MECHANICAL RESONANCE: A QUALITATIVE EXPLANATION

The concept of Mechanical Resonance is fundamental when we speak about engineering, especially in the field of structures and mechanics. It's a phenomenon regarding the dynamic behaviour of a system (whatever you can think about). 

What do we mean by "dynamic behaviour"? Simply, dynamic is what moves, the contrary of static, that is, standing, not moving. From a mathematical and physical point of view, a dynamic phenomenon changes during time, i.e, is described by equations in which time is a variable; instead, a static phenomenon doesn’t depend on time, is described by equations in which time doesn’t appear as a variable. If we take some pictures of a static phenomenon during the time, the pictures are all the same, nothing changed during the time.

In reality, every system, although it seems to be static, it moves. Let consider, for example, a house: from a macroscopic point of view, a house is static, but in reality, its structure is continuously subjected to vibrations, generated by soil motions or by people walking inside. Vibrations, oscillations are dynamic phenomena.

This is a really important aspect to be taken into account during the design phase of whatever structure: not only we have to guarantee that the structure is able to carry the static loads (in the case of a house, the weight of the people, furniture and of the structure itself) but we have to guarantee also that the structure doesn't assume an unexpected and dangerous dynamic behaviour, for example, we don't want that it starts to vibrate intensely, risking a collapse.  And here comes the concept of Mechanical Resonance. 

Mechanical Resonance 

Mechanical Resonance is a particular situation in which our system starts to vibrate intensely, eg, with big amplitudes of oscillations. This happens when a structure is excited with a particular frequency, named Resonance Frequency (RF).

Each system is characterized by many Resonance Frequencies (conceptually infinite). These frequencies are particular frequencies such that, if we excite the system with a dynamic force (for example an oscillating force) having a frequency equal to one of the RFs, we can make the system vibrating intensely without spending too much energy, namely, we are making the system resonating. On the contrary, if we excite the system with a force having a frequency far (much lower or higher) from the RFs of the system, we will make a lot of effort to make it vibrating intensely, namely, we will have to spend much more energy to reach the same oscillations amplitude as the one reached in resonance.

For this reason, we can see Mechanical Resonance from an energetic point of view: Mechanical Resonance is the situation in which the energy transfer between the force and the forced system is efficient, the energy is transferred easily. On the contrary, far from Mechanical Resonance the energy transfer is much less efficient.

But let clarify what Resonance Frequencies are and how we can choose and manipulate them.

As said before, Resonance Frequencies are a proper characteristic of a system. When we decide the material and the geometry of a system, we fix also the RFs. Indeed, RFs depend on the mass (material, volume, density) and the stiffness (material, geometry-shape) of the system. The higher the stiffness, the higher the RFs; the higher the mass, the lower the RFs.

So, if we want to design a safe structure, we have to know what the frequencies of all the possible forces that will act on our structure during its entire life could be. Knowing this, we can realize a structure such that its Resonance Frequencies are far from the frequencies of the forces. In this way, the oscillations of the structure will be controlled and not too big. Again, it's always a matter of frequencies. We don’t want our system to have any RF near to one of the frequencies of the forces. We don’t want this marriage between frequencies.

This graph shows the response of a structure as a function of the frequencies of the loads. The peaks correspond to the Resonance Frequencies of the structure. If we excite the structure with one of these frequencies, it will oscillate intensely, its oscillation amplitude will be big. If we excite the system with a frequency far from the peaks, for example, 40 Hz looking at the picture, the system will respond a little, with little oscillation amplitudes.

Example: Earthquakes and Antiseismic Buildings 

Let make an example, based on antiseismic buildings: usually, earthquakes have frequencies not higher than 20 Hz. If we realize a house that has at least one Resonance Frequency near to 20 Hz, we will risk a lot, since Mechanical Resonance is going to happen. For this reason, we have to realize a house having a structure with RFs much higher than 20 Hz. We can do this by increasing the stiffness of the structure (as said before, the higher the stiffness, the higher the RFs). To increase the stiffness of the structure, we can use more iron in reinforced concrete (iron is a relatively stiff material). In this way, we will have a structure whose minimum RF is, let's say, 50 Hz and so far from the 20 Hz of the earthquake. In this way, if an earthquake happens, the structure will oscillate a little, since its RFs are much higher than the frequency of the earthquake and the energy transfer between earthquake (soil oscillation) and house (house oscillation) will be inefficient.

This video illustrates greatly the concept of Mechanical Resonance. The plate is moved using the same power during the whole test duration, in other words, the electric energy consumed by the machine that moves the plate is constant during the whole test duration. Only the oscillation frequency of the plate is changed. When we are far from the Resonance Frequency of a body, this body oscillates very little (in this case, the bodies are made in a way that they have only on RF, to simplify the test). When the oscillation frequency of the plate is near to the RF of the body (4 Hz for the right side body, as indicated in the video), the body vibrates crazily. Then, increasing the frequency of the plate and going far from the RF of the body, its oscillation amplitude decreases again.

Also in a bridge's design, Mechanical Resonance is a constraint and it is really important to take it into account. Indeed, vehicles on a bridge generate dynamic forces whose frequencies depend on the velocity of the vehicles. The bridge mustn’t have a RF near to one of these frequencies, otherwise, Mechanical Resonance occurs and intense oscillations start.

Another example of Mechanical Resonance is brake disks whistling: this happens when the brake pad oscillates and rubs on the disk surface with the same frequency of the disk (wheel) rotation. This is a situation that happens usually at low velocities and makes the disk vibrating quite intensely, generating sound waves.

Conclusions

In this article, I wanted to clarify the concept of Mechanical Resonance, making understanding that it represent a key point in any design of dynamic systems. Its understanding is fundamental to avoid catastrophic events.

ScienceFull.