| 3/5/2012 |
| Mechanical Engineering Dynamics lab report.UFMEWL-10-2Vassos Tapakoudes
Demonstrate the patterns and relationships that stiffness and resonant frequencies follow under different circumstances on an air track. Stiffness is a measure of the resistance of a material to deformation under applied force. Resonant frequencies are the frequencies that a system appears to oscillate at greater amplitudes.
Theoretical calculations and background information pg.2
Experimental design and procedure pg.4
Analysis result and conclusion pg.7
Reflection to other experiment pg.9
Advantages and disadvantages of resonant frequencies
* Fatigue failure of components.
* Annoyance, sound and disturbance.
* Damaging systems close to it.
* Decreasing the efficiency of a system.
* Effective for appropriate designs and systems.
* Clock operation system
* Vibrating systems
The second factor tested in the four experiments taken, was stiffness. When a force is applied to a body, the body deforms. The measurement of the ability the body has to resist deformation is called stiffness. Stiffness is a constant force factor when Hooke’s law is applied in a system, as result stiffness will affect the output result constantly. Stiffness is a factor that will affect the operation of a system again. High stiffness can either benefit or harm a system. As a result specific stiffness should be chosen for each operation.
Also mode shape is investigated in the fourth experiment. Mode shape demonstrated the expected curvature of a mass vibrating at a particular mode. Since mode shape is multiplied by a function that varies with time, mode shape describes the curvature of vibration at all points in time. However magnitude of curvature will change. Factors affecting the mode shape are the boundary conditions and the shape.
Theoretical calculations are been done in order to find stiffness and resonant frequencies.
Experiment one (spring constant)
In the first experiment we are using F=k*x in order to find the constant K. experimental procedure is needed using a vertical stand to measure the extension and input it in the formula.
Experiment 2 (1 DOF system)
The second experiment has to do with a 1-DOF system. One trolley and rubber bands are used. Natural frequency of the oscillator is calculated theoretically in order to compare it with the experimental.
Experiment 3 (2 DOF system)
In this case we have an extra trolley and an extra rubber band fitted in the system in order to produce a 2-DOF system that is approximately symmetrical. To achieve this, set rubber band 2 connected with mass 2.then connecting spring is connected to mass 2 and mass 1 and mass 1 is connected to the shaker. Natural frequencies are calculated theoretically using the formula bellow:
Experiment 4 (asymmetric coupled oscillator)
Finally an asymmetric coupled oscillator is tested. An extra rubber band is connected parallel to rubber band 1. By using the mechanical impedance matrix to be equal to 0 at resonance, calculate the natural frequencies f1 and f2 of each shape. The procedure is shown below:
Experimental design and procedure
Four experiments are going to take place in order to find frequencies under different circumstances (e.g. 2 DOF systems). Excel operates as a very simple simulator and performs calculations and demonstrates relationships in graphs.
* An air track allowing 2 similar masser (trolleys) to travel horizontally with negligible...