Lecture 2 Understanding Vibrations Flashcards
Methods that vibrating systems store energy
potential energy (stiffness of spring) kinetic energy (mass or inertia)
What can be said about the transfer of energy for vibrations
vibrations involves transfer of energy between potential and kinectic
What do real systems do
also dissipate energy, through damping
What does being linear mean,
can analyse force and structure separately
can look at source, find magnitude and freq, then combine to see how structure will respond to particular source, with linearity can compare to any source
What are the main factors affecting vibration
response (due to structure mass stiffness damping)
Forcing excitation (source)
Path (how the two connect)
May have feedback (how the response affects the source)
What does a single event look like
single peak
What does a steady state signal look like
sine wave
what does an arbitrary signal look like
weird combinations of frequencies and magnitudes
general equation for sinusoidal motion
x = a sin(wt + phi)
where a is amplitude, w is frequency, t is time and phi phase shift
alternative form of sinusoidal motion (displacement)
x = Acos(wt) + Bsin(wt)
where A = a sin(phi) and B = a cos (phi)
Velocity equation and how is it found
x. = -Awsin(wt) + Bwcos(wt)
by taking the time derivative
Acceleration equation
x.. = - Aw^2 * cos (wt) - Bw^2 * sin(wt) = -w^2 x
eulers equation of sin and cos
e^j*theta = cos(theta) + j * sin(theta)
eulers equation of motion
x = a*e^jwt
x. = jwae^jwt = jw x
x. . = -w^2e^jwt = -w^2 x
what does eulers equation prove about direction of acceleration
if plot on an argand diagram you can see displacement and acceleration are always in opposite directions
what ways can vibrations systems be studied
time history - single response
frequency response - steady state vibration
joint time frequency analysis - arbitrary vibration
What does fourier transform allow
translate data between time and freq domains
What will a fourier transform show for a continuous sine wave at constant frequency
equal amplitude sing peak at same freq as the sine wave
draw the time history and freq response for continuous sine waves at multiple freq
see book
draw the time history and freq response for two sine waves at close freq
see book
individual parts of a linear system
can be analysed separately
any signal can be made up from
a series of sine waves
motion can be analysed using
trigonometric or complex exponential functions
The response of a structure to forcing depends on
mass stiffness and damping
