This Demonstration solves a Bessel equation problem of the first kind. The equation is for a thin elastic circular membrane and is governed by the partial differential equation in polar coordinates: ... . Here ... , a function of the coordinates and time, is the vertical displacement and ... , a constant independent of coordinates and time, which is determined by the density and tension in the membrane. The initial conditions are ... and ... , ... . In this example we assume circular symmetry. Thus the ... term can be removed from the equation, yielding the traditional form of Bessel's equation: ... . Using separation of variables with ... and the separation constant ... reduces the problem to two ordinary differential equations: ... , ... . The solution of these ODE equations is done using the techniques outlined in [1] for series solutions of ordinary differential equations. The general solution has the form: ... , ... . The boundary conditions that determine the constants ... , ... , ... , and ... are that ... , meaning that the function vanishes on the perimeter ... . The Bessel function of the first kind, ... , can be expressed by the series ... . Then with ... , ... , ... equal to the zeros of ... , the solution satisfying the boundary conditions is given by ... with ... .


    Education Levels:


      EUN,LOM,LRE4,work-cmr-id:262235,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/BoundaryValueProblemUsingSeriesOfBesselFunctions/,ilox,learning resource exchange,LRE metadata application profile,LRE


      Access Privileges:

      Public - Available to anyone

      License Deed:

      Creative Commons Attribution 3.0


      This resource has not yet been aligned.
      Curriki Rating
      'NR' - This resource has not been rated
      'NR' - This resource has not been rated

      This resource has not yet been reviewed.

      Not Rated Yet.

      Non-profit Tax ID # 203478467