Simulation of Two DOF System (Translation)

1. Team Members and Roles assigned

Name

Roll No.

Roles

Harsh Singh

12ME55

Team Leader

Shreyas Suresh Shenoy

12ME129

Reporter

Sylvester Jerome Dsouza

12ME141

Time Keeper

Ayush Malewar

12ME79

Quality Auditor

Team Leader will be responsible for the timely completion of the project and to coordinate with all the team members.

Reporter will be responsible for the well documentation and presentation of all activities undertaken by the team.

Responsibility of the Time Keeper is to make sure that the project is completed on time along with meeting all the time deadlines that were assigned to all at the initial stages of the project. He needs to make sure that the project is going well on time.

It is the responsibility of the Quality Auditor to verify all documentation and plan which the team has decided to do.

2. Team Approach and Timeline

We prepared the Gantt chart and the series of work to be undertaken in the project was listed.

Each member of the team was assigned a specific work and given the required deadline to finish the work.

Some of the topics which required detailed discussion and analysis were assigned to all the members, to work in synchronous manner.

3. Inputs to the program

M1- Mass of the first block (in kilograms)

M2- Mass of the second block (in kilograms)

K1- Spring constant of the first spring (in N/m)

K2- Spring constant of the second spring (in N/m)

C1- Damping coefficient of the first viscous damper (Ns/m)

C2- Damping coefficient of the second viscous damper (Ns/m)

F0- Amplitude of the external applied force (N)

w- Frequency of the external input

xo - Initial position of the masses

vo - Initial velocity of the masses

Further variables can be added to the program at a later stage.

4. Free Vibration Analysis

Where X1 and X2 are constants that denote the maximum amplitudes ofx1 (t) and x2 (t) and is the phase angle.

5. Forced Vibration Analysis

The equation of motion of a general two degree of freedom system underexternal forces can be written as:

The equation can be solved to obtain:

4. Outputs from the program and Flowchart

Displacement vs Time graph.

Velocity vs Time graph.

Acceleration vs Time graph.

Amplitude ratio vs Frequency ratio.

The simulation of the system in motion.

Modal solution.

START

READ MASS, STIFFNESS, DAMPING COEFFICIENT

READ EXTERNAL FORCE AMPLITUDE AND FREQUENCY

NO

YES

IF FORCE AMPLITUDE == 0

FORCED VIBRATION ANALYSIS

FREE VIBRATION ANALYSIS

CALCULATE DAMPED NATURAL FREQUENCY, DISPLACEMENT AMPLITUDE, PHASE ANGLE

PLOT DISPLACEMENT - TIME, VELOCITY TIME, ACCELERATION TIME AND AMPLITUDE RATIO FREQUENCY RATIO GRAPHS

END

5. Engineering Model

x1

Mass 1

(M1 )

Equivalent Viscous Damping

(C)

Stiffness (K1 )

x2

Mass 2

(M2 )

Stiffness (K2 )