Damping in Structural Dynamics

When you hit a glass or metal pot, you will certainly hear a noise, but its intensity disappears after some seconds. However, if we lived in a world without deadening, then we would hear this tone forever. In fact, there are various procedures in physics through which the kinetic and elastic energy created in the metal pot dissipates into other forms of energy. Today, we are going to dive into the physical phenomena which cause deadening in different vibrating structures.

How Is Damping Quantified?

We can describe sound damping in different ways. Below, you can find many popular descriptions.

The amplitude decay is one of the most popular examples of damping during free vibrations (like in case of the bowl described above). Based on how large the damping is, the decay rate is determined. So it is normal that the vibration amplitude reduces rapidly after some time. So in this case, the decreased energy during a cycle is proportional to the amplitude of the cycle itself.

We can take the example of the equation of motion for a system with only one degree of freedom with viscous damping and no external loads,

After division with the mass, m, there is the normalized form, often described as

Here, we should say that is the undamped natural frequency while is called the damping ratio.

To make the motion be occasional, the damping ratio must be limited to the range

In order for the motion to be cyclic, the damping ratio must be limited to the range   In the system, the amplitude of the free vibration will decompose with the factor

where T0 is the period of the undamped vibration.

Decay of free vibration for three different values of the damping ratio.

Another measure in use is the logarithmic decrement, δ. This is the logarithm of the ratio between the amplitudes of two subsequent peaks:

Here T is the period.

The connection between the logarithmic decrement and the damping ratio is

Another example where the effect of damping has a great role is when a structure is subjected to a harmonic excitation

Another case in which the effect of damping has a prominent role is when a structure is subjected to harmonic excitation at a natural frequency. Exactly at resonance, the vibration amplitude reaches to infinity, unless there is some damping in the system. The amplitude at resonance is controlled only by the amount of damping.

Damping Sources

In fact, there are various damping sources when we consider this from the physical point of view. It’s worth mentioning that out nature always finds a way to dissolve the energy.

Internal Losses in the Material

Every real material can dissolve some energy in case of being strained. So it’s like an internal friction. In case you look at a stress-strain curve, you will see something that is more like a thin ellipse. Very often, loss factor damping is a good representation for material damping because the energy loss during each cycle has quite weak dependencies on frequency and amplitude. This is based on experience! However, as the mathematical foundation for loss factor deadening depends on complex-valued quantities, the underlying assumption is harmonic vibration. Therefore, this deadening model can be used for frequency-domain analyses.

Based on the detailed composition as well as sources you discuss, the loss factor designed for a material can be featured with a large variation. Here you can see roughly done estimates.

When the exact physics of the damping in the material is not evident, loss factors can be used in such cases. In some material models, like viscoelasticity, the dissipation is an inherent property of the model.

Friction in Joints

We all know that the structures are connected together by bolts or rivets. If these joined surfaces are sliding relative to one another in the process of vibration, it’s through the friction that the energy is dissolved. The energy loss in each cycle is independent to some extent. Here we can say that the friction is like the internal losses in the material.

In mechanical engineering bolted joints are quite normal. It is based on the design how the amount of this dissipation can vary in bolted joints. If low damping is essential, then the bolts need to be closely spaced and well-tightened in order to avoid that macroscopic slip between the joined surfaces.

Sound Emission

A vibrating surface will displace the surrounding air so that sound waves are dissolved. These sound waves take energy to some extent due to which an energy loss happens according to the point of view of the structure.

Why invest in sound damping material?

Reasons are a lot why you should invest in sound damping material. Driving your vehicle every single day means that your car should also be comfortable. However, road noise cannot let you feel comfortable. Nothing is more distracting and awful than road noise coming from outside or just from your own car engine. By installing damping material, you can easily reduce car noise and excess vibration that makes you feel so uncomfortable.

It’s high time to take care of upgrading your car and enjoying the feel of high-end vehicle. As you already know how damping happens, you will probably value the role of car sound damping material.

The market is full of many types of low-quality products but you should rely on the most trustworthy team. Here at SoundSkins, the professional team aims to provide quality damping material so that you will achieve having a peaceful ride.

Their sound damping material is a budget-friendly option, so you can rest assured that you will not spend a lot but you will surely experience incredible sound damping results. This insulation will also prevent noise from escaping.

So, if you don’t want other people on the road to hear you then invest in sound deadening. Simply place your order at SoundSkins and feel what it’s like having a calmer drive.