Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using
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Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods E. Zarouni • M. Jalilian Rad • H. Tohidi
Received: 24 January 2014 / Accepted: 26 April 2014 Ó Springer Science+Business Media Dordrecht 2014
Abstract In this paper, free vibration analysis of fiber reinforced composite (FRC) conical shells resting on Pasternak-type elastic foundation is investigated. Two kinds of fiber distribution in the thickness direction, namely, uniformly distributed and functionally graded are considered. The material properties of FRC conical shells are estimated through a volume fraction power law. The equations of motion are derived through variational formulation. The governing equations are developed based on the classical shells theory and Sanders assumptions. Galerkin and Ritz methods are employed to solve the governing equations and determine natural frequencies of the conical shell. The conical shell assumed to be clamped at the both ends. Results are presented on the effect of fiber volume fraction, semi-vertex angle, thickness to radius ratio and elastic foundation stiffness parameters
E. Zarouni Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran e-mail: [email protected] M. Jalilian Rad (&) Department of Mechanical Engineering, koohdasht Branch, Islamic Azad University, Koohdasht, Iran e-mail: [email protected]; [email protected] H. Tohidi Department of Mechanical Engineering, Saghez Branch, Islamic Azad University, Saghez, Iran e-mail: [email protected]
on the frequency characteristics of the conical shells. A comparative study between Ritz and Galerkin methods is carried out. Validity of the present study is confirmed by comparing the results with the data available in the open literature for a special case. A good agreement is observed between them. Keywords Free vibration Conical shell FRC composite Elastic foundation Ritz method Galerkin method
1 Introduction Fiber reinforced composite (FRC) structures are considerably used in engineering applications, such as the military, petrochemical, mechanical, aerospace, nuclear structures, turbo-machinery, submarine and ship building industries. Especially, conical shells are widely used as components of turbo-machinery and many of these machines operate within an environment of elastic materials, for instance, underwater, underground, etc. Therefore, vibrations of these structures and the effect of elastic foundation are very critical. Various foundation models have been proposed, such as Winkler, Filonenko-Borodich, Vlasov and Pasternak models etc., but the Pasternak model have widely used to describe the mechanical behavior of the foundation. Many studies on the vibration
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analysis of conical shells have been carried out (Goldberg et al. 1960; Serpico 1963; Chang 1978; Khatri and Asnani 1995). The vibration of conical shells with different boundary conditions were investigated by
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