STRUCTURAL DYNAMICS ASSESSMENT #1 - QUESTIONS ON UNDAMPED AND DAMPED VIBRATION

 

JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY

CONTINOUS ASSESSMENT TEST FOR FOURTH YEAR SECOND SEMESTER BACHELOR OF SCIENCE IN CIVIL ENGINEERING

ECE 2416 – THEORY OF STRUCTURES VI (STRUCTURAL DYNAMICS)

DATE: 27/01/2021                                                                                                                                   TIME:  1 HR

Instructions to candidates

• Attempt ALL questions
• Total score = 20 marks

1.    A single-degree of freedom system having a mass of 20 kg and a stiffness of 35 N/mm is given an initial displacement of 10 mm and initial velocity of 100 mm/s. Find: (a) the natural frequency; (b) the period of vibration; (c) the amplitude of vibration; and (d) the time at which the third maximum peak occurs.

2.    A machine weighing 1500 kg is mounted centrally on a 3-m-span simply supported steel beam. A piston that moves up and down in the machine produces a harmonic force of magnitude of 3000 kg and frequency of 50 rad/sec. Neglecting the weight of the beam and assuming 10% of the critical damping. Determine the amplitude of the motion of the machine and the force transmitted to the beam supports.

3.   A reinforced-concrete tank rests on a 20 m-tall concrete column. A cable attached to the tank applies a lateral force of 80 kN and pulls the tank horizontally by 5 cm. The cable is suddenly cut, and the resulting free vibration is recorded. At the end of four complete cycles, the time is 2.0 sec, and the amplitude is 25 mm. Calculate the damping ratio, the damping coefficient and, the number of cycles required for the displacement amplitude to decrease to 5 mm. If the water tank when full is subjected to a dynamic impulse force as shown by Fig. 1, determine the maximum shear and bending moment at the base of the tower. Note: The capacity of the water tank is 40 m³.

Fig. 1