Force Transmissibility - Vibration Isolation and Transmissibility - Dynamics of Machinery

TL;DR

Force transmissibility is the fraction of input force that is transmitted to the foundation in a lumped parameter system, and it can be graphically determined using vector diagrams.

Transcript

hello everyone in this video we'll discuss about force transmissibility now what is force transmissibility it is basically the fraction of input amplitude which is transmitted to other side of the spring so let's assume if there is some body or a mass a rotating body which is fixed on a foundation right so what exactly happens that whatever is the ... Read More

Key Insights

• 🧑‍🏭 Force transmissibility is a crucial factor in understanding the relationship between applied force and transmitted force in lumped parameter systems.
• 👻 The graphical approach using vector diagrams allows for a visual representation of the different force components involved in the system.
• 🥳 The formula for force transmissibility includes terms related to spring stiffness, damping coefficient, and the frequency ratio.
• 🥺 Resonance conditions can lead to high amplitudes of transmitted force, which may pose a risk to the system.
• ✋ Dampers and stops can be used to control and limit the force transmissibility in practical applications.
• 🥳 The maximum force transmissibility occurs when the frequency ratio is equal to the square root of 2.
• ✋ Lower damping and higher stiffness result in higher force transmissibility, while higher frequency ratios decrease it.

Questions & Answers

Q: What is force transmissibility in a lumped parameter system?

Force transmissibility refers to the fraction of input force that is transmitted to the foundation in a system with mass, spring stiffness, and damping. It determines the relationship between the applied force and the force transmitted to the ground.

Q: How is force transmissibility calculated using the graphical approach?

The graphical approach involves plotting vector diagrams to determine the displacement, velocity, acceleration, and force components in the system. The resultant force from the vector diagram represents the transmitted force, which can be used to calculate the force transmissibility.

Q: What factors affect the force transmissibility in a lumped parameter system?

The force transmissibility depends on the stiffness of the spring, the damping coefficient, and the frequency ratio. Higher stiffness and lower damping increase the force transmissibility, while a higher frequency ratio can decrease it.

Q: What is the significance of resonance in force transmissibility?

Resonance occurs when the frequency ratio is equal to 1, leading to maximum force transmissibility. At resonance, the amplitude of the transmitted force can be significantly higher, which may result in damage or breakage in the system.

Summary & Key Takeaways

• Force transmissibility is the ratio of transmitted force to applied force in a lumped parameter system.

• The graphical approach uses vector diagrams to determine the displacement, velocity, acceleration, and force components in the system.

• The formula for force transmissibility includes spring stiffness, damping coefficient, and the frequency ratio.