Free vibration analysis of metal foam core sandwich beams on elastic foundation using Chebyshev collocation method

• Published in: Archive of applied mechanics (1991) Vol. 89; no. 11; pp. 2335 - 2349
• Main Authors: Wang, Yan Qing, Zhao, Hu Long
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2019; Springer Nature B.V
• Subjects: Beam theory (structures); Boundary conditions; Chebyshev approximation; Classical Mechanics; Collocation methods; Computer simulation; Elastic foundations; Engineering; Free vibration; Metal foams; Original; Resonant frequencies; Sandwich structures; Theoretical and Applied Mechanics; Thickness; Timoshenko beams; Vibration analysis; Winkler–Pasternak foundation; Metal foam core sandwich beam; Timoshenko beam theory; Free vibration; Chebyshev collocation method
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-019-01579-0

In this paper, free vibration of a metal foam core sandwich (MFCS) beam embedded in Winkler–Pasternak elastic foundation is studied using the Chebyshev collocation method (CCM). This method can achieve high precision within the range allowed by the effective number of bits of computers. Three foam distribution types along the thickness direction are considered for the core. The Timoshenko beam theory is adopted and Hamilton’s principle is utilized to derive the boundary conditions and governing equations of the model. The numerical results show that natural frequencies of the sandwich beam initially increase and then decrease with the rise in thickness of metal foam core. By arranging the foam distribution in the core, natural frequencies of the sandwich beam can be significantly changed. Moreover, natural frequencies of the uniform foam distribution beam are insensitive to the foam coefficient. For the beam with non-uniform foam distribution, however, the natural frequencies increase or decrease with the foam coefficient, depending closely on the foam type. In addition, the present method is validated by comparing with the published ones for special cases.