Clarkson University
Department of Mechanical and Aeronautical Engineering
AEIME 455 Mechanical Vibrations
Spring 2004 OPTIONAL QUIZ
Friday, March 5, 2004
Name:
§OLUTI6M$
Student No.:
Instructions: Read the problems carefully and space your time so as
Response for Problem 3.48 using Transfer Function Block and Matlab/Simulink
Department of Mechanical and Aeronautical Engineering Clarkson University AE/ME 455 Mechanical Vibrations March 29, 2005 Homework Assignment No.6 Due Tuesday, April 12, 2005
1. Fi
AE/ME 455 Formula Page for Exam II
Simple harmonic function
z (t ) = a cos t + b sin t = C cos(t ) = C sin(t + o )
b
a
= tan 1 ;
C = a2 + b2 ;
a
b
o = tan 1
Harmonically excited single degree of freedom system
2
2
& + 2n x + n x = n sin t
&
x
xss (t )
AE/ME 455 Formula Page for Exam II
Simple harmonic function
z (t ) = a cos t + b sin t = C cos(t ) = C sin(t + o )
b
a
= tan 1 ;
C = a2 + b2 ;
a
b
o = tan 1
Harmonically excited single degree of freedom system
2
2
& + 2n x + n x = n sin t
&
x
xss (t )
Department of Mechanical and Aeronautical Engineering Clarkson University AE/ME 455: Mechanical Vibrations and Control Spring Semester 2005 2004 Catalog Data for ME 455/AE 455 Credits: (3). Fundamentals, free vibration, harmonically excited vibration, tra
2. Pressure Transducers
2.1. Purposes
To learn about the software and hardware necessary to acquire pressure data using pressure transducers. Use a micromanometer pressure standard to calibrate a single channel and multiple channel piezo-electric pressure
3. Wing Pressure Distribution
3.1. Purposes
Measure the pressure profile on the upper and lower surface of a symmetric wing at different air speeds and angle of attack. Learn about Bernoullis equation and the interaction of static and dynamic pressures.
3
1. Wing Vibration
1.1. Purposes
Study shed-vortex induced vibration of a low aspect ratio wing. A number of experimental variations are performed to isolate the effect of mass, damping and spring stiffness of the wing. Perform experiments in support of AE
1. Wing Vibration
1.1. Purposes
Study shed-vortex induced vibration of a low aspect ratio wing. A number of experimental variations are performed to isolate the effect of mass, damping and spring stiffness of the wing. Perform experiments in support of AE
1.12. Supplement - Error Analysis for a Fourier Transform
Using the computer to acquire data, we obtain a voltage vs. time data file. Although not recorded, each point in the file has a voltage error and time error. Both of these are due to quantization e
DEx - prototype ?
1.10. Supplement on Lumped Mass of the Vibrating Wing
For the wing tip plucking experiment, each point along the wing is moving with some velocity. We can derive an equivalent vibrating mass (lumped mass) located at the end of the wing b
1.9. Supplement on Logarithmic Decrement Theory
1. With the solution of the free vibration, the oscillation is when B2 is imaginary
Converting to a real term for oscillations,
Using the Euler formula, the exponentials can be written as sines and cosines
2
1.8. Supplement for Moment of Inertia Formula
Strength of Materials Approach - use image processing on a wing section digital photo
1. The applied bending moment applied to a section of a wing is a function of the distance, x, from the wing tip
The applie
1.7. Supplement for Vibrating Wing Data Processing
The calculation of damping involves all aspects of the plucking experiment. From Logarithmic Decrement Theory (see 1.8.)
This formula requires the calculation of many parts.
A. Calculating the ratios of a
2. Strain Gauge Behavior
2.1. Purposes
Use beam bending to examine the behavior of strain gauge and supporting circuitry. A Wheatstone bridge and amplifier are used to convert displacement into a voltage signal.
2.2. Background
Chapter 11 of the textbook,
1. Vibrating Beam Natural Frequency and Damping
1.1. Purposes
Study free and forced vibration of a simple beam. Different beam materials and different end-masses are used to investigate natural frequency and linear damping theory. Perform experiments in s
1.12. Supplement on Introduction to Fourier Transforms
A number of experiments generate a cyclic voltage vs. time such as an electrical tachometer and vibrating wing accelerometer. The signal can have a dominant frequency with a wave shape such as sine, s
1.11. Supplement on Introduction to Fourier Series
As we have observed in the laboratory, many measurements are taken using transducers and electronics. The result is that we record voltage vs. time and have constructed a LabVIEW VI to perform this task.
3. Venturi Flow Behavior
3.1. Purposes
Measure the pressure profile of a venturi at different flow rates and calculate discharge coefficient performance for flow metering. Learn about Bernoullis equation and the interaction of static and dynamic pressures