SECTION 1
REVIEW OF FUNDAMENTALS
S1-1
SINGLE DOF SYSTEM
This section will introduce the basics of Dynamic
Analysis by considering a Single Degree of Freedom
(SDOF) problem
Initially a free vibration model is used to describe the
natural frequency
Damping
Free Vibration Response of SDOF
Systems
Response: Free or forced
In this chapter: Free response, i.e. no
external forces are applied.
k
c
m
mx cx kx 0
x 2 n x n 2 x 0
k
natural frequency
m
c
damping ratio
2 km
n
We know from theory of DE that
Character
FORCED VIBRATIONS
INTRODUCTION
When a mechanical system undergoes free vibrations, an initial force (causing some
displacement) is impressed upon the system, and the system is allowed to vibrate under the
influence of inherent elastic properties. The syst
CHAPTER 11 FORCED VIBRATION (SINGLE DEGREE OF FREEDOM SYSTEM)
In this chapter, the steady state response of harmonically excited single degree of freedom
systems will be discussed. Simpler phasor diagram method will be used to obtain the steady state
resp
FORCED VIBRATION &
DAMPING
Damping
a process whereby energy is taken from the
vibrating system and is being absorbed by
the surroundings.
Examples of damping forces:
internal forces of a spring,
viscous force in a fluid,
electromagnetic damping in galvano
7.9 Examples of forced
vibration
Manhattan Press (H.K.) Ltd.
1
7.9 Examples of forced vibration (SB p. 291)
Examples of forced vibration
1. Bridges
Crosswind in valley caused the bridge to
Go to
resonate and collapse
More to Know 3
Manhattan Press
2
7.9
Ch3.9:ForcedVibrations
We continue the discussion of the last section, and now
consider the presence of a periodic external force:
m u (t ) u (t ) k u (t ) F0 cos t
Forced Vibrations with Damping
Consider the equation below for damped motion and external
SECTION 1
REVIEW OF FUNDAMENTALS
S1-1
SINGLE DOF SYSTEM
This section will introduce the basics of Dynamic
Analysis by considering a Single Degree of Freedom
(SDOF) problem
Initially a free vibration model is used to describe the
natural frequency
Damping
MAK4041-Mechanical
Vibrations
Important Notes:
The course notes were
compiled mostly from
1) The book by Graham
Kelly, Mechanical
Vibrations, Theory and
Applications, 2012.
2) Bruel Kjaer Technical
notes,
3) Dan Russels webpage:
http:/www.acs.psu.edu/dru
Indian Institute of Technology Kharagpur
Development of Low Noise High
Pressure Fuel Pump for GDi
Engine Applications
KUMAR SAURABH
16ME63R51
M.Tech First Year in Mechanical Systems Design
Department of Mechanical Engineering
isolated from engine vibratio
Solving the Harmonic Oscillator
Sava Dediu
CRSC/SAMSI, May 22 2006
Contents
1.
2.
3.
4.
5.
6.
7.
Simple illustrative example: Spring-mass system
Free Vibrations: Undamped
Free Vibrations: Damped
Forced Vibrations: Beats and Resonance
Will this work for th
%given values
M=4;
k=305;
wn=sqrt(k/M);
disp(['Natural Frequency=', num2str(wn)]);
n=input('Enter value of n(INTEGER B/W (-5,0) in m=M/p in which p = 10^n, n =
');
p = 10^n;
m = M/p;
e=input('enter eccentricity of
mass from the rotating centre, e = ');
L=
SECTION 1
REVIEW OF FUNDAMENTALS
S1-1
SINGLE DOF SYSTEM
This section will introduce the basics of Dynamic
Analysis by considering a Single Degree of Freedom
(SDOF) problem
Initially a free vibration model is used to describe the
natural frequency
Damping