Closed-Form Solution for the Eigenmodes of Euler-Bernoulli Beams in Pinned-Pinned-Free Configuration | IEEE Conference Publication | IEEE Xplore

Closed-Form Solution for the Eigenmodes of Euler-Bernoulli Beams in Pinned-Pinned-Free Configuration


Abstract:

Euler-Bernoulli beams are commonly used elements in modeling the dynamics of mechanical structures. For static boundary conditions, the beam dynamics are well understood ...Show More

Abstract:

Euler-Bernoulli beams are commonly used elements in modeling the dynamics of mechanical structures. For static boundary conditions, the beam dynamics are well understood and analytical expressions for the normalized eigenmodes and characteristic equations are available. Until now, cantilever beams as shown in Fig. 2, are modeled as a series connection of two general beams and solved numerically. This paper provides an analytical solution for the normalized eigenmodes of cantilever beams with inner pinned support at an arbitrary position. The eigenfrequencies can be computed by finding the roots of an analytically given characteristic equation. Using a provided solution interval for each root, it is possible to compute each eigenfrequency within a fixed number of iterations for any given precision in a deterministic way.
Date of Conference: 19-21 August 2019
Date Added to IEEE Xplore: 05 December 2019
ISBN Information:
Conference Location: Hong Kong, China

References

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