Homotopy analysis of a forced nonlinear beam model with quadratic and cubic nonlinearities

• Autorzy: Shahlaei-Far S. , Nabarrete A. , Balthazar J. M.

Identyfikatory

DOI

10.15632/jtam-pl.54.4.1219

• Języki publikacji: EN

Abstrakty

EN

This study investigates forced nonlinear vibrations of a simply supported Euler-Bernoulli beam on a nonlinear elastic foundation with quadratic and cubic nonlinearities. Applying the homotopy analysis method (HAM) to the spatially discretized governing equation, we derive novel analytical solutions and discuss their convergence to present nonlinear frequency responses with varying contributions of the nonlinearity coefficients. A comparison with numerical solutions is conducted and nonlinear time responses and phase planes are compared to the results from linear beam theory. The study demonstrates that apart from nonlinear problems of free vibrations, HAM is equally capable of solving strongly nonlinear problems of forced vibrations.

Słowa kluczowe

EN

forced nonlinear vibration; HAM; quadratic and cubic nonlinearities; Galerkin method

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2016
• Tom: Vol. 54 nr 4
• Strony: 1219--1230
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Shahlaei-Far S.

• Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil

autor

Nabarrete A.

• Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil

autor

Balthazar J. M.

• Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.