Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
32 Cards in this Set
- Front
- Back
|
Euler's identity
|
e^(i*theta) = cos(theta) + i*sin(theta)
|
|
|
Natural frequency for x(t)=2*e^(i5t) + 2*e^(-i5t)
|
5 rad/s
|
|
|
omega_d
|
omega_d = omega_n * sqrt(1-zeta^2)
|
|
|
Is x(t)=2*e^(i5t) + 2*e^(-i5t) un, under, critically,or over damped?
|
Undamped because eigenvalues have no real part
|
|
|
Damping from eigenvalues
|
Over/under: complex roots
critical: only real undamped: only imaginary |
|
|
Phase angle of cosine form of x(t)=2*e^(i5t) + 2*e^(-i5t)
|
Because it is 4cos(5t) then phi is 0. if it were -4cos(5t) it would be pi radians
|
|
|
a FRF represents
|
signal gain (magnitude) and signal phase shift (phase angle)
|
|
|
Magnitude of complex number a+ib
|
sqrt(a^2 + b^2)
|
|
|
Tangent of complex number a+ib
|
tan = b/a
|
|
|
Complex number 2+i2 in complex form
|
2sqrt(2)*e^i*(pi/4) (equals magnitude * e^i*theta)
|
|
|
T/F: if a system with damping is subject to harmonic forcing fcos2t then xc is xcos2t
|
false. That would be the particular solution.
|
|
|
T/F: If a system with proportional damping is subject to harmonic forcing fcos2t then Utilde (mass normalized modeshape matrix) cannot be used to decouple because there is damping
|
False. If M and K are symmetric and C is proportional, and all 3 are diagonal, then the equations are decoupled.
|
|
|
Eigenvector equation
|
(lambda^2 * M + lambda * C + K)*a = 0
|
|
|
characteristic determinant
|
det(lambda^2 * M + lambda * C + K)
|
|
|
characteristic equation
|
det(lambda^2 * M + lambda * C + K) = 0
|
|
|
modeshape equation
|
(k-omega^2*M)*m = 0
|
|
|
Coupled v uncoupled
|
only uncoupled if M, C and K matrices are all DIAGONAL
|
|
|
T/F: Utilde can be used to diagonalize M into identity matrix
|
True
|
|
|
Matrix equation for Xbar of xp with forcing fbarsin5t
|
xbar=(-25M + i5C + K)^-1*fbar
|
|
|
If eigenvalues are pure imaginary, what is C?
|
zero matrix because it's undamped
|
|
|
Matrix expression giving x_free for (zdot)=Az+Ef
|
x_free=[I O]e^At * z(0)
|
|
|
Name the mode associated with zero natural frequency
|
rigid body mode
|
|
|
Name the mode associated with the nonzero natural frequency
|
breathing mode
|
|
|
Modeshape associated with omega=0
|
m=1;1;...n (column matrix, nDof would be n 1's tall)
|
|
|
What does zero natural frequency mean?
|
system is unconstrained in that mode
|
|
|
Is decoupling still useful for repeated natural frequencies?
|
Yes
|
|
|
T/F: In general, xp is the same as xforced
|
False
|
|
|
T/F: in general, xp and xforced approach each other asymptotically as time incresaes?
|
True
|
|
|
T/F: For a damped system, xc and xfree both approach zero as time increases?
|
True
|
|
|
T/F: For a damped system, xp always approaches zero as time increases?
|
False
|
|
|
Complete the convolution equation:
f(t) * g(t) = integral( |
=integral[0;t] ( f(tau) * g(t-tau) dtau )
|
|
|
What does a vibration absorber do in the frequency band called its bandwidth?
|
It suppresses the system response.
|
