Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions
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Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions Yan Qing Wang
. Chao Ye . Jean W. Zu
Received: 8 July 2018 / Accepted: 16 August 2018 Ó Springer Nature B.V. 2018
Abstract This study investigates the free vibration of metal foam circular cylindrical shells under various boundary conditions. The elasticity modulus and mass density of the shells vary gradually and continually in the thickness direction. Two types of porosity distribution are taken into account including symmetrical and unsymmetrical distributions. Love’s shell theory is employed to formulate the governing equations and then the Rayleigh–Ritz method is utilized to solve natural frequencies of the system. The results show that the porosity coefficient has important effect on the natural frequencies of metal foam shells. Its effect also relates to the boundary conditions of the shells. Moreover, different porosity distributions make the metal foam shells possess different vibration characteristics, which is quite obvious at large porosity coefficient. As the circumferential wave number increases, the natural frequencies of the metal foam shells tend to the same under various boundary Y. Q. Wang (&) C. Ye Department of Mechanics, Northeastern University, Shenyang 110819, China e-mail: [email protected] Y. Q. Wang Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China J. W. Zu Schaefer School of Engineering and Science, Stevens Institute of Technology, Hoboken, NJ 07030, USA
conditions. Additionally, the present results are verified by the comparison with the published ones in the literature. Keywords Metal foam Circular cylindrical shell Free vibration Love’s shell theory Rayleigh–Ritz method
1 Introduction A metal foam is a cellular structure consisting of a solid metal with gas-filled pores comprising a large portion of the volume. The defining characteristic of metal foams makes this type of materials ultralight. Additionally, metal foams have an excellent energy absorption performance, making them ideal for structures under dynamic or impact loads (Avalle et al. 2007; Kim et al. 2005; Mukai et al. 1999; Rajendran et al. 2008). Due to their unique mechanical characteristics, metal foams have wide applications in aerospace, automotive, and ship industries. For example, aluminum foams are used in automotive energy absorption and minimizing the weight of vehicles (Banhart 2001; Smith et al. 2012). In order to identify the mechanical properties of metal foams, some research has been conducted on bending, buckling and vibration analysis of metal foam structures. Among them, Magnucki and
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Y. Q. Wang et al.
Stasiewicz (2004) studied the elastic buckling problem of metal foam beams. Magnucka-Blandzi (2009) studied the dynamic stability of metal foam circular plates. Belica et al. (2011) investigated the dynamic stability of metal foam cylindrical shells subjecte
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