FUNDAMENTAL EQUATIONS OF VIBRATIONS
Free Vibration of Single-Degree-of-Freedom Systems
Equation of Motion: mx cx kx 0
k
c
; ; cc 2m n ; d n 1 2
m
cc
n
Underdamped Response
xt Ae
nt
v0 n x0 2 x0 d 2
sind t ; A
2
d
; tan 1
x 0 d
v0 n x0
Critically Damped
m
MEMB343 MECHANICAL VIBRATIONS
TEST (4th of December 2014)
1. The free vibration reSponse of a spring mass damper system is observed to have a
frequency of 2 rad/s, an amplitude of 10 mm, and a phase shift of 1 rad, from time t=0.
Assuming that the dam
MEMB443
Mechanical Vibrations
HARMONICALLY EXCITED
VIBRATION OF SINGLE-DEGREEOF-FREEDOM SYSTEMS
RESPONSE DUE TO BASE EXCITATION
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Differentiate betwe
MEMB443
Mechanical Vibrations
HARMONICALLY EXCITED
VIBRATION OF SINGLE-DEGREEOF-FREEDOM SYSTEMS
DAMPED FORCED VIBRATIONS
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Compute the homogeneous (t
MEMB443
Mechanical Vibrations
HARMONICALLY EXCITED
VIBRATION OF SINGLE-DEGREEOF-FREEDOM SYSTEMS
RESPONSE DUE TO ROTATING
UNBALANCE
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Differentiate be
MEMB443
Mechanical Vibrations
HARMONICALLY EXCITED
VIBRATION OF SINGLE-DEGREEOF-FREEDOM SYSTEMS
UNDAMPED FORCED VIBRATIONS
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Compute the homogeneous
MEMB443
Mechanical Vibrations
FREE VIBRATION OF SINGLEDEGREE-OF-FREEDOM SYSTEMS
DAMPED FREE VIBRATIONS
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Determine the equation of motion of a damped
MEMB443
Mechanical Vibrations
FREE VIBRATION OF SINGLEDEGREE-OF-FREEDOM SYSTEMS
ENERGY METHOD
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Derive the equation of motion of a single-degree-of-f
MEMB443
Mechanical Vibrations
FUNDAMENTALS OF
VIBRATIONS
SIMPLE HARMONIC MOTION
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Determine if a vibration motion can be classified as simple
harmoni
MEMB443
Mechanical Vibrations
FUNDAMENTALS OF
VIBRATIONS
BASIC CONCEPTS
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Understand the concepts of degree-of-freedom, and discrete
and continuous s
MEMB443
Mechanical Vibrations
FREE VIBRATION OF SINGLEDEGREE-OF-FREEDOM SYSTEMS
UNDAMPED FREE VIBRATIONS
MEMB443
Mechanical Vibrations
LEARNING OBJECTIVES
Upon completion of this lecture, you should be able to:
Determine the equation of motion of an und