• Structural Engineering and Mechanics
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• 제6권5호
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• pp.497-516
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• 1998

A relatively simple two-dimensional multilayered shell model is presented for predicting both global quantities and stress distributions across the thickness of multilayered thick shells, that is based on a third-order zig-zag approach. As for any zig-zag model, the layerwise kinematics is accounted for, with the stress continuity conditions at interfaces met a priori. Moreover, the shell model satisfies the zero transverse shear stress conditions at the upper and lower free surfaces of the shell, irrespective of the lay-up. By changing the parameters in the displacement model, some higher order shell models are obtained as particular cases. Although it potentially has a wide range of validity, application is limited to cylindrical shell panels in cylindrical bending, a lot of solutions of two-dimensional models based on rather different simplyfying assumptions and the exact three-dimensional elasticity solution being available for comparisons for this benchmark problem. The numerical investigation performed by the present shell model and by the shell models derived from it illustrates the effects of transverse shear modeling and the range of applicability of the simplyfying assumptions introduced. The implications of retaining only selected terms depending on the radius-to-thickness ratio are focused by comparing the present solutions to the exact one and to other two-dimensional solutions in literature based on rather different simplyfying assumptions.

• Structural Engineering and Mechanics
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• 제80권6호
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• pp.727-736
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• 2021

In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.

• Geomechanics and Engineering
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• 제39권4호
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• pp.347-356
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• 2024

The aim of the present investigation is focused on the nonlinear forced vibration analysis of porous FGM sandwich beam with a viscoelastic core resting on nonlinear elastic foundation. The analytical formulation incorporates both normal and shear deformations in the core by utilizing the Zig-Zag theories. The harmonic balance method is integrated with a one-mode Galerkin's procedure designed for a simply supported beam. The nonlinear geometric coupling and viscoelastic effects result in a frequency amplitude equation that is nonlinear and governed by multiple complex coefficients. The damping and frequency response curves are depicted and analyzed across various geometrical and mechanical configurations of sandwich beams. The results indicate that the porosity effects and elastic coefficients of the foundation exert a significant influence on the damping and nonlinear vibration response of these beams.