Free Vibration Characteristics of Rotating Functionally Graded Porous Circular Cylindrical Shells with Different Boundar
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RESEARCH PAPER
Free Vibration Characteristics of Rotating Functionally Graded Porous Circular Cylindrical Shells with Different Boundary Conditions Xuan‑Hung Dang1 · Van‑Loi Nguyen1 · Minh‑Tu Tran1 · Bich‑Phuong Nguyen Thi1 Received: 21 August 2020 / Accepted: 9 November 2020 © Shiraz University 2020
Abstract The free vibration of rotating functionally graded porous (FGP) circular cylindrical shell with different boundary conditions is presented analytically in this study. The porous material properties are assumed to be graded in the thickness direction of the cylindrical shell according to three types of porosity distributions. By using Love’s shell theory and Hamilton’s principle, the governing equations of the rotating FGP cylindrical shell are derived, in which the effects of the centrifugal and Coriolis forces due to rotation are also taken into account. The natural frequencies of the rotating FGP cylindrical shell structure subjected to different boundary conditions are determined by applying Galerkin’s method together with beam functions of longitudinal mode functions. To validate the present results, comparisons between the results of the present method and previous studies are performed; a very good agreement is achieved. Besides, some influences of porous material properties, boundary conditions, circumferential wave number, geometric parameters, Coriolis acceleration, rotating speed on natural frequency as well as critical speed of the rotating FGP cylindrical shell are given. Keywords Free vibration · Rotating cylindrical shell structure · Functionally graded porous (FGP) material · Different boundary conditions · The Galerkin’s method
1 Introduction Shell structures have been applied widely in many industries because of good strength-to-weight ratio in comparison with other structure shapes; hence, these structures usually get much more attention for many scientists all over the world; especially, the rotating cylindrical shell structures are important parts of many machines such as gas turbine engines, aircraft engines, rockets, centrifuges, electric motors and rotor systems. These rotating structures subjected to many dynamic loadings during their working time, which may affect their performance and durability. Hence, free vibration analysis of the structures plays an important role in design and performance for various purposes. Until now, there are many studies on dynamic behaviors of the non-rotating shell structures made of the isotropic and laminated composite materials published in the existing * Van‑Loi Nguyen [email protected]; [email protected] 1
Department of Strength of Materials, National University of Civil Engineering, 55 Giai Phong Road, Hai Ba Trung District, Hanoi, Vietnam
literature (see, Arnold and Warburton 1949; Soldatos and Hadjigeorgiou 1990; Mustafa and Ali 1989; Reddy 1984; Lam and Qian 1999; Lam and Qian 2000; Qatu 2004; Nayak and Bandyopadhyay 2005; Tran et al. 2017a, b; Izadi et al. 2018). Works associated with the rotating cylindrical shells made of t
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