Consider the following statements regarding forced vibration : 1. Forced vibration is generally caused by some periodic applied force present in the machine tool, such as that from gear drives. 2. The amplitude of vibration can be increased by increasing the stiffness or by damping the system. 3. The basic solution to forced vibration is to isolate or remove the forcing element. Which of the above statements are correct?
Analyzing Forced Vibration Statements
The question asks to identify the correct statements about forced vibration from the given three statements.
Statement 1 Analysis: Cause of Forced Vibration
Statement: Forced vibration is generally caused by some periodic applied force present in the machine tool, such as that from gear drives.
- Forced vibration occurs when an external periodic force acts on a system.
- Examples of such forces in machinery include imbalances, gear meshing, or reciprocating components.
- Therefore, this statement accurately describes the cause of forced vibration.
Conclusion: Statement 1 is correct.
Statement 2 Analysis: Amplitude Factors
Statement: The amplitude of vibration can be increased by increasing the stiffness or by damping the system.
- Increasing stiffness typically raises the natural frequency. While this can shift the resonance condition, it doesn't universally increase amplitude.
- Increasing damping *always* reduces the amplitude of vibration, especially near resonance.
- Therefore, this statement is incorrect as damping reduces amplitude.
Conclusion: Statement 2 is incorrect.
Statement 3 Analysis: Solution to Forced Vibration
Statement: The basic solution to forced vibration is to isolate or remove the forcing element.
- Reducing or eliminating forced vibration involves addressing its source or the transmission path.
- Removing the periodic forcing element (e.g., balancing a rotor) or isolating the system (e.g., using vibration dampers or mounts) are primary methods.
- Therefore, this statement correctly identifies fundamental solutions.
Conclusion: Statement 3 is correct.
Final Conclusion
Based on the analysis, statements 1 and 3 are correct, while statement 2 is incorrect.
The correct option is the one that includes only statements 1 and 3.
Important Questions from Forced Vibration
Which method is used to find the natural frequencies of a system with multi degrees of freedom?
The ratio of the amplitude of the steady-state response of forced vibrations to the static deflection under the action of a static force is known as
When the frequency of the forced vibration is equal to the frequency of the free vibration, this condition is called ______.
The amplitude of the steady-state reaction divided by the static deflection under force application is known as _______.
Consider a forced single degree-of-freedom system governed by \(\rm \ddot x(t) + 2 ζ ω_n \dot x (t) + ω_n^2 x(t) = ω_n^2 \cos (ω t)\), where ζ and ωn are the damping ratio and undamped natural frequency of the system, respectively, while ω is the forcing frequency. The amplitude of the forced steady state response of this system is given by [(1 − r2)2 + (2ζr)2]-1/2, where 𝑟 = ω/ω n. The peak amplitude of this response occurs at a frequency ω = ωp. If ωd denotes the damped natural frequency of this system, which one of the following options is true?
