Short Answer:

Transmissibility is the ratio of the force transmitted to the foundation through a vibrating system to the force applied to it. It shows how much vibration or force is passed from the machine to its support. Transmissibility depends mainly on the frequency ratio and damping in the system.

In simple terms, transmissibility helps to understand how effectively a vibration isolation system works. A low transmissibility means better isolation because less vibration is transmitted. It is a very important factor in designing machinery foundations and vibration isolators.

Detailed Explanation :

Transmissibility

Transmissibility is a very important concept in mechanical vibrations. It is used to measure how much vibration or dynamic force from a machine or structure is passed on to its foundation or support. In practical applications such as engines, compressors, and other rotating machines, vibrations are unavoidable. These vibrations can cause damage, noise, and discomfort if not controlled properly. Therefore, understanding and controlling transmissibility is necessary for smooth operation and safety.

Transmissibility is defined as the ratio of the transmitted force to the exciting force acting on the vibrating system. Mathematically, it is expressed as:

Where:

•  = transmissibility
•  = transmitted force to the base or foundation
•  = applied or exciting force

The transmitted force is the reaction of the spring and damper to the motion caused by the external excitation. When the machine vibrates, part of this vibration is absorbed by the isolator (spring or damper), and the remaining part is transmitted to the foundation. The objective of vibration isolation is to minimize this transmitted force, which is achieved when transmissibility is less than 1.

For a damped system subjected to harmonic excitation, transmissibility is given by the formula:

Where:

•  = damping ratio
•  = frequency ratio (excitation frequency to natural frequency)

This equation shows that transmissibility depends on both the frequency ratio and damping ratio of the system.

Let us understand the behavior of transmissibility under different frequency conditions:

1. When   (low-frequency region):
   The transmissibility  , which means the transmitted force is greater than the applied force. In this case, the system amplifies the vibration instead of isolating it. Hence, vibration isolation is not effective.
2. When  :
   The transmissibility becomes equal to 1. This is the point where transmitted and applied forces are equal. It is the boundary between the amplification and isolation regions.
3. When   (high-frequency region):
   The transmissibility  , which means that less vibration is transmitted to the foundation. This is the desired condition for effective vibration isolation. Thus, for good isolation, the excitation frequency should be much greater than the natural frequency.

Damping also plays a significant role in transmissibility. When damping is small, transmissibility is very high near resonance, and the system experiences large vibration amplitudes. As damping increases, the transmissibility peak at resonance decreases, but in the isolation region ( ), higher damping can slightly increase transmissibility. Therefore, in practice, damping should be selected carefully to balance between reducing resonance and achieving good isolation.

Transmissibility curves are often used to visualize the system behavior. These curves show how transmissibility changes with different values of frequency ratio and damping. Engineers use these curves to design isolators, choose proper materials, and determine the operating conditions of machines.

For example, in an engine mounted on a vehicle, the engine’s vibrations should not pass to the vehicle body. Rubber or spring isolators are used between the engine and frame to reduce transmissibility. Similarly, in industrial machines or HVAC systems installed on building floors, vibration isolators are used to prevent transmitted vibrations from reaching other structures and causing noise or damage.

Thus, transmissibility is an essential design parameter in all systems that experience dynamic forces. A well-designed system ensures low transmissibility, which results in effective vibration isolation, reduced wear, improved performance, and longer equipment life.

Conclusion:

Transmissibility is the ratio of the transmitted force to the applied force in a vibrating system. It helps to measure how much vibration is passed from the source to the foundation. Transmissibility depends on the frequency ratio and damping ratio. For effective vibration isolation, transmissibility must be less than one, which occurs when the excitation frequency is higher than the natural frequency. Controlling transmissibility is important in mechanical and structural design to prevent damage and ensure smooth operation.