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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
ME 6201- F INAL EXAMINATION
NAME:
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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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Please ork all problems, howingall work.
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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
ME6201
Homework #4 - Solution
Fall 2012
*
*
*
*
*
*
1. A unit vector n that is normal to the plane p x1 , x2 , x3 x1 x2 5 x3 25 0 is found by
e e 5e3 .
p
setting n
. Therefore, n 1 2
p
27
*
*
(a) Determine the traction vector and its magnitude acting o
ME6201
Homework #4
Due October 31, 2012
1. The Cauchy stress tensor at a point is given by
12 24 5
24 10 0 MPa ,
5 0 10
(a) Determine the traction vector and its magnitude acting on the plane
*
*
*
x1 x2 5 x3 25 0 .
(b) Find the component of this trac
ME 6201
Homework #3 - Solution
Fall 2012
1. In terms of the Lagrangian coordinates, the motion is given as
*
x1
1 0 sin(k1t ) x1
*
0 x2 .
x2 [ F ][ x] 1 k2t
*
x3
0 0
1 x3
The inverse relation may be found by inverting the three relations given
ME 6201
Homework #3
Due October 10, 2012
1. Consider the time-dependent motion
*
*
*
x1 x1 x3 sin k1t , x2 x1 k2 t x2 , and x3 x3 ,
where xi* represents the spatial coordinate system, xi represents the material
coordinate system, t is the time, and k1 and
ME 6201
Homework #2 - Solution
Fall 2012
*
*
1. Consider the motion x1* x1 , x2 x2 k 2 x1 cx3 , and x3 x3 k x2 .
a)
Find the deformation gradient, F
*
x1 1
dx*
*
F , where x* x2 k 2
dx
*
x3 0
1
Therefore, F k 2
0
b)
.
0 0 x1
1 c x2 .
k 1 x3
0 0
ME 6201
Homework #2
Due: September 26, 2012
*
*
*
1. Consider the motion x1 x1 , x2 x2 k 2 x1 cx3 , and x3 x3 k x2 .
a)
b)
c)
d)
Find the deformation gradient, F .
Determine the Jacobian.
Find the inverse of the motion, F 1 .
Find the displacements in ter
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
12/3/2012
Instrumentation Basics
ME 4760
Instrumentation
Microphones
An acoustic to electric transducer that
converts acoustic energy into an
electrical signal
Some Types:
Dynamic (electromagnetic generation)
Piezoelectric
Condenser (capacitance chan
ME 4760, Fall 2006, Homework 11
No Due Date! Will not be graded!
Note that the tables in this MSWord file may be easily cut and pasted into Excel!
1) The table below lists octave band sound power levels for an HVAC air handler connected to a
duct feeding
ME 4760 Fall 2006 - Homework #10 Solution
Dr. Ken Cunefare Due 11/09/2006
6.2.2) Find transmission loss (TL) and transmission coefficient (TC) for a 0.75-m2 test sample,
89 dB sound level in the source room and 70 dB in the receiving room, with 3.0-m2 equ
ME 4760 Fall 2006 - Homework #9 Solution
Dr. Ken Cunefare Due 11/07/2006
5.5.2) For 68-dBA daytime and 66-dBA nighttime sound levels, predict community impact in
terms of sleep disturbance.
Using equation 1.9.2, we have
cfw_
= 10 log cfw_[1/ 24] 15 10
LD
ME 4760 Fall 2006 - Homework #8 Solution
Dr. Ken Cunefare Due 10/26/2006
4.4.2) Same as Problem 4.4.1, except that hearing thresholds are between 0 and 25 dB in the left
ear.
a) Find the percent hearing impairment based on the AAO/ACO formula.
Average hea
ME 4760 Fall 2006 - Homework #7 Solution
Dr. Ken Cunefare Due 10/12/2006
Grading Methodology:
1) Compute SEL per day = 4 points
2) Compute Lday, Lnight, and LDN per day = 4 points
3) Determine L1, L10, L50, L90, and L99 per day = 4 points
4) Determine L1,
ME 4760 Fall 2006 - Homework #6 Solution
Dr. Ken Cunefare Due 10/05/2006
3.2.2) Fifty sound level readings are taken at 10-s intervals. They are distributed as follows.
Cumulative readings vs. level are:
87
86
85
84
83
82
81
80
1-2
3-8
9-20
21-40
41-43
44
ME 4760 Fall 2006 - Homework #5 Solution
Dr. Ken Cunefare Due 10/03/2006
2.3.2) Find the eigenfrequencies of a 12-m-long by 10-m-wide by 3.5-m-high rectangular room
at 20C. Consider up to three half-waves in the length and width directions and two half-wa
ME 4760 Fall 2006 - Homework #4 Solution
Dr. Ken Cunefare Due 09/19/2006
2.2.3) Repeat Problem 2.2.2 if the directivity index is 12.0.
a) Determine the maximum directivity factor
Since DI = 10logQ we have
Qmax = 10 DI /10 = 1012 /10 = 15.85
b) Find the ma