BME Dynamics and Vibrations 2 — Questions and Answers
Question 1: The transmissibility ratio in vibration isolation is less than 1 when the frequency ratio (r = ω/ωn) is:
- r < 1
- r = 1
- r > √2 (Correct answer)
- r < √2
Correct answer: r > √2
Vibration isolation is effective (transmissibility < 1) only when the excitation frequency exceeds √2 times the natural frequency of the isolator.
Question 2: For a rotating unbalance, the centrifugal force causing vibration is proportional to:
- Speed only
- Unbalance mass × eccentricity × ω² (Correct answer)
- Bearing stiffness
- Shaft length
Correct answer: Unbalance mass × eccentricity × ω²
The centrifugal force from a rotating unbalance is F = meω², where m is unbalance mass, e is eccentricity, and ω is angular speed.
Question 3: The work-energy theorem states that the net work done on a particle equals:
- Change in potential energy
- Change in kinetic energy (Correct answer)
- Total mechanical energy
- Product of force and time
Correct answer: Change in kinetic energy
The work-energy theorem states that the net work done equals the change in kinetic energy: W_net = ΔKE = ½mv₂² - ½mv₁².
Question 4: A Fourier series is used in vibration analysis to:
- Solve differential equations numerically
- Decompose periodic excitation into harmonic components (Correct answer)
- Calculate natural frequencies analytically
- Determine damping coefficients
Correct answer: Decompose periodic excitation into harmonic components
A periodic forcing function can be decomposed into sinusoidal harmonics using Fourier series, allowing response to each harmonic to be analyzed separately.
Question 5: In a two-degree-of-freedom system, the number of natural frequencies equals:
- 1
- 2 (Correct answer)
- 3
- Infinity
Correct answer: 2
A system with n degrees of freedom has exactly n natural frequencies (and n corresponding mode shapes).
Question 6: Gyroscopic effects in a rotating machine cause:
- Increased unbalance force
- Precession of the spin axis when a torque is applied (Correct answer)
- Reduced natural frequency
- Increased damping
Correct answer: Precession of the spin axis when a torque is applied
A spinning body exhibits gyroscopic behavior where an applied moment causes precession — rotation of the spin axis perpendicular to the applied torque.
BME Dynamics and Vibrations 2
The transmissibility ratio in vibration isolation is less than 1 when the frequency ratio (r = ω/ωn) is: