Abstract
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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Acknowledgements
The authors acknowledge the financial support from FEDER–Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación by means of the project PGC2018-101514-B-I00; from the University of Cádiz PR2017-090 project and from Junta de Andalucía to the research group FQM–377. The authors also thank Prof. J.L. Romero from the University of Cádiz for his time and advice in the preparation of this contribution.
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Ruiz, A., Muriel, C., Ramírez, J. (2020). Parametric Solutions to a Static Fourth-Order Euler–Bernoulli Beam Equation in Terms of Lamé Functions. In: Ortegón Gallego, F., García García, J. (eds) Recent Advances in Pure and Applied Mathematics. RSME Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-41321-7_7
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