Eigenvalue Problems of Vibrations and Stability

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Notes

Actually \( (EI\varphi^<\prime\prime>)^ <\prime\prime>= \omega^ \rho A\varphi \) leads to \( EI\varphi^ <\prime\prime \prime\prime>+ 2EI^<\prime>\varphi^ <\prime\prime\prime>+ EI^<\prime\prime>\varphi^ <\prime\prime>= \omega^ \rho A\varphi , \) while (2.119) ignores (to keep the example simple) the 2nd and 3rd term of the left-hand-side, which are zero everywhere except at the discontinuous jumps in EI, i.e. at \( x = \tfracl(1 \pm \varepsilon ). \) The consequence of this for the accuracy in results is not obvious. You could compare to exact results, e.g. by Krishnan (1998), and also see Jang and Bert (1989).

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Authors and Affiliations

  1. Section of Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark, Lyngby, Denmark Jon Juel Thomsen
  1. Jon Juel Thomsen