1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
ME SEMESTER- I EXAMINATION SUMMER 2018
Subject Code:712002N Date: 08/05/2018
Subject Name: STRUCTURAL DYNAMICS
Time: 02:30 PM to 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Solve all the questions by member stiffness matrix method or member flexibility matrix method. Assume the value of EI as 36000kN-m2 whenever required.
Q.1

Discuss the importance of damping in vibrating system. Also explain any one method to evaluate the damping coefficient for the system.
07

Differentiate between the lumped mass matrix and consistent mass matrix. Also give the consistent mass matrix for truss element.
07
Q.2

Derive the equation of the motion for force free damped system having initial displacement of X0 and initial velocity of u0.
07

A single spring mass system has M 200 kg, C 50 N-sec/m and K 1000 N/m. Calculate natural frequency, damping ratio and damped frequency. If this mass is displaced by 10mm and released to vibrate, calculate the time elapsed before the mass has maximum displacement of 2mm.
07
OR

A simple spring mass system has natural time period of 1.987 seconds. If the mass increased by 10 kg the time period increases to 2.084 sec. In original system if stiffness increased by 100 N/m then time period reduces to 1.895 sec. Calculate the mass and stiffness of the original system.
07
Q.3

A single spring mass system has mass of 100 kg and spring of stiffness 2 kN/m. if it is acted upon by an impulsive force as shown in the figure derive the equation of the motion of the mass. And hence calculate the displacement and velocity of the mass at 2 sec.
10

A rigid bar of length 8m and total mass of 5000 kg is supported by two springs at two ends. The stiffness of spring at left end is 10kN/m while the same for the right spring is 15kN/m. write down the differential equations of the motion of the bar.
04
OR
Q.3

A single spring mass system has mass of 500 kg and spring of stiffness 20 kN/m. if it is acted upon by a periodic force for which one period is as shown in the figure derive the equation of the motion of the mass.
14
Q.4

Derive the natural frequency of simple support beam of span 8m. It is loaded by total load of 4t. The flexural rigidity of the beam is 5000kN-m2. Assume the displacement function as
10

A system having the natural period of 0.5 sec is allow to vibrate freely. The two successive amplitude of the system were measured as 10.0 mm and 9.8 mm. calculate the damping ratio of the system. And then calculate the time required for the system to reduce its amplitude to 1mm.
04
OR
2
Q.4

Derive the natural frequency of cantilever beam of span 4m. It is loaded by total load of 10t. The flexural rigidity of the beam is 10000kN-m2. Assume the displacement function as
10

A water tank of capacity 5 lakh liters and height of 10m is supported by a shaft having internal diameter of 2.3 m and external diameter of 3.0 m. The total mass of the water tank is idealized as 5000tons concentrated at top of the shaft. The modulus of elasticity of the concrete is 20GPa. Calculate the time period when it is empty and when it is full.
04
Q.5
For a two springs and two mass model, spring stiffness are 1000kN/m and 600kN/m from and masses are 50000 kg and 30000 kg respectively from support. If the mass 30000kg is displaced by 10mm and released, derive the equation of the motion of the masses.
14
OR
Q.5
For a two springs and two mass model, spring stiffness are 1000kN/m and 600kN/m from and masses are 50000 kg and 30000 kg respectively from support. If the mass 50000 kg is acted upon by a force of 200sin(5t), derive the equation of the motion of the masses.
14

Figure.1
1 sec
20N
1 sec
Figure.2
20N
1 sec
20N