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Unformatted text preview: Clarkson University AE/ME 455
AE/ME 555 CE 512 Exam 1 Instructor: Dr. C. Cetinkaya September 26, 2006
Fall 2006
Student Name : SQ ( \fh '3 F‘s 3
Student Number
Circle One : Undergraduate Graduate Instructions: Read these instructions before starting the exam. 1. Show all necessary equations and make clear sketches. Please write neatly and cross out all work which
you do not wish to be considered. Use correct units for all the quantities in your solutions. 2. Print your name and student number above and on each page of work and attach all pages of work. Print
your name and student number on additional sheets that you use. 3. This exam package (ﬁve pages) consists of four problems. The undergraduate students (AB/ME 455) are
responsible of the ﬁrst three problems worth 100 points. The graduate students (AEfME 555 CE 512)
are responsible for all the four problems worth 125 point (grades will be normalized to 100). Make sure
your examination package includes all the problems. 4. The exam is closed book and closed notes. Calculators are allowed. No computer is allowed. A onepage
formula sheet that is prepared by the student is allowed. This formula sheet shall be returned with the exam package. 5. The exam duration is 60 minutes for the undergraduates. The graduate students have additional 15
minutes for the extra problem. 6. Return this exam package with your formula sheet. Name: ...... . ............................ . . Student Number: ........... . .
1. (25 points) Determine the natural frequency (can) of this system and calculate a value of the damping coefﬁcient 0 such that its steadystate response amplitude is 0.02 m.
Note: No partial credits for this problem. Doublecheck your calculations. Solution: 20 cos 6.3I N
Friction
f1‘ee
LU“: I; 2 £0 : L111? rel/SC; m
be: 6.3 real/bu“
4 : 2 I; — 8
1:13:2CJXJ =§chi:01
{0 Z I“
2.
X: 190 * £0.02. =7 388 R'D‘FSP’ZP’S mac
2:3“ “““‘“"‘“'"““;3 _
(Lun1__~.x_l : $0‘3,‘
/ 1‘ e K
41 («.1 673 H La» 5‘3
7: E' 13 10/3}: __.—‘; :7 C: 31268333 K5($&L
(1”  85943
AM“ +9 CONP‘CK C’— ‘xwxpﬁcs ﬁber —H\t 42mm. cmxpﬁocle 13 ‘J‘QO
vibra—m_*we_ Sysbvx can“ A; 0.0Z_IV\_ Enter your ﬁnal results here with their corresponding units. Solutions are required above. (10 pts) a». = .ffifﬁ...‘.‘d/Se¢— (15 pts) c = bah“ Namez. . . . SOS. ............................. .. Student Number: ........... .. 2. (50 points) Generate the equation of motion in x and determine the natural frequency (can) of the mass m of this onedegreeof—freedom (steering) system. Here J is the polar moment of inertia of the (gear crank) disk with the radius of r, and k; and k2 are the rotational and linear stiffness coefﬁcients of the rod and the spring, respectively. (Steering wheel) No slippage between the gear and the mass m. Hint: The energy method can be used. Solution: Name: . . . . . ........................... .. Student Number: ........... . . 3. (25 points) Calculate the natural frequency (con) and the damping ratio (0 of this system for m=10 kg,
0 = 100 kg/s, k1 = 4000 N/m, k2=2000 N/m, and k3 = 1000 N/m. Assume no friction on the rollers. Calculate the critical damping of the system and determine the nature of its damping (e. g. overdamped, underdamped or critically—damped). Note: No partial credits for this problem. Double~check your calculations. Solution: l
«1*: _.____——— = 666.6% H/m Enter your ﬁnal results here with their corresponding units. Circle one. Solutions are required above. :23
(15 pts) C = ..... (a) overdamped @iderdamped (c) critically—damped (10 pts) m=?:‘.;.(?...‘“=‘/5¢L 4. (Grad students onlx, 25 points) The power generator is modeled as a damper in this system with m=89 kg,
c = 20 kg/s, k1 = 100 N/m, and k2=500 N/m. Assume no friction on the rollers. In steadystate motion of the system, calculate the power generation as a function of time and the average power from this generator. Solution: 25 cos 3: ...
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 Fall '10
 Centinkaya
 Bachelor's degree, Damping ratio

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