Nonlinear resonance responses of size-dependent functionally graded cylindrical microshells with thermal effect and elas
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ORIGINAL ARTICLE
Nonlinear resonance responses of size‑dependent functionally graded cylindrical microshells with thermal effect and elastic medium G. G. Sheng1 · X. Wang2 Received: 2 July 2020 / Accepted: 11 September 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The nonlinear resonance responses of functionally graded (FG) cylindrical microshells with the elastic medium is investigated by considering thermal and scale effects. First, using the modified couple stress theory, the nonlinear dynamics model for FG microshell are established. Then the reduced nonlinear differential equations are derived by Galerkin’s method and static condensation. Finally, subharmonic, superharmonic and primary resonances of FG cylindrical microshells are analyzed by a perturbation method. In addition, the bifurcation characteristics of the nonlinear dynamic responses are investigated by some numerical examples. The effects of key parameters (modal damping, excitation frequency, foundation medium, scale parameter and thermal effect) on the nonlinear resonance responses are also discussed by numerical simulation. Keywords Modified couple stress theory · Shell · Superharmonic and subharmonic resonance · Functionally graded material · Method of multiple scales
1 Introduction The research of micro-structures (MEMS and NEMS) has important meanings, and the micro-structures have widely prospect in application [1–3]. The study in the dynamic behavior of micro-structures has become to be one of the main factors in structural design. According to laboratory research, the classical elasticity theory is unable to take account of size effects of micro-structures in static and dynamic analyses. Thus, non-classical elasticity theories have been considered to investigate mechanical properties of micro-structures, including strain gradient theory and couple stress theory [4–7]. The size effects are considered, and the higher-order stresses are included in the non-classical elasticity theories.
* G. G. Sheng [email protected] 1
School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114, Hunan, People’s Republic of China
School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China
2
Many researchers developed the mechanical models of micro-structure, where modified couple stress theory (MCST) was adopted since it only contains single material scale parameter and couple stress tensor is symmetric, compared with other size-dependent continuum theory [8]. Moreover, some characteristics about size-dependent and length scale parameter have been validated by an experimental study [9]. For microbeams and microplates, MCST has been widely used in mechanical analyses [10, 11]. In these studies, different elasticity theories are compared and analyzed. Some researchers also analyzed the static and dynamic behaviors of microshell structures. Due to the complexities of s
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