Tutorial 1 ENT 346 Vibration Mechanics1. The static equilibrium position of a massless rigid bar, hinged at point O and connected with springs k1 and k2, is shown in Fig. 1. Assuming that the displacement (x) resulting from the application of a force F at point A is small, find the equivalent spring constant of the system, ke, that relates the applied force F to the displacement x as F = kex. Figure 1: Rigid bar connected by springs 2. Fig.2 shows a uniform rigid bar of mass m that is pivoted at point O and connected by springs of stiffness k1 and k2. Considering a small angular displacement θ of the rigid bar about the point O, determine the equivalent spring constant associated with the restoring moment. Figure 2: Rigid bar connected by springs Tutorial 1 ENT 346, prepared by Dr. Tan Wei Hong A simplified model of a petroleum pump is shown in Fig. of the system at location A. Figure 4: Petroleum pump Tutorial 1 ENT 346. where the rotary motion of the crank is converted to the reciprocating motion of the piston. meq. Tan Wei Hong . prepared by Dr. Figure 3: Springs connected in series-parallel 4.3. Find the equivalent spring constant of the system shown in Fig. Find the equivalent mass. 4.3. Figure 5 6. Find a single equivalent damping constant for the following cases: i) When three dampers are parallel. ii) When three dampers are in series. of the system so that the force F at point A can be expressed as F = ceqv. Tutorial 1 ENT 346. iii) When three dampers are connected to a rigid bar (Figure 6) and the equivalent damper is at site c1. 7.5. Determine the equivalent damping constant. 5. Tan Wei Hong . Two translational dampers. ceq. with damping constant c1 = 10 N-s/m and c2 = 15 N-s/m are connected to the bar as shown in Fig. prepared by Dr. Figure 6: Dampers connected to a rigid bar 7. Find the equivalent mass of the system shown in Fig. where v is the liner velocity of point A. A massless bar of length 1 m is pivoted at one end and subjected to a force F at the other end. are placed symmetrically about the middle vertical axis as shown in Fig. 10. prepared by Dr. Determine the displacement and velocity of the machine. an unbalanced vertical force of magnitude P = 2mω2r cos θ.81 m/s2. Use the value of g as 9.Figure 7: Rigid bar connected by dampers 8.5g. Tutorial 1 ENT 346. The initial conditions are & (0) = 1. The vibration table shown in Fig. 9. 8. causing the table to vibrate. Two equal masses. and identify the constants A1 and A2. Design a vibration table that can develop a force in the range 0-100 N over a frequency range 25-50 Hz. m each. where θ = ωt and ω = angular velocity of gears. 8 is used to test certain electronic components for vibration. ii) Express the motion in the form x(t) = A1 cos ωt + A2 sin ωt. will be developed.0 m/s. During rotation. It consists of two identical mating gears G1 and G2 that rotate about the axes O1 and O2 attached to the frame F. given by x(0) = 3 mm and x i) Find the constant A and α. A machine is found to vibrate with simple harmonic motion at a frequency of 20 Hz and an amplitude of acceleration of 0. Tan Wei Hong . A machine is subjected to the motion x(t) = A cos (50t + α) mm. Tan Wei Hong . prepared by Dr.Figure 8: A vibration table Tutorial 1 ENT 346.