Homework 1 - Solution
1. For the given second order ordinary differential equation with initial conditions x 4x 20x 3 sin 5t, x0 1, x0 -1 we first formulate the general solution as the superposition of homogeneous and particular solutions: x
ME 3504
3rd ed. In [
HW 10
Kirk
]
HW instructions for Chapter 4 concerning MDOF systems:
See latest posted syllabus on course web page for due date.
Prob 4.1 [4.1] as text indicates, only taken up if assigned in lecture
Prob 4.2 [4.2] as text indicates
Pr
To: 3504
From: R. G. Kirk
Date:
2008
Subject: ME3504 Vibrations HW no. 11 Assignment
Reference: Inman 2nd ed., Engineering Vibrations Selected Problem ( modified ),
J. P. den Hartog notes on damped absorber design, class notes and discussion
See latest po
ME 3504: DYNAMIC SYSTEMS VIBRATIONS
CRN 14451
Spring: 2012
Randolph 331
8:00 9:15 AM
Professor Kirk
COURSE POLICIES AND COURSE INFORMATION
Objectives:
The broad objective of this course is to apply the science of dynamics to engineering
problems. You will
Tacoma Narrows Failure
http:/www.youtube.com/watch_popup?v=j-zczJXSxnw&pop_ads=0
The technical version of resonance:
http:/www.youtube.com/watch?v=17tqXgvCN0E&NR=1
The fun version:
http:/www.youtube.com/watch?v=yFeqDmlR1rs
Resonance of a complex structure
MATLAB
SIMULINK
Sample Code
May be useful for
HW 4
and/or
MSP1
ME3504
SS
2004
Example Euler and modified Euler calculations
SIMULINK called from MATLAB
Use of ode45 function for MATLAB time step integration of equations
2 June 2004
R. G. Kirk
1
Euler and
To get started, type one of these: helpwin, helpdesk, or demo.
For product information, type tour or visit www.mathworks.com.
help ode45
version 5 wording
ODE45 Solve non-stiff differential equations, medium order method.
[T,Y] = ODE45('F',TSPAN,Y0) with
ME 3504/3514
Vibrations / Systems Dynamic
R. G. Kirk
8-26-99/ S 2012
Laws of Mechanics
1.
Newton's 1st Law: Definition of Momentum, mv . A body at rest or in motion will
remain at rest or in motion unless acted upon by some external force.
2.
Newton's 2nd
ME 3514 Fall 2003
R. G. Kirk
MATLAB or SIMULINK or a combination of both can be
very powerful to solve many engineering problems.
The following examples will illustrate how you can solve simple time integration
problems using these tools. The total soluti
ME 3504
rd
3 ed. In [
VIBRATIONS
RGK
]
Homework no. 1 for ME 3504.
For due date, see web page.
Problem 1.2 [1.2]
Do not work the text problem, do the following:
(a) Include a viscous damping to ground term, then solve in general terms, by the
undetermined
ME 3504
rd
3 ed. In [
RGK
VIBRATIONS
]
Homework no. 2 for ME 3504
For due date see web page
The problems as assigned, but solved by two methods.
1.47 [1.52] a) b) please add a torsional spring, K-theta, at the support point of pendulum.
1.49 [1.54] a) b)
ME 3504
3rd ed. In [
HW 9
Kirk
]
HW for Chapter 5 concerning Isolation Design:
See latest posted syllabus on course web page for due date.
Prob 5.2 [5.2]
Work only if assigned in lecture.
We will discuss this in class prior to your working on your solutio
ME 3504
3rd ed. In [
HW 8
Kirk
]
See latest posted syllabus on course web page for due date.
The problems are as follows:
Prob. 3.24 [3.28]
Derive the expressions for a sub n and b sub n for the square wave.
Why is a sub 0 equal to zero ? write the integr
ME 3504
HW 7
rd
3 ed. In [ ]
HW from current syllabus for Chapter 3 concerning Convolution Integral:
See latest posted syllabus on course web page for due date.
Kirk
Prob 3.5 [3.5] Be able to work, this one will not be turned in for grade.
