Results 1 to 8 of 8

Math Help - Can someone confirm my working out please

  1. #1
    Member
    Joined
    Apr 2009
    Posts
    108

    Can someone confirm my working out please

    The question comes something like this...

    The dynamic beam equation (without loading) for displacement

    is
    Given by d^2/dx^2 (I*E d^2u/dx^2)= A d^2u/dt^2

    Where I,A are constant and E is a function of x --> E(x)

    Find two ODE's by separation of variable..

    So I assumed the equation is in the form u(x,t)=B(x)*C(t)

    I find U(xx)= B''(x)C(t) and U(tt)=B(x)C''(t)

    Then I differentiate it again, but with E(x), using product rule

    I get

    I*C(t){B''''(x)E(x)+2B'''(x)E'(x)+B''(x)E''(x)}=A* B(x)*C''(t)

    I separate C(t) and B(x) and then equate everything to a constant say Z, then I get this...

    B''''E+2B'''E'+B''E''=IZ/A *B

    C''=I*Z/A * C

    I'm not sure, because my first equation is non linear?

    But I feel confident it's right.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I'm not sure, because my first equation is non linear?
    Why do you say that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2009
    Posts
    108
    I never liked non linear equations to be honest, they seem to always bring problems... hence getting it wrong.

    But I feel everything I've done seems ok....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I'm saying I don't think your equation is nonlinear. Why do you think it is?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Apr 2009
    Posts
    108
    Hmmm.. I see, I interpreted B''''E as x*y, they are both a function of x.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Well, even in looking at the original pde: it's linear in u. u and none of its derivatives appear to anything except the first power, and there are no functions of u or any of its derivatives. It's a linear pde.

    I think everything in the OP is fine, until you get to the separation step. The parameters I and A should only appear in one or the other of the B and C ordinary differential equations. Also, double-check what's in the numerators and the denominators of those ode's.

    Incidentally, a pde being nonlinear does not imply that separation of variables won't work. It probably won't work. Dym's equation is a (rare) nonlinear pde that succumbs to separation of variables.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Apr 2009
    Posts
    108
    Thanks for your input

    Your a champ!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're welcome. Did you have any other questions? Did you get your final answer?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Please confirm this for me :)
    Posted in the Algebra Forum
    Replies: 6
    Last Post: February 20th 2010, 05:46 AM
  2. is this correct,please help confirm
    Posted in the Calculus Forum
    Replies: 10
    Last Post: February 16th 2010, 05:36 AM
  3. can someone confirm this
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 30th 2009, 12:16 PM
  4. can someone confirm this
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2009, 10:36 AM
  5. can someone confirm that this is right
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 27th 2009, 12:11 PM

/mathhelpforum @mathhelpforum