Vibration Analysis Questions -

Q1. Determine the influence coefficients for the points (1), (2) and (3) of the uniform cantilever beam shown in Fig.

Q2. Establish the stiffness and flexibility matrix for the system shown in Fig.

Q3. Determine the modal matrix P and the weighted modal matrix P^~ for the system shown in Fig. Show that P or P^~ will diagonalize the stiffness matrix.

Q4. Three equal springs of stiffness k N/m are joined at one end, the other ends being arranged symmetrically at 120° from each other, as shown in Fig. Prove that the influence coefficients of the junction in a direction making an angle 0 with any spring are independent of 0 and equal to 1/1.5k.

Q5. Estimate the fundamental frequency of the lumped mass cantilever beam shown in Fig.

Q6. Consider a vertical uniform bar shown in Fig. Use Rayleigh method to find the fundamental frequency for the longitudinal vibration.