Prob 3.6 [3.6]
Homework 6 - Solution
1. Draw the FBDs for the two blocks:
x2 x1 m2 k2 x2
c ( x2 - 2 x1 )
k1 x1 r C F
m1
Note that the displacement at the top of the disk is twice the displacement x 1 at the disk's center. Apply Newton's 2nd law: M C J C
Homework 3 - Solution
1. The equation of motion for the free vibration of the underdamped shock absorber is mx cx kx 0 x 2 n x 2 x 0, IC: x 0 0 and 0 n (a) The system parameters stiffness and damping coefficient based on the design spec
Homework 5 - Solution
1. (a) The system is shown here again with additional variables:
A B
m m
4r
r
k
x
kT
O
The total kinetic energy has three parts: rotational kinetic energy of the rod, as well as translational and rotational kinetic ene
Homework 2 - Solution
1. The response can be plotted from the solutions of the equation of motion for different damping ratios: (I) Overdamped case: 1: xt - 2 - 1 n x 0 - 0 2 n - 1
2
e
1t
2 - 1 n x 0 0 2 n - 1
2
e 2t
where 1 -
Chapter 2 The Laplace Transform
Objective: Mathematical preparation for the study of next chapters Contents: 2.1 Introduction 2.2 2 2 Complex Numbers and Harmonic Motion 2.3 Laplace Transformation 2.4 Inverse Laplace Transformation p 2.5 Solving Line
Chapter 2 The Laplace Transform
Objective: Mathematical preparation for the study of next chapters Contents: 2.1 Introduction 2.2 Complex Numbers and Harmonic Motion 2.3 Laplace Transformation 2.4 Inverse Laplace Transformation 2.5 Solving Linear Dif
2.5 Solve ODE by Laplace Transform
Example
+ 2 x + 10 x = 0 x x(0) = 0 x ( 0) = 1
Laplace:
solution
L [ + 2 x + 10 x ] = L [0] x
s 2 X s sx(0) x(0) + 2[sX s x(0)] + 10 X s = 0
PFE:
1 s 2 + 2 s + 10 1 1 3 Xs = = ( s + 1) 2 + 32 3 ( s + 1)
Chapter 2 The Laplace Transform
Objective: Mathematical preparation for the study of next chapters Contents: 2.1 Introduction 2.2 2 2 Complex Numbers and Harmonic Motion 2.3 Laplace Transformation 2.4 Inverse Laplace Transformation p 2.5 Solving Line
ME 3504
3rd ed. In [
]
R. G. Kirk
HW no. 3
See latest posted syllabus on course web page for due date.
Problems 1.69, 1.72, [1.78, 1.81]
log decrement problems
Following Problems as instructed here:
Problems 1.73 [1.82]
Design work for system parameters
U
ME 3504
3rd ed. In [
HW no. 4
Vibrations
Dr. Kirk
]
See latest posted syllabus on course web page for due date.
Syllabus Problem 1.84 + [1.95 +]
The plus sign means the following:
The equivalent car mass m, equivalent car stiffness k, and equivalent car d
ME 3504
3rd ed. In [
]
HW no. 5 ( from Chapter 2):
R. G. Kirk
See latest posted syllabus on course web page for due date.
Prob 2.21[2.26] optional; extra credit for a complete derivation and comparison to
Inman solution as given by Eq 2.30 [2.38], page 99
ME 3504
3rd ed. In [
R. G. Kirk
]
HW no. 6-a change from current syllabus ( from Chapter 2):
See latest posted syllabus on course web page for due date.
Prob 2.22 [2.27] Solve for damping as requested in statement of problem.
Prob 2.23 [2.28] Not on sylla
ME 3504
3rd ed. In [
R. G. Kirk
]
HW no. 6-b ( from Chapter 2):
See latest posted syllabus on course web page for due date.
Prob 2.43 [2.51]
as is, can it be
Prob 2.45 [2.53]
as is, can it be
Prob 2.48 [2.56]
Please over plot with legend in MATLAB for
zet