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Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

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Abstract

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams. The analyses include three models for porosity distribution and two scenarios for thermal distribution. The material properties are assessed under two conditions, i.e., temperature dependence and temperature independence. The theoretical framework for the beams is based on the higher-order shear deformation theory, which incorporates shear deformations with higher-order polynomials. The governing equations are established from the Lagrange equations, and the beam displacement fields are approximated by the Chebyshev polynomials. Numerical simulations are performed to evaluate the effects of thermal load, slenderness, boundary condition (BC), and porosity distribution on the buckling and vibration behaviors of metal foam beams. The findings highlight the significant influence of temperature-dependent (TD) material properties on metal foam beams’ buckling and vibration responses.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, 71309, Viet Nam

    N. D. Nguyen

  2. Faculty of Engineering and Technology, Kien Giang University, Chau Thanh, 92000, Viet Nam

    T. N. Nguyen

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Nguyen, N.D., Nguyen, T.N. Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams. Appl. Math. Mech.-Engl. Ed. 45, 891–910 (2024). https://doi.org/10.1007/s10483-024-3116-5

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  • DOI: https://doi.org/10.1007/s10483-024-3116-5

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