Parametric Solutions to a Static Fourth-Order Euler–Bernoulli Beam Equation in Terms of Lamé Functions

  1. Ruiz, A. 1
  2. Muriel, C. 1
  3. Ramírez, J. 1
  1. 1 Universidad de Cádiz
    info

    Universidad de Cádiz

    Cádiz, España

    ROR https://ror.org/04mxxkb11

Libro:
Recent Advances in Pure and Applied Mathematics

Editorial: Springer

ISSN: 2509-8888,  2509-8896

ISBN: 9783030413200,  9783030413217

Año de publicación: 2020

Páginas: 93-103

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-030-41321-7_7 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

The exact general solution to a static fourth-order Euler–Bernoulli beam equation has been obtained and it has been written in terms of a fundamental set of solutions to a Lamé equation. This permits to express the general solution in parametric form in terms of Weierstrass elliptic functions. Three-parameter families of solutions have been also reported by setting particular values to one of the arbitrary constants of integration in the general solution. One of these families is expressed in terms of the Weierstrass ℘-function and ζ-function whereas two of them are given in terms of either trigonometric or hyperbolic functions. Graphical representations of particular solutions are also shown for different values of the arbitrary constants of integration.

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