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Free Vibrations of a Nonlinearly Deformable Isotropic on the Average Composite Rectangular Membrane

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Mechanics of Composite Materials Aims and scope

A refined vibration equation of a rectangular membrane is derived in this paper. It allows determining the natural frequencies as functions of the mechanical characteristics of an asymmetrically stretched membrane. The dynamic equation is generalized to the case of a nonlinearly deformable isotropic on the average composite material. An approximate analytical solution of the problem is found employing a new homogenization technique. This method is based on estimation of the effective deformation characteristics of the composite material. The range of its effective characteristics is obtained from the rule of mixtures for the stresses and strains found assuming Voigt and Reuss hypotheses. The nonlinear behavior of the material is modeled using the bilinear Prandtl diagrams as constitutive equations for components of the composite. The effective elastic moduli, hardening modulus, yield stress, and the natural frequencies as functions of elastoplastic characteristics of the composite are obtained analytically in a closed form.

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This work was performed at the support of Erasmus+ and the School of Computing and Mathematics (Keele University, Staffordshire).

Gratitude

I. A.Tarasyuk expresses his gratitude to Prof. Yu. D. Kaplunov and Dr. D. A. Prikazchikov for their invaluable help and support.

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Authors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    I. A. Tarasyuk, A. S. Kravchuk & G. I. Mikhasev

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  1. I. A. Tarasyuk
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  2. A. S. Kravchuk
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  3. G. I. Mikhasev
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Correspondence to I. A. Tarasyuk.

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Translated from Mekhanika Kompozitnykh Materialov, Vol. 54, No. 1, pp. 113-128, January-February, 2018.

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Tarasyuk, I.A., Kravchuk, A.S. & Mikhasev, G.I. Free Vibrations of a Nonlinearly Deformable Isotropic on the Average Composite Rectangular Membrane. Mech Compos Mater 54, 79–88 (2018). https://doi.org/10.1007/s11029-018-9720-1

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  • DOI: https://doi.org/10.1007/s11029-018-9720-1

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