Darren Aiken
EML5223
1/18/2006
HOMEWORK 1:
Problem 1.6:
Derive the equation of motion of the compound pendulum consisting of uniform
rod and disk.
Summing moments, we have:
F d = IO
(1)
where F is the moment force due to gravity, d is the distance to the
Problem 3.1
A Control tab of an airplane elevator is hinged about an axis in the elevator,
shown as point O in Fig 3.28.
Calulate the natural frequency wn of the control tab in terms of wr and the
parameters of the experimental setup.
2
Equilibrium Moment
Structural Dynamics HW #6
Name: HyoSoo Kim
Date: 02/27/2006
Problem 7.13
Derive the stiness matrix for the system by means of potential energy expression
potential energy of the system from the free-body-diagram
V=
1
[k1 x2 +k2 (x2 x1 )2 +k3 (x3 x2 )2 +:+
EML 5223 Structural Dynamics
HW 5
Gun Lee
UFID# 8195-4073
Problem 6.2
m1 = 0.5 , m 2 =m -> Equilibrium position
L
L
L
y2
y1
m2
m1
L
L
T
L
y2
y1
T
T
m2 g
m1 g
Principle of virtual work:
y
W = m1 g T 1 + T
L
y2 y1
y2
y y
T 2 1 y2 = 0
y1 + m2 g T
L
L
L
Structural Dynamics
EML5223
Bret Stanford
HW 8
March 22nd, 2006
8.4) Use the Newtonian approach to derive the boundary-value problem for a shaft in torsional vibration
restrained by torsional springs at both ends.
Looking at a differential element of the
Gregory Garcia
Structural Dynamics HW 7
Due 3/8/06
Problem 7.43
Given: The system shown in the figure below.
Find: a) Estimates of the 2 lowest natural frequencies of the system shown above
b) Calculate error incurred and draw conclusions regarding suitab
4-3-2006
Name:
IN TERM EXAM
1. The string in the figure is in constant tension T. Derive the Lagrange equations of
motion (i.e., from Hamiltons principle) for the case of m1=m2=m, L1=L2=L3=L
to obtain
2T
T
mx1 +
x1 x2 + mg = F1
L
L
2T
T
mx2 x1 +
x2 + mg =
Homework #4
Name: HyoSoo Kim
UFID:8989-3565
Date:02/06/2006
Problem 4.4
Derive the ramp response by nding the particular and homogeneous
solutions of the ordinary di. equation.
The unit ramp fuction is
r(t) = tu(t)
(1)
from t = 0
For a viscously damped si
Darren Aiken
EML5223
1/18/2006
HOMEWORK 1:
Problem 1.6:
Derive the equation of motion of the compound pendulum consisting of uniform
rod and disk.
Summing moments, we have:
F d = IO
(1)
where F is the moment force due to gravity, d is the distance to the
EML 5223 Structural Dynamics
H.W. #2 Problems 2.5, 2.19, 2.24, 2.26. Due 1/23
Gun Lee
Problem 2.5
Determine the natural frequency of the system for the gear ratio RA / RB = n = 2 . The
gears are made of the same material and have the same thickness.
A
k e
Structural Dynamics HW #6
Name: HyoSoo Kim
Date: 02/27/2006
Problem 7.13
Derive the stiness matrix for the system by means of potential energy expression
potential energy of the system from the free-body-diagram
V=
1
[k1 x2 +k2 (x2 x1 )2 +k3 (x3 x2 )2 +:+
Structural Dynamics
EML5223
Bret Stanford
HW 8
March 22nd, 2006
8.4) Use the Newtonian approach to derive the boundary-value problem for a shaft in torsional vibration
restrained by torsional springs at both ends.
Looking at a differential element of the
The two results can be combined to obtain the characteristic equation
It is:
smh {3L cos L 5111 .815) sm L cosh [3L + smh L) : (J
For k = 0.5 EI/L, the roots are 61L = 3.2136, 62L = 6.3212, 53L = 9.4505, The
natural modes and natural frequencies a
4-3-2006
Name:
IN TERM EXAM
1. The string in the figure is in constant tension T. Derive the Lagrange equations of
motion (i.e., from Hamiltons principle) for the case of m1=m2=m, L1=L2=L3=L
to obtain
2T
T
mx1 +
x1 x2 + mg = F1
L
L
2T
T
mx2 x1 +
x2 + mg =
EML 5223 Structural Dynamics
H.W. #2 Problems 2.5, 2.19, 2.24, 2.26. Due 1/23
Gun Lee
Problem 2.5
Determine the natural frequency of the system for the gear ratio RA / RB = n = 2 . The
gears are made of the same material and have the same thickness.
A
k e
Gregory Garcia
Structural Dynamics HW 7
Due 3/8/06
Problem 7.43
Given: The system shown in the figure below.
Find: a) Estimates of the 2 lowest natural frequencies of the system shown above
b) Calculate error incurred and draw conclusions regarding suitab
Solution of first in-term exam
1. Done as example on 1/25.
(a) The equation of motion is mx + cx + k1 x = F (t ) . Here, F(t)=k2(y-x).
(b) The constant term in the Fourier series of y is its average B+0.5A. So the first
term of the response is the steady
EML 5223 Structural Dynamics HW 10
Gun Lee(UFID8195-4073)
Problem 9.1 Tubular shaft of radius r ( x ) = r[1 + x ( L x ) / L ] , thickness t , mass per unit volume
2
modulus G . t
r ( x) . Shaft is symmetric with respect to x = L / 2 .
Mass moment of inert
Problem 3.1
A Control tab of an airplane elevator is hinged about an axis in the elevator,
shown as point O in Fig 3.28.
Calulate the natural frequency wn of the control tab in terms of wr and the
parameters of the experimental setup.
2
Equilibrium Moment