asymmetric damping matrix 2

[castwerks]

I'm having a hard time wrapping my head around the concept of an asymetric damping matrix.

What would be a good real world example of this?

Could distributing stiffness and damping coefficients over a finite area (for use in a FE model) produce these asymmetric matrices?

 

[GregLocock]

I don't know of an example, but I don't think an FE model is going to do it

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[electricpete]

An asymmetric matrix can be decomposed into a symmetric matrix plus a skew-symmetric matrix (A[i,j]=-A[j,i]).

Gyroscopic effects in rotating machinery are represented by skew-symmetric terms in the damping matrix.


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(2B)+(2B)' ?

 

[electricpete]

Some interesting tid-bits which are nicely described Adams in "Rotating Machinery Vibration".

Symmetric terms in the stiffness matrix represent conservative forces.
Example: typical spring behavior.

Symmetric terms in the damping matrix represent non-conservative forces.
Example: typical damping behavior.

Skew symmetric terms in the stiffness matrix represent non-conservative forces.
Example: gyroscopic effect. Note that we use "forces" in the generalized sense.
Something like:
d^2/dt^2 (I * theta_x) - w*I*theta_y = Mx
d^2/dt^2 (I * theta_y) + w*I*theta_x = My
where theta_x and theta_y are tilt angle of the disk

Skew symmetric terms in the damping matrix represent conservative forces.
Example: skew-symmetric component of fluid bearing stiffness. Radial displacement of CCW rotating shaft in the x direction causes force in the y direction (oil flows tangentially in the clearance).


=====================================
(2B)+(2B)' ?

 

[electricpete]

d^2/dt^2 (I * theta_x) - w*I*theta_y = Mx
d^2/dt^2 (I * theta_y) + w*I*theta_x = My

Clarification - w here represents radian speed of rotation (not radian frequency of vibration)


=====================================
(2B)+(2B)' ?

 

[electricpete]

Sorry, I had my last two examples swapped. Corrected in bold below and added a few details:

Some interesting tid-bits which are nicely described Adams in "Rotating Machinery Vibration".

Symmetric terms in the stiffness matrix represent conservative forces.
Example: typical spring behavior.

Symmetric terms in the damping matrix represent non-conservative forces.
Example: typical damping behavior.

Skew symmetric terms in the stiffness matrix represent non-conservative forces.
Example: skew-symmetric component of fluid bearing stiffness. Radial displacement of CCW rotating shaft in the x direction causes force in the y direction (oil flows tangentially in the clearance). Radial displacement in y direction causes force in -x direction
Fy = Kxy * x
Fx = - Kxy * y

Skew symmetric terms in the damping matrix represent conservative forces.
Example: gyroscopic effect. Note that we use "forces" in the generalized sense.
Something like:
d^2/dt^2 (I * theta_x) - w*I*theta_y = Mx
d^2/dt^2 (I * theta_y) + w*I*theta_x = My
where theta_x and theta_y are tilt angle of the disk

=====================================
(2B)+(2B)' ?