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Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load

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Abstract

Due to the significant effect of porosity on the mechanical response of functionally graded (FG) structures, this paper presents a comprehensive model to investigate the vibration response of FG porous thick beam under the dynamic sine pulse load including the damping effect by using adopted finite element model, for the first time. The multilayer thick beam is modeled as two-dimensional plane stress problem. The distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric-distribution, X-distribution and O-distribution). The damping effect is included in the model by using the Kelvin–Voigt viscoelastic constitutive model. Constitutive equations, gradation and porosity functions are described in detail. Forced motion equations are derived by using Lagrange energy principles. Twelve-node 2D plane element with 3 × 3 integration points is proposed to discretize the beam and get the element matrices and force vectors. The numerical time integration method of Newmark is proposed to solve the system numerical and get the displacement response of the structure. Effects of layer stacking sequence, material gradation index and porosity parameter on the dynamic’s response of thick FG porous damped beam are presented. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials.

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Authors and Affiliations

  1. Department of Civil Engineering, Bursa Technical University, 16330, Bursa, Turkey

    Ş. D. Akbaş

  2. Mechanical Engineering Department, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia

    Y. A. Fageehi & A. E. Assie

  3. Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Kingdom of Saudi Arabia

    M. A. Eltaher

  4. Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    A. E. Assie & M. A. Eltaher

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  1. Ş. D. Akbaş
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  2. Y. A. Fageehi
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  4. M. A. Eltaher
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Correspondence to M. A. Eltaher.

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Akbaş, Ş.D., Fageehi, Y.A., Assie, A.E. et al. Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load. Engineering with Computers 38, 365–377 (2022). https://doi.org/10.1007/s00366-020-01070-3

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