2.092/2.093
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I
FALL 2009
Quiz #1-solution
Instructor:
TA:
Prof. K. J. Bathe
Seounghyun Ham
Problem 1 (10 points):
a)
x
(1)
u (1) (x)=H U= 1 60
x
60
0 U
x
x
(2)
u (2) (x)=H U= 0 1U
100 100
where U= [ U1
U2
T
U
28 FLOATING STRUCTURE IN WAVES
28
92
Floating Structure in Waves
We consider the pitch and heave dynamics of a large oating structure in a random sea. You
can consider this a two-dimensional problem.
The structure has two main, identical struts that pierc
41 FLOATING STRUCTURE HEAVE AND ROLL
41
165
Floating Structure Heave and Roll
Consider the heave and roll response of a two-hull structure with the parameters below:
mass (metric tons)
body rotary inertia (kg-m2 )
beam of each hull b (m)
open space betwee
40 METACENTRIC HEIGHT OF A CATAMARAN
40
164
Metacentric Height of a Catamaran
Consider the roll stability of a catamaran described as follows: total beam is 6b, where b is
the beam of each hull, the draft is T , and each hull is rectangular in cross-secti
2.092/2.093
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I
FALL 2009
Quiz #2
Instructor:
TA:
Prof. K. J. Bathe
Seounghyun Ham
Problem 1 (10 points):
A planar (two-dimensional) analysis of a fluid-structure system is to be performed. The simple
model shown
31 IDENTIFICATION OF A RESPONSE AMPLITUDE OPERATOR FROM DATA: REDUX112
31
Identication of a Response Amplitude Operator
from Data: Redux
The problem here is almost exactly the same as in HW5, for which you have the full solution.
The only dierences are:
38 MONTE CARLO AND GRID-BASED TECHNIQUES FOR STOCHASTIC SIMULATION145
38
Monte Carlo and Grid-Based Techniques for Stochastic Simulation
In this problem you will compare the performance of random vs. regular sampling on a
specic stochastic dynamics proble
33 POSITIONING USING RANGING: 2D CASE
33
119
Positioning Using Ranging: 2D Case
1. Two sensors, denoted 1 and 2 and located at dierent locations in the x y plane,
make a range measurements to a target t. Let the range from Sensor 1 to the target
be r1 and
2.092/2.093
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I
FALL 2009
Quiz #2-solution
Instructor:
TA:
Prof. K. J. Bathe
Seounghyun Ham
Problem 1 (10 points):
1 x
y
1 x
f
his = 1 (1 y ) ; hi = 1 1+ .
4 2 2
4 2
his, x =
1
x
1
(1 y ) ; his, y = 1 .
4 2
8
29 FLIGHT CONTROL OF A HOVERCRAFT
29
98
Flight Control of a Hovercraft
You are tasked with developing simple control systems for two types of hovercraft moving
in the horizontal plane. As you know, a hovercraft rests on a cushion of air, with very little
37 NYQUIST PLOT
37
140
Nyquist Plot
Consider the attached images; here are a few notes. In the plant impulse response, the initial
condition before the impulse is zero. The frequency scale in the transfer function magnitude
plots is 103 104 radians per se
MATH-3000: Bridge
1.1. Propositions and Connectives
1.1. Propositions and Connectives
Denition. A proposition is a sentence that has exactly one truth value: it is either true (T) or
false (F).
Examples. . . .
Denition. Let P and Q be propositions.
The n
36 CONTROL OF A HIGH-SPEED VEHICLE
36
134
Control of a High-Speed Vehicle
An instability in certain aircraft and in some high-speed marine vehicles is characterized
by a pair of complex right-half plane poles, and is due to inadequate aerodynamic stabilit
43 SPECTRAL ANALYSIS TO FIND A HIDDEN MESSAGE
43
180
Spectral Analysis to Find a Hidden Message
As you know, the fast Fourier transform (fft() in MATLAB), turns time-domain signals x
into frequency-domain equivalents X. Here you will analyze a given signa
39 HURRICANE IDA WIND RECORD
39
156
Hurricane Ida Wind Record
The remnants of Hurricane Ida swept through Norfolk, Virginia during the period 10-15
November 2009, with 25cm of rain and high winds.The data le homework9.txt contains
wind data recorded at We
MATH-3000, Spring-2017
Homework #8
Your name:
MATH-3000 Bridge to Higher Mathematics
Homework 8 Section 4.1-4.2
Directions: Do the homework on your own paper and attach to this homework assignment
sheet. Clearly show all your work. For full credit, all yo
MATH-3000, Spring-2017
Homework #1
Your name:
MATH-3000 Bridge to Higher Mathematics
Homework 1 Sections 1.1-1.3
Directions: Do the homework on your own paper and attach to this homework assignment
sheet. Clearly show all your work. For full credit, all y
34 DEAD-RECKONING ERROR
34
124
Dead-Reckoning Error
An unmanned, untethered underwater vehicle operating near large metallic marine structures
has to navigate without a magnetic compass, and in some cases without any acoustic ranging
available. In these c
42 SUBMERGED BODY IN WAVES
42
174
Submerged Body in Waves
A xed, submerged body has a circular cross-section of constant diameter one meter, with
length twenty meters. For the calculations below, use the Morison formulation for waveinduced force, with Cd
30 DYNAMIC PROGRAMMING FOR PATH DESIGN
30
109
Dynamic Programming for Path Design
Given the transition costs in red, what are the maximum and minimum costs to get from
node 1 to node 11? This situation is encountered when planning paths for autonomous
age
Amendment to Problem Set 4
The previous equation has been changed to
be:
1
0 x1
1
e
1
x
= e
2
1
e
1
2 e
x
e
3
1.
=
0
1
0
x1
1
1
1 1 1 x = 1
2
1
2 1
x3
1
x1 =
3
x2 = 2
x3 = 6
=
1
0
x1
1
0
1 0 1 x = 0
2
35 LANDING VEHICLE CONTROL
35
129
Landing Vehicle Control
A controlled vehicle that is landing onto a target in the horizontal plane is equipped with
a vision-based navigation system. The system gives very good resolution at low altitudes,
2
but, unfortun
2.092/2.093
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I
FALL 2009
Quiz #1
Instructor:
TA:
Prof. K. J. Bathe
Seounghyun Ham
Problem 1 (10 points):
Consider the solution of the problem shown below. A rod is spinning in steady-state at rad/sec.
The rod is
44 FEEDBACK ON A HIGHLY MANEUVERABLE VESSEL
44
185
Feedback on a Highly Maneuverable Vessel
The directional behavior of a highly maneuverable vessel is modeled by
0.1s + 1
= 2
s + 0.6s 0.05
where the rudder deection is and the heading is . You note that b
32 MOTOR SERVO WITH BACKLASH
32
114
Motor Servo with Backlash
Consider the following: a motor is attached to a load through a gearbox, and the gearbox
has a backlash behavior. Physically, backlash is a decoupling of gear teeth (due to imprecise
meshing),
MATH-3000: Bridge
1.2. Conditionals and Biconditionals
1.2. Conditionals and Biconditionals
Denition. For propositions P and Q, the conditional statement P Q is the proposition
if P , then Q. In a conditional proposition P Q, P is called the antecedent an