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

• Published in: Applied mathematics and mechanics Vol. 45; no. 5; pp. 891 - 910
• Main Authors: Nguyen, N. D., Nguyen, T. N.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2024; Springer Nature B.V; Faculty of Civil Engineering,Ho Chi Minh City University of Technology and Education,Ho Chi Minh City 71309,Viet Nam%Faculty of Engineering and Technology,Kien Giang University,Chau Thanh 92000,Viet Nam
• Edition: English ed.
• Subjects: Applications of Mathematics; Boundary conditions; Chebyshev approximation; Classical Mechanics; Euler-Lagrange equation; Fluid- and Aerodynamics; Free vibration; Material properties; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Metal foams; Partial Differential Equations; Polynomials; Porosity; Ritz method; Shear deformation; Temperature dependence; Thermal analysis; Thermal buckling; Vibration response; 11R09; Chebyshev function; buckling; metal foam beam; higher-order beam theory (HOBT); Ritz method; vibration; O32; higher-order beam theory(HOBT)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-024-3116-5

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.