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Exact Solution of Bending Free Vibration Problem of the FGM Beams with Effect of Axial Force

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Computational Modelling and Advanced Simulations

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 24))

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Abstract

In this contribution a fourth-order differential equation of the functionally graded material (FGM) beam deflection with longitudinal variation of the effective material properties has been derived where the second order beam theory has been applied for establishing the equilibrium- and kinematics beam equations. Not only the shear forces deformation effect and the effect of consistent mass distribution and mass moment of inertia but also the effect of large axial force has been taken into account. Numerical experiments will be done concerning the calculation of the eigenfrequencies and corresponded eigenmodes of chosen one-layer beams and multilayered FGM sandwich beams. Effect of the axial forces on the free vibration has been studied and evaluated. The solution results will be compared with those obtained by using a very fine mesh of 2D plane elements of the FEM software ANSYS.

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Acknowledgements

This research was supported by Grant Agency VEGA 1/0093/10.

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Authors and Affiliations

  1. Department of Mechanics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Bratislava, Slovakia

    Justín Murín

  2. Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria

    Mehdi Aminbaghai

  3. Department of Mechanics, Slovak University of Technology in Bratislava, Ilkovičova 3, 812 19, Bratislava, Slovakia

    Vladimír Kutiš

Authors
  1. Justín Murín
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  2. Mehdi Aminbaghai
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  3. Vladimír Kutiš
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Corresponding author

Correspondence to Justín Murín .

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Editors and Affiliations

  1. in Bratislava, Department of Mechanics, Slovak University of Technology, Ilkovičova 3, Bratislava, 812 19, Slovakia

    Justín Murín

  2. AFA General Milan Rastislav Štefánik, Demänová 393, Liptovsky Mikulas, 031 19, Slovakia

    Vladimír Kompiš

  3. Department of Mechanics, Slovak Univ. of Technology in Bratislava, Ilkovičova 3, Bratislava, 812 19, Slovakia

    Vladimír Kutiš

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Murín, J., Aminbaghai, M., Kutiš, V. (2011). Exact Solution of Bending Free Vibration Problem of the FGM Beams with Effect of Axial Force. In: Murín, J., Kompiš, V., Kutiš, V. (eds) Computational Modelling and Advanced Simulations. Computational Methods in Applied Sciences, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0317-9_8

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  • DOI: https://doi.org/10.1007/978-94-007-0317-9_8

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0316-2

  • Online ISBN: 978-94-007-0317-9

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