. Two rigid modes can be described as bouncing and rocking.

Solutions include changing the resonant frequency to move it away from the operating speed by modifying the stiffness or mass and increasing damping to directly reduce the amplitude. (The different methods for implementing these corrective measures are topics for another article.

The objective of this article is a comparison to rotor critical speeds.) 

With a rotor critical speed, the problem is different. First, the stiffness, mass and damping of rotors mounted on rolling element bearings can almost never be effectively changed, and damping is typically very low. (Note: Mounted rotor natural frequencies of large journal bearing machines typically can be changed to some degree by modifying the bearing dynamics.

) Second, no rotor is ever intentionally designed to have a critical speed close to its operating speed. The problem in this case is not that the operating speed is close to resonance, but that, at the rotor critical speed, the rotor distorts and non-linear effects cause excessive vibration. At that point, it becomes a flexible rotor rather than a rigid rotor.

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A rigid rotor operates below the first rotor critical speed and may have numerous unbalance forces distributed along its axis. The sum of these unbalance forces can be corrected in any two planes with common, two-plane dynamic balancing methods.

In these rigid modes, the rotor may flex slightly, but the motions at the bearings accurately represent the unbalance condition.

However, once the rotor becomes flexible, above the first rotor critical speed, the distribution of unbalance forces will distort the rotor, causing an unbalanced condition that was not present in the rigid modes. This flexible mode unbalance causes increased vibration that persists at higher speeds. 

With structural resonance, the force is constant while the vibratory response of the structure changes with speed. With a rotor critical speed, the force changes as the rotor distorts to conform to unbalance forces distributed along the axis of the rotor.

The solution to rotor critical speed is to eliminate the unbalance forces in the planes along the axis of the rotor.

Usually, it is not possible to detect where the unbalance forces are with the rotor in the rigid mode, so the rotor must be operated above the rotor critical speed (in the flexible mode) to detect the effects of the unbalance.

Bending Modes 

As the speed of a rotor increases, it will go through a series of bending modes: first bending mode, second bending mode, third bending mode and so forth (see Figure 3).

What Is Resonance?
Figure 3. Examples of a series of bending modes

Rotors for multistage pumps and gas and steam turbines may operate above the first or second rotor critical speed, and generators sometimes operate above the third rotor critical speed. 

Rotors for large, two-pole electric motors normally may operate above the first rotor critical speed but seldom above the second. Rotors that are designed for such flexible rotor operation have provisions for additional balancing planes to accommodate dynamic balancing procedures that eliminate the residual unbalance forces that cause flexible rotor distortion. 

These dynamic balancing procedures may require that the rotor spin at operating speed, which can only be done safely with specially designed balancing machines in a spin pit. Alternatively, the individual components of flexible rotors, such as impellers, can be balanced before assembly. 

Understanding the difference between structural resonance and rotor critical speeds will help clarify the discussion for maintenance and service personnel, especially when the topic is multistage pumps, turbines, or large, two-pole motors. 

Resonance – Definition, Examples & Resonant Frequency With Formula

We hear the word “resonance” used a lot in physics, but let us take a second to ask “What is Resonance?” In order to explain the word, we first need to be thorough with the following terms:

  • PeriodThe amount of time it takes to complete one cycle.
  • Frequency – The number of cycles in one second is the frequency of oscillation.

Now that we have briefed you with the Period and Frequency, let us understand resonance in the next section.

What is Resonance?

Resonance occurs when a material oscillates at a high amplitude at a specific frequency. We call this frequency resonant frequency. The dictionary defines resonance as,

“the state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency of the stimulus is the same, or nearly the same, as the natural vibration frequency of the system.”

Physics defines Resonance as

A phenomenon in which an external force or a vibrating system forces another system around it to vibrate with greater amplitude at a specified frequency of operation.

Some Examples of Resonance

Below we have listed examples of resonance that we can witness in our daily lives:

    The best examples of resonance can be observed in various musical instruments around us. Whenever any person hits, strikes, strums, drums or tweaks any musical instrument, the instrument is set into oscillation or vibration at the natural frequency of vibration of the instrument.

    A unique standing wave pattern defines each frequency of vibration as a specific instrument. These natural frequencies of a musical instrument are known widely as the harmonics of the specified instrument.

