Anna University, Chennai

VIBRATIONS & AEROELASTICITY

**P****AR****T B**

1. Drive expression and obtain the natural frequency of vibration of a spring mass system in vertical position using 1. Newton’s law and 2. Energy method.

2. Drive expression and obtain the natural frequency of vibration of a spring mass system in horizontal position.

3. Obtain the expressions for the equivalent spring constants of spring when they are set in parallel and in series.

4. Using the energy method, obtain the equation governing free vibration for a simple pendulum system. Deduce the natural frequency of the same.

5. Consider a bar undergoing free axial vibrations. Derive and obtain the governing differential equation.

6. Derive the expression for torsional vibration.

7. Derive an expression for the natural frequency of the free longitudinal vibration by

(i)Equilibrium method (ii) Energy method (iii)Rayleigh’s method

8. Determine equation of motion when a liquid column vibrating in a ‘U’tube by

(i)Newton’s method (ii) Energy method and hence find its natural frequency.

9. Derive and obtain the governing differential equation for a beam undergoing free bending vibration. Solve for natural frequencies and mode shape of a simple supported beam.

10. Consider a single degree of freedom spring mass damper system subject to a single frequency harmonic excitation. Obtain the steady-state system response. Define the magnification factor and phase angle.

11. Derive and obtain the governing differential equation for the damped free vibrations of a single degree of freedom system. Then solve the same for the following cases :

(i) Over damping

(ii) Under damping. When is a system said to be critically damped?

12. Explain the application of Lagrange’s equation in vibration.

13. State Hamilton principle, obtain the governing equation.

14. Describe an approximate method for determining the frequency and mode shapes of a simply supported beam of arbitrary mass distribution undergoing flexural vibrations.

15. Obtain the natural frequency and mode shape of the system fig.

16. Obtain the natural frequency of the system fig.

17. Determine the natural frequency and amplitude ratios of the fig.

18. Deduce the expression for the free longitudinal vibration in terms of spring stiffness, its inertia effect and suspended mass.

19. Explain the different types of vibration measuring instruments?

20. Explain the working principle of frahms reed tachometer.

21. Discuss the design of a dynamic vibration absorber unit.

22. Write short notes on following

(i) loss of aileron control

(ii) divergence of a 2d using

(iii) stall flutter

23. Consider a 2-d wing with aileron attached. Derive and obtain an expression for the aileron control reversal speed.

24. Distinguish resonance and flutter.

25. Explain Collar’s triangle and different aeroelastic phenomen

26. Briefly discuss the different methods of flutter prevention,