Estimation of natural frequencies of pure bending vibrations of composite nonlinearly elastic beams and circular plates

Estimation of natural frequencies of pure bending vibrations of composite nonlinearly elastic beams and circular plates

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In the paper, it is represented a linearization method for the stress-strain curves of nonlinearly deformable beams and circular plates in order to generalize the pure bending vibration equations.It is considered composite, on average isotropic prismatic beams of a constant rectangular cross-section and circular plates of a constant thickness made of nonlinearly elastic materials.The technique consists in determining the approximate Youngs moduli from the initial stress-strain state of beam and plate subjected to the action of the bending moment.

The paper proposes two criteria for linearization: the equality of the specific potential energy of deformation and the minimization of the standard deviation in the state equation approximation.The method allows obtaining in the closed form the estimated value of the elbeco adu ripstop pants natural frequencies of layered and structurally heterogeneous, on average isotropic nonlinearly elastic beams and circular plates.This makes it possible to significantly reduce the resources in the vibration analysis and modeling 6-0 igora vibrance of these structural elements.

In addition, the paper shows that the proposed linearization criteria allow to estimate the natural frequencies with the same accuracy.Since in the general case even isotropic materials exhibit different resistance to tension and compression, it is considered the piecewise-linear Prandtls diagrams with proportionality limits and tangential Youngs moduli that differ under tension and compression as the stress-strain curves of the composite material components.As parameters of the stress-strain curve, it is considered the effective Voigts characteristics (under the hypothesis of strain homogeneity) for a longitudinally layered material structure; the effective Reuss characteristics (under the hypothesis of strain homogeneity) for a transversely layered beam and an axially laminated plate.

In addition, the effective Youngs moduli and the proportionality limits, obtained by the authors homogenization method, are given for a structurally heterogeneous, on average isotropic material.As an example, it is calculated the natural frequencies of two-phase beams depending on the component concentrations.