    If a second interconnected object or instrument vibrates or oscillates at that specified frequency then the first object can be forced to vibrate at a frequency higher than its natural harmonic frequency. This phenomenon is known as resonance i.e.

    one object vibrating or oscillating at the natural frequency of another object forces the other object to vibrate at a frequency higher than its natural frequency.

  1. Swing
  2. One of the familiar examples of resonance is the swing. It is common knowledge that the swing moves forward and backwards when pushed. If a series of regular pushes are given to the swing, its motion can be built. The person pushing the swing has to sync with the timing of the swing.

    This results in the motion of the swing to have increased amplitude so as to reach higher. Once when the swing reaches its natural frequency of oscillation, a gentle push to the swing helps to maintain its amplitude due to resonance.

    But, if the push given is irregular, the swing will hardly vibrate, and this out-of-sync motion will never lead to resonance, and the swing will not go higher.

  3. Bridge
  4. Group of soldiers marching on the bridge are asked to break their steps very often because their rhythmic marching can set extreme vibrations at the bridge’s natural frequency.

    The bridge can break apart if the synchronized footsteps resonate with the natural frequency of the bridge.

    One of the examples of the above is the Tacoma Bridge Collapse, where the frequency of the air matched with the frequency of the bridge leading to its destruction.

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To learn more about other related concepts of resonance, below are the links:

  • Sharpness Of Resonance
  • Free Forced And Damped Oscillations

How to Calculate Resonant Frequency?

A resonant frequency is the natural vibrating frequency of an object and is usually denoted as f with a subscript zero (f0). Resonance is witnessed in objects that is in equilibrium with acting forces and could keep vibrating for a long time under perfect conditions.

To find the resonant frequency of a single continuous wave, we use the formula,


  • v is the wave velocity
  • λ is the distance of the wavelength

Different Types of Resonance

There are many types of resonance, and they are:

Mechanical Resonance

Mechanical resonance can be defined as the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system’s natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies.The resonant frequency of a spring is calculated using the given formula:

(f_{0} = (frac{1}{2pi } imes sqrt{frac{k}{m}}))


  • m is the mass of the spring
  • k is the spring constant

Acoustic Resonance

Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration.

Acoustic resonance is an important consideration for instrument builders as most acoustic instruments such as the length of tube in a flute, the strings and body of a violin and the shape of a drum membrane use resonators. Acoustic resonance is also important for hearing.

Electrical Resonance

What Is Resonance?

Resonance: Definition & Transmission of Waves – Video & Lesson Transcript | Study.com

How do people make beautiful music with wine glasses? How do you break a wine glass by singing loudly in front of it? Sound waves allow us to do some pretty neat things when we know how to use them. Light waves, too, interact in special ways with the objects around them.

The behavior of sound and light waves explains why we hear sounds from musical instruments and why we see color and objects. A trumpet increases the amplitude of a sound wave. A colored object increases the amplitude of a light wave.

These changes in amplitude are caused by an important principle called resonance. In this lesson, we'll talk about resonance and how it affects the transmission of sound and light.

Resonant Frequency

We already know that waves originate from vibrations. Sound waves come from mechanical vibrations in solids, liquids, and gases. Light waves come from the vibration of charged particles.

Objects, charged particles, and mechanical systems usually have a certain frequency at which they tend to vibrate. This is called their resonant frequency, or their natural frequency.

Some objects have two or more resonant frequencies.

You know when you drive on a bumpy road and your car begins to bounce up and down? Your car is oscillating at its resonant frequency; or really, the resonant frequency of the shock absorbers.

You may notice that when you're riding in a bus, the bouncing frequency is a little bit slower. That's because the bus's shock absorbers have a lower resonant frequency.

When a sound or light wave strikes an object, it is already vibrating at some particular frequency. If that frequency happens to match the resonant frequency of the object it's hitting, then you'll get what's called resonance. Resonance occurs when the amplitude of an object's oscillations are increased by the matching vibrations of another object.

This relationship is difficult to imagine without an example. So, let's explore the subject of resonance further in the context of light waves.

Transmission and Resonance of Light Waves

What Is Resonance?

We hear the word used a lot, but what is resonance? First, in order to explain we have to explain the terms we will use.

  • A period is the amount of time it takes to complete one cycle
  • The number of cycles in one second is the frequency of an oscillation.
  • Frequency is measured in Hertz, named after the 19th-century German physicist Heinrich Rudolf Hertz
  • One Hertz is equal to one cycle per second.

