Question:
Transmissibility of vibration intensity from tractor body to driver seat is a function of
A. Damping ratio
B. Chasis frequency
C. Undamped natural frequency of seat
D. Input amplitude of vibration
Choose the correct answer from the options given below:
Transmissibility of vibration intensity from tractor body to driver seat is a function of
A. Damping ratio
B. Chasis frequency
C. Undamped natural frequency of seat
D. Input amplitude of vibration
Choose the correct answer from the options given below:
A. Damping ratio
B. Chasis frequency
C. Undamped natural frequency of seat
D. Input amplitude of vibration
Choose the correct answer from the options given below:
Show Hint
Vibration transmissibility is a dimensionless ratio.
It is determined solely by the system's dynamic properties—the damping ratio (\( \zeta \)) and the frequency ratio (\( r \))—and is independent of the input amplitude.
It is determined solely by the system's dynamic properties—the damping ratio (\( \zeta \)) and the frequency ratio (\( r \))—and is independent of the input amplitude.
Updated On: Aug 4, 2026
- B and C only
- A and D only
- A, B and C only
- B, C and D only
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Vibration transmissibility (\( TR \)) is the ratio of the vibrational force (or displacement) transmitted to a receiver (such as the driver's seat) to the input vibrational force (or displacement) generated by the source (the tractor chassis).
It is modeled using single-degree-of-freedom mass-spring-damper systems.
Key Formula or Approach:
The transmissibility ratio (\( TR \)) for a damped, spring-supported system under harmonic excitation is given by:
\[ TR = \sqrt{\frac{1 + (2\zeta r)^2}{(1 - r^2)^2 + (2\zeta r)^2}} \]
where:
- \( \zeta \) is the damping ratio of the system.
- \( r = \frac{\omega}{\omega_n} \) is the frequency ratio.
- \( \omega \) is the excitation (chassis) frequency.
- \( \omega_n \) is the undamped natural frequency of the suspension system (the seat).
Step 2: Detailed Explanation:
Let us analyze the parameters in our equation:
1. Damping ratio (\( \zeta \)): The damping ratio measures how rapidly oscillations decay after a disturbance.
It directly affects the peak transmissibility value at resonance. This matches statement A.
2. Chassis frequency (\( \omega \)): The excitation frequency is determined by the rotational speed of the engine, the transmission system, and the terrain interaction. This matches statement B.
3. Undamped natural frequency of the seat (\( \omega_n \)): This is a characteristic property of the seat suspension system, determined by the seat mass and the stiffness of the spring support. This matches statement C.
4. Input amplitude of vibration: In a linear vibration model, the transmissibility is a ratio of amplitudes.
Because the system is linear, this ratio is independent of the absolute input amplitude. This makes statement D incorrect.
Therefore, the transmissibility of vibration intensity depends on the damping ratio (A), chassis frequency (B), and undamped natural frequency of the seat (C).
Step 3: Final Answer:
The transmissibility is a function of A, B, and C only.
Vibration transmissibility (\( TR \)) is the ratio of the vibrational force (or displacement) transmitted to a receiver (such as the driver's seat) to the input vibrational force (or displacement) generated by the source (the tractor chassis).
It is modeled using single-degree-of-freedom mass-spring-damper systems.
Key Formula or Approach:
The transmissibility ratio (\( TR \)) for a damped, spring-supported system under harmonic excitation is given by:
\[ TR = \sqrt{\frac{1 + (2\zeta r)^2}{(1 - r^2)^2 + (2\zeta r)^2}} \]
where:
- \( \zeta \) is the damping ratio of the system.
- \( r = \frac{\omega}{\omega_n} \) is the frequency ratio.
- \( \omega \) is the excitation (chassis) frequency.
- \( \omega_n \) is the undamped natural frequency of the suspension system (the seat).
Step 2: Detailed Explanation:
Let us analyze the parameters in our equation:
1. Damping ratio (\( \zeta \)): The damping ratio measures how rapidly oscillations decay after a disturbance.
It directly affects the peak transmissibility value at resonance. This matches statement A.
2. Chassis frequency (\( \omega \)): The excitation frequency is determined by the rotational speed of the engine, the transmission system, and the terrain interaction. This matches statement B.
3. Undamped natural frequency of the seat (\( \omega_n \)): This is a characteristic property of the seat suspension system, determined by the seat mass and the stiffness of the spring support. This matches statement C.
4. Input amplitude of vibration: In a linear vibration model, the transmissibility is a ratio of amplitudes.
Because the system is linear, this ratio is independent of the absolute input amplitude. This makes statement D incorrect.
Therefore, the transmissibility of vibration intensity depends on the damping ratio (A), chassis frequency (B), and undamped natural frequency of the seat (C).
Step 3: Final Answer:
The transmissibility is a function of A, B, and C only.
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