SIUE Mechanical Engineering Lab Report

ME 356L

Experiment 4 Two Degrees of Freedom System

Spencer Wallace

November 2, 2011

Group 7

Objectives

This experiment is done to gain a better understanding of resonance frequency with

vibrations. In this experiment we will find the natural frequency and use two different vibration

modes.

Background

Resonance is very important to understand because in practical application it is a key

factor to take into consideration when designing any type of mechanical system. You must be

sure that never in the operating conditions of a system it will be near the resonance or failure

may occur.

Setup and Measuring Principles

We use a free standing grounded forced vibration apparatus with two weights. It has

attached to it two sets of springs with two weights in between. At the top are two LVDT which

we will use to measure the motion of the two masses.

As in most labs we will need to calibrate both LVDTs and also center them on the

apparatus so our measurements will be even. Next we needed to find the Spring constants for

the springs involved using the computer program. We found the spring stiffness in in/kg and

later we will convert that into a spring constant. We added mass to the plates to measure the

displacement (in/kg).

After we find spring constants and calibrate LVDTs we run the forced vibration test. We

were given a table to follow with different frequency of vibration and amplitudes to follow and

take down data. We will use this data to observe the behavior of springs at natural frequency.

Data Reduction and Questions

The first thing we are asked to do is find the spring constants. We measured in/kg from

the computer so we need to convert that to lb/in. 1 kg = 2.2 kg so for the first spring:

.6834∈ ¿kg×1kg2.2lbs

=.3106 ¿lb

=3.22 lb¿ ¿

With the same conversion our spring constant for the second spring comes out to 7.16 lb/in.

We are next asked to estimate the natural frequency. We turn on the generator and

LVDT software and adjust the frequency and the amplitude and observe the spring behavior. It

appears the natural frequency is around 3 Hz.

0.00 0.05 0.10 0.15 0.20 0.25-1.00E+00

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00Below Resonance 2.9 Hz

Displace 1 (in)Displace 2 (in)

Time

0.00 0.05 0.10 0.15 0.20 0.25-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00Above Resonance 4 Hz

Displace 1(in)

Displace 2 (in)

Time

1) The motion of the plates was very interesting. Before resonance the displacements were

slow and relatively small once it approached resonance it became much faster and

much larger at resonance. After resonance the displacements tended to be larger. At

the second resonance the two plates were completely motionless.

2) The theoretical and experimental natural frequencies did work out to be relatively

similar. With our calculated spring constants we were able to make a good estimation of

a resonance frequency.

3) In any man made system there will be many types of damping. There will be friction

from the guide rails and vibrations of the system into the table are both losses of energy

and will contribute to slowing the resonance to have a more realistic vibration

magnitude.