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

DOI10.1007/978-3-030-41321-7_7zbMath1453.34001OpenAlexW3015545068MaRDI QIDQ5119622

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Publication date: 31 August 2020

Published in: Recent Advances in Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-41321-7_7

zbMATH Keywords

exact general solutionWeierstrass \(\mathcal{P}\)-functionstatic fourth-order Euler-Bernoulli beam equation

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Lamé, Mathieu, and spheroidal wave functions (33E10)

Uses Software

• DLMF

Cites Work

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• A note on the integrability of a remarkable static Euler-Bernoulli beam equation
• Solvable structures associated to the nonsolvable symmetry algebra \(\mathfrak{sl}(2,\mathbb{R})\)
• Integrability by quadratures for systems of involutive vector fields
• Dynamic Euler-Bernoulli beam equation: classification and reductions
• Exact general solution and first integrals of a remarkable static Euler-Bernoulli beam equation
• Symmetry analysis of a class of autonomous even-order ordinary differential equations
• Lie and Noether symmetries for a class of fourth-order Emden–Fowler equations
• Invariant boundary value problems for a fourth-order dynamic Euler-Bernoulli beam equation
• Symmetries and integrability of a fourth-order Euler–Bernoulli beam equation
• First integrals and parametric solutions of third-order ODEs admitting $ {\mathfrak{sl}(2, \mathbb{R})} $
• DYNAMICS OF TRANSVERSELY VIBRATING BEAMS USING FOUR ENGINEERING THEORIES
• Unbestimmte Integrale