Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

3d mass-spring-damper

  1. Dec 4, 2005 #1

    dduardo

    User Avatar
    Staff Emeritus

    I know a 2d mass-spring-damper is expressed:

    F = m g j − k D (sin θ i + cos θ j) − b (Vx i + Vy j)

    m = mass
    g = gavity
    k = spring constant
    D = string length displacement
    Vx = Velocity X
    Vy = Velocity Y

    But how would you extend this to three dimensions?
     
  2. jcsd
  3. Dec 4, 2005 #2

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    You'll just need to express the components of the radial vector using polar and azimuth angles: [itex](\sin \theta \cos \phi, \sin \theta \sin phi, \cos \phi)[/itex] where z is "up."

    ([itex]\theta[/itex] is the polar angle and [itex]\phi[/itex] is the azimuthal angle in standard spherical coordinates.)
     
  4. Dec 4, 2005 #3

    dduardo

    User Avatar
    Staff Emeritus

    Ah, spherical coordinate system. I should have realized that. So it should be the following for a case where the spring is anchored from above and the mass is dangling:

    m (ax i + ay j + az k) = m g j − k D (sin(θ)cos(phi) i + sin(theta)sin(phi) j + cos(phi) k) − b (Vx i + Vy j + Vz k)

    Now let's say a spring-damper is added to each face of a cube. I guess you could consider this new system a spring lattice but the ends of the springs are anchored instead of going to other masses. Could you apply a perpendicular rotation to the equation above for each face and sum up the forces due to each spring?

    Just a note: I would eventually want to linearize the system by assuming very small deflections.
     
    Last edited: Dec 4, 2005
  5. Dec 4, 2005 #4

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    Sure, you could do that. It sounds like you're trying to analyze the motion of an atom in a lattice?
     
  6. Dec 4, 2005 #5

    dduardo

    User Avatar
    Staff Emeritus

    No i'm trying to model the motion of the mass inside of a 3d MEMS (Micro electro-mechanical system) accelerometer. The system is basically composed of a cube in the center that is held in place by piezoelectric bridges. When the bridges are compressed they generate a voltage. Based on position of the mass I can figure out what type of votage i'm generating which thus tells me the acceleration.
     
    Last edited: Dec 4, 2005
  7. Nov 20, 2008 #6
    Mr dduardo you did not mentioned what does 'F' mean here ?
     
  8. Nov 20, 2008 #7
    I am looking for a finite element model (actually a 2D spring mass lattice model which has springs not only at its sides but also 4 sides spring crossings at the center like 'x' or 2 sides spring crossings at the center like '/'), can be extended upto infinite length. I need the equations of motion for frequency and (phase)velocity with pre-stress and stressed conditions.
    If any body does know any helping material, paper, book, website or software for this. Then let me know, it would be a nice help for me.Thanks !
     
  9. May 2, 2010 #8
    how would you do the same for an n-dimensional case?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?