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Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments

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Abstract

This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study.

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Authors and Affiliations

  1. School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200030, People’s Republic of China

    Zhen-Xin Wang & Hui-Shen Shen

  2. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200030, People’s Republic of China

    Hui-Shen Shen

Authors
  1. Zhen-Xin Wang
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  2. Hui-Shen Shen
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Correspondence to Hui-Shen Shen.

Appendix

Appendix

In Eqs. (28)–(31)

(36)

In Eqs. (33) and (34)

(37)

for initially thermal stressed plates (immovable edge condition)

(38)

and for initially compressed stressed plates (movable edge condition)

(39)

in which P cr is the critical buckling load for the UD plate (or sandwich plate) under uniaxial compression in the X direction, and η is the load proportion ratio, defined by σ y =ησ x . In the above equations (with others are defined as in [12]).

(40)

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Wang, ZX., Shen, HS. Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments. Nonlinear Dyn 70, 735–754 (2012). https://doi.org/10.1007/s11071-012-0491-2

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