ME 6201- F INAL EXAMINATION
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On CampusStudents
Monday, ecember 2,20L1, l :30 p m - 2 :20p m
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Distance eamingStudents y Wednesday, ecember 9,2011or by
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Prior arrangement ith D.L. McDowell
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Acoustics I Assignment 2
Due January 22, 2013
Each problem worth 15 points
1. Show that the Fourier coefficients of a string fixed at both ends and pulled aside a
1 8h
distance h at its midpoint are An = 2 2 sin
ME 6201
Homework #3
Dr. D.L. McDowell
Due: Oct. 10, 2005
1. Consider the time-dependent motion
*
*
*
x1 = x1 kx2 t , x2 = x2 + ( k 1) x3 sinh(t ) , and x3 = x3
a)
b)
Express the velocity field in terms of both material and spatial coordinates.
Express the
ME 6201
Homework #1 - Solution
Fall 2012
Assume Cartesian coordinates for all problems listed below.
1. Given
1 4 1
A 1 3 8 ,
0 0 10
7 0 2
B 5 10 0 ,
2 0 5
1
c 0 ,
1
2
d 5
15
For indicated rank of all tensors represented by matrices above, write
ME 4760 Fall 2006 - Homework #2 Solution
Dr. Ken Cunefare Due 09/07/2006
1.5.6) An 80-dB, 125 Hz pure tone and an 82-dB, 160 Hz pure tone are combined.
a) Find the root-mean-square sound pressure of each wave and of the combined wave
L p 100 / 20
prms1 =
ME 4760 Fall 2006 - Homework #1 Solution
Dr. Ken Cunefare Due 09/05/2006
1a) Prove that Equation (1.3.2) in Wilson is a solution of the wave equation.
Equation (1.3.2) describes a forward traveling pure-tone sound wave:
p = P cos k ( x ct )
The wave equa
ME 6201
Homework #5
Dr. D.L. McDowell
Due: Nov. 9, 2005
1.
For the given motion and Cauchy stress tensor
*
x1 = x1 + x2 ln t ,
*
x2 = x2 + x3et ,
*
x3 = x3
2 1 0
[ ] = 1 4 0 MPa
0 0 3
please verify by evaluation that E = F T D F and J : D = pk 2 : E .
ME 6201
HOMEWORK #2 (prob. #2 modified 9/16/99)
Due September 27, 1999
1. For the motion
x1 x1 x2 t 2 , x2 x1 t x3 t , x3 x2 x3 ln t
(a) determine the Jacobian
(b) find the inverse of the motion, i.e. x ( x , t)
(c) determine the velocity at t = 10 sec fo
ME 6201
Example Homework #1
1. Show that
(a) u v w = u i v k wk ei
~ ~ ~
~
(b) u v w = ijq u i v j wk e q e k
~ ~ ~
~
(c) u v w s = u i v j w j s p ei e p
~ ~ ~
~
for u , v , w , and s vectors.
~
~
~
2. Determine the components of the vector v j = jk
FinalReview
ME4760:EngineeringAcoustics&NoiseControl
Dr.EricaRyherd
FORMAT
PartI:Concepts
2530minutes
Closedbook,closednotes,nocalculatorsallowed
Befamiliarwithbasicconcepts,terminology,etc.
1
FORMAT
PartII:Problems
Remainderofexamtime
Closedbook
Cal
ERRATA AND ADDITIONS FOR "Noise Control: from Concept to Application"
1st printing.
November 10, 2010
p8,
line above Example 1.2 title, change Appendix B to Appendix A
p19,
3 lines from the bottom of the page, the equation should be:
p1 ' A1e jt and p2 '
Noise control
250
For wave propagation along the direction of ribs or corrugations the bending stiffness
per unit width may be calculated by referring to Figure 6.2, and using the following
equation.
(6.7)
The summation is taken over all sections in width
Uploading Assignments
using T-Square
You will be using T-Squares Assignment feature to upload
scans of your homework files for grading. Please follow the
directions shown in the following slides to do this.
You will receive marked up files after grading i
ME
ME 6201 Introduction to Continuum Mechanics
D.L. McDowell
Topics on final exam
Basic tensor math
Finite strain kinematics
Rate of deformation and spin
Cauchy stress, equilibrium and surface traction
Eigenvalues and eigenvectors
Constitutive laws, inclu
ENGINEERING ACOUSTICS AND NOISE CONTROL Syllabus
The George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME 4760, Fall 2012, 3 CR
COURSE OBJECTIVES:
Study of acoustics related to noise and its control; acoustic terminology,
ME 6201 Fall 2001
MIDTERM EXAMINATION SOLUTION KEY
1.
For the displacement field given by
2
u1 = x2
,
u2 = exp( k x1) ,
u3 = 0
a. State the Eulerian coordinates in terms of Lagrangian coordinates
b. Determine the components of the Green-St. Venant Strain
ME6201
Homework #7
Due December 5, 2012
1
1. Given the strain tensor ij
ij ij kk for an isotropic, linear elastic solid, where
E
E
is the Poissons ratio, and E is Youngs modulus, derive the stress-strain relation and
strain energy density functions i
ME6201
Homework #7
Due December 5, 2012
1 +
1. Given the strain tensor ij =
ij ij kk for an isotropic, linear elastic solid, where
E
E
is the Poissons ratio, and E is Youngs modulus, derive the stress-strain relation and
strain energy density functio
ME6201
Homework #6
Due November 21, 2012
1. Which of the following are frame indifferent expressions? (show all work)
(a) pk (2) G E
This equation is necessarily frame indifferent as all terms are couched in
Lagrangian coordinates.
(b) Green-Naghdi rate
ME6201
Homework #6
Due November 21, 2012
1. Which of the following are frame indifferent expressions? (show all work)
(a) pk (2) = G ( E )
(b) Green-Naghdi rate of Cauchy stress given by
Og
= +
(c) = C : D
(d) = B : E
Here, = R RT , F = R U , is the Cau
ME6201
Homework #5
Due November 7, 2012
1. In the current configuration, the traction vectors acting at a point on three mutually
orthogonal planes with outward unit normal vectors e1 , e2 , and e3 are given by
2
3
3
2
*
*
*
*
t1 x* e1 x1 x* e 2 , t 2 x