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Nonlinear Dynamic Behaviour of a Rectangular Thin Plate with a Bifurcation Diagram

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Engineering Design Applications

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 92))

Abstract

Nonlinear dynamics of rectangular isotropic thin plates with different boundary conditions are investigated. The plate governing equations of motion are nonlinear partial differential equation (PDE). The nonlinearity is caused by large deflection. The finite element method was used to discretize the continuous structures and convert the PDE into a second order ordinary differential equation (ODE).The implicit Newmark’s scheme and Newton-Raphson’s iteration were used to perform the time integration. Comparisons with the literature are presented in terms of backbone curve and frequency responses for three cases: (1) a simply supported plate with in-plane immovable edges, (2) out-of-plane restrained and in-plane immovable edges, (3) a fully clamped in-plane immovable edge. The model’s results showed excellent agreement, particularly for the first case, validating the procedure. Using the same set of results, bifurcation diagrams were extracted as well. The bifurcation diagrams are an important analysis tools extensively used in nonlinear dynamics showing in a glance the boundaries between different oscillatory modes. To the author’s knowledge, bifurcation diagrams have not been found for thin plates.

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Abbreviations

APDL:

Ansys parametric design language

BCM:

Boundary collocation method

BEM:

Boundary element method

FFT:

Fast Fourier transform

FEM:

Finite element method

ODE:

Ordinary differential equation

PDE:

Partial differential equation

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Acknowledgements

The support of this work by the faculty of aerospace and aeronautical engineering, Gaziantep University in Turkey, is gratefully acknowledged.

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Authors and Affiliations

  1. Gaziantep University, Gaziantep, Turkey

    Sohayb Abdul Karim

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  1. Sohayb Abdul Karim
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Correspondence to Sohayb Abdul Karim .

Editor information

Editors and Affiliations

  1. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen am Neckar, Germany

    Andreas Öchsner

  2. Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität, Magdeburg, Germany

    Holm Altenbach

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Abdul Karim, S. (2019). Nonlinear Dynamic Behaviour of a Rectangular Thin Plate with a Bifurcation Diagram. In: Öchsner, A., Altenbach, H. (eds) Engineering Design Applications. Advanced Structured Materials, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-79005-3_19

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  • DOI: https://doi.org/10.1007/978-3-319-79005-3_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-79004-6

  • Online ISBN: 978-3-319-79005-3

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