A resonance occurs when a structure or material naturally oscillates at a high amplitude at a specific frequency. This frequency is known as a structural resonant frequency. Typically a structure will have many resonant frequencies.

A dictionary definition of resonance gives us –

“the state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency of the stimulus is the same, or nearly the same, as the natural vibration frequency of the system.”

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When the damping in a structure is small, the resonant frequencies are approximately equal to the natural frequencies of the structure, which are the frequencies of free vibrations of the molecules of the material itself.

Furthermore, an individual resonance is the condition when a natural frequency of a structure or material and the frequency at which it is being excited are equal or very nearly equal. This results in the structure or material vibrating strongly and is the classical resonance state. This resonance state can often lead to unexpected behaviour of the structure or material.

The lowest natural frequency, often called the fundamental frequency, is related to the material of which the structure is made. The greater the mass or density of the material the lower the fundamental frequency of vibration.

The natural frequency is also related to the speed that a waveform can propagate through the structure. This is determined largely by the molecular make up of the material. Gas, for example, has many free molecules with high kinetic energy, so the waveform can move quickly through the material.

A solid has far fewer free molecules and is much denser, therefore the waveform moves more slowly.


Resonance, An object free to vibrate tends to do so at a specific rate called the object's natural, or resonant, frequency. (This frequency depends on the size, shape, and composition of the object.

) Such an object will vibrate strongly when it is subjected to vibrations or regular impulses at a frequency equal to or very close to its natural frequency. This phenomenon is called resonance. Through resonance, a comparatively weak vibration in one object can cause a strong vibration in another.

By analogy, the term resonance is also used to describe the phenomenon by which an oscillating electric current is strengthened by an electric signal of a specific frequency.

An example of resonance is provided by a motor that causes vibration in a piece of furniture in another part of the same house. These vibrations occur because the furniture has a natural frequency equal to the frequency of the vibrations set up by the motor.

The furniture is said to be in resonance with the motor. Resonance can also be observed in an automobile when a certain partan ash tray, for examplevibrates when the car is traveling at a certain speed.

The ash tray is in resonance with the vibrations of the engine at that speed.

Mechanical resonance can produce vibrations strong enough to destroy the object in which they occur.

For example, soldiers marching over a bridge can set up extreme vibrations at the bridge's natural frequency and shake it apart. For this reason soldiers break step to cross a bridge.

In 1940 wind gusts at Puget Sound Narrows, Tacoma, Washington, caused a suspension bridge to vibrate at its natural frequency and the bridge collapsed.

In music, resonance is used to increase the intensity (loudness) of a sound.

The comparatively weak vibrations produced at the end of an organ pipe, for example, cause a column of air in the pipe to vibrate in resonance, thus greatly increasing the loud-ness of the sound.

This principle also applies to the human voice, in which the vibrations of the vocal cords are reinforced by resonant vibrations in the oral and nasal passages.

Electrical resonance is used to tune radios and television sets. Tuning consists of establishing a circuit with a resonant frequency equal to the assigned frequency of the desired station.

What is Resonant Frequency?

In this Quartz Resonators series video, we answer the question “What is Resonant Frequency?”

Resonant frequency is the oscillation of a system at its natural or unforced resonance.

Resonance occurs when a system is able to store and easily transfer energy between different storage modes, such as Kinetic energy or Potential energy as you would find with a simple pendulum.

Most systems have one resonant frequency and multiple harmonic frequencies that get progressively lower in amplitude as they move away from the center.

In the case of a quartz resonators, the Resonant Frequency is the desired frequency of oscillation that you want to achieve.

There are two methods of using Resonant Frequencies to derive a clock. Crystals operating at or below 50 MHz are referred to as resonating at their fundamental or natural frequency. Shown in the graph here in red, when producing clocks that need to generate frequencies above 50 MHz you are taking advantage of harmonic frequencies. Harmonics are multiples of the fundamental frequency.

Shown in the graph as 2nd, 3rd, 4th and 5th harmonic. As an example, a third harmonic would be three times the original frequency. In this case, the fundamental frequency of 110 hz x 3 = 330 hz.

You can isolate and amplify the harmonics to give you a higher cleaner frequency than you would if you multiplied the original frequency.

This opens up the available frequency spectrum to quartz based resonators.

Watch the above video to learn more about Resonant Frequency then click on the button below to start searching for the exact part you need!

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