Characteristics of free and forced vibration of SDOF and MDOF mechanical systems

Title of experiment: Characteristics of free and forced vibration of SDOF and MDOF mechanical systems

Objectives

1. To verify experimentally characteristics of free vibration of SDOF system (natural frequency determination, forced vibration)
2. To verify experimentally characteristics of 2DOF system (two system resonance)

A. Experimentation on TM150 Universal Vibration System

Mechanical elements
A. Rigid beam
B. Revolute joint
C. Spring
D. Exciter unit

Auxiliaries
- Mounting plate
- Bolts
- Electronics and function generator
- Sensor and data acquisition system

A1. Free vibration

i. Write down the linearised equation of motion when no external force is applied.

System Equation:

ii. Write the expression of the different parameters in Table 1.
iii. How would you obtain these values through measurements?
Fill the Value and Unit columns in Table 1 after obtaining them from measurements?

iv. Experimentally verify the natural frequency of the system and compare it with the calculated value:
- Draw the time domain vibration signal (accelerometer) and complete the following diagram by defining ?? axis
- Extract from the diagram the information to complete Table 2

A2. Forced vibration (SDOF)

i. Consider that the exciter is producing a centrifugal excitation at the centre of the beam. Now, write down the system equation considering the external force acting at the centre of the beam.

System Equation:

ii. Find the particular solution (vibrations after the transient has expired, i.e. steady state):

θ_P(t) = ....

iii. Derive the expression of maximum amplitude of angular displacement (Θ).

Θ_P(...) = ....

iv. Install the accelerometer on the test rig. The accelerometer will give you the displacement y at the point of measurement (at length ?? from the joint). How can you obtain Θ_P from this measurement?

Θ_P(...) = ....

v. Perform experimentation to fill up the following table. For each excitation frequency, save a one second data file obtained from the accelerometer in .txt format.

Draw the curve of maximum angle (Θ) versus frequency (f) of external force. Position of accelerometer from the revolute joint α =

A3. Forced vibration (2DOF)

i. Install the additional spring/mass. How many DOFs does the system have now?

NDOF:

ii. How do you expect the curve of Θ_P(Ω) to be in this case?

Perform experiments to fill the following table. For each excitation frequency, save one second data file obtained from the accelerometer in .txt format. Draw the curve of maximum angle versus frequency of external force.