Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments
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Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments Chun-Sheng Chen . Hai Wang . Tsyr-Jang Chen . Wei-Ren Chen
Received: 8 July 2019 / Accepted: 1 September 2020 Ó Springer Nature B.V. 2020
Abstract This paper studies the parametric instability of hybrid nanocomposite plates under an arbitrary periodic load in thermal environments. The hybrid nanocomposite plate is a three-layer board. It has metal layers on both surfaces and one core reinforced with functionally graded (FG) carbon nanotubes (CNTs). The Galerkin method with a reduced eigenfunction transformation is applied to establish the governing equations of motion. According to the Bolotin method, a set of Mathieu-type differential equations is formed to determine dynamic instability regions and dynamic instability index (DII). The inplane periodic stress is taken to be a combination of pulsating axial and bending stresses in the example problems. The effects of the layer thickness ratio, CNTs volume fraction, CNTs distribution type, temperature, bending stress, static and dynamic load on the dynamic instability of hybrid nanocomposite plates are investigated and discussed. C.-S. Chen T.-J. Chen Department of Mechanical Engineering, Lunghwa University of Science and Technology, Guishan Shiang 33306, Taiwan H. Wang Department of Mechanical Engineering, Ming Chi University of Technology, Tai-Shan 24301, Taiwan W.-R. Chen (&) Department of Mechanical Engineering, Chinese Culture University, Taipei 11114, Taiwan e-mail: [email protected]
Keywords Dynamic instability Bolotin’s method Volume fraction Instability regions Dynamic instability index
1 Introduction Due to the high strength to weight ratio, composite materials have been widely and successfully used in aerospace and other industries. The problems of dynamic instability due to parametric resonance of composite plate are induced by a time varying in-plane load. Therefore, it is necessary to accurately determine the dynamic instability region of the structure during the structural design process. There have been some related studies on the parametric resonance of composite plates (Wang and Dawe 2002; Bourada et al. 2015; Sahoo and Singh 2018; Rasool and Singha 2019). The performance of functionally graded (FG) materials is excellent for reinforced composites (Liew et al. 2015). Shariyat (2009) dealt with the vibration and dynamic buckling of FG plates with surfacebonded or embedded piezoelectric sensors and actuators under thermo-electro-mechanical loading conditions. The initial geometric imperfections of the plate and temperature-dependent material properties were added to the study. A simple negative velocity feedback control was applied to actively control the
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dynamic response. The results showed that the geometric imperfections and temperature-dependent properties significantly affect the buckling loads. Fu et al. (2012) derived the nonlinear gove
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