Nonlocal strain gradient forced vibrations of FG-GPLRC nanocomposite microbeams
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ORIGINAL ARTICLE
Nonlocal strain gradient forced vibrations of FG-GPLRC nanocomposite microbeams Qiannan Wu1 • Haohao Chen1 • Wan Gao1 Received: 14 May 2019 / Accepted: 4 June 2019 Ó Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract In the current investigation, based upon the nonlocal strain gradient theory of elasticity, an inhomogeneous size-dependent beam model is formulated within the framework of a refined hyperbolic shear deformation beam theory. Thereafter, via the constructed nonlocal strain gradient refined beam model, the nonlinear primary resonance of laminated functionally graded graphene platelet-reinforced composite (FG-GPLRC) microbeams under external harmonic excitation is studied in the presence of the both hardening-stiffness and softening-stiffness size effects. The graphene platelets are randomly dispersed in each individual layer in such a way that the weight fraction of the reinforcement varies on the basis of different patterns of FG dispersion. Based upon the Halpin–Tsai micromechanical scheme, the effective material properties of laminated FGGPLRC microbeams are achieved. By putting the Hamilton’s principle to use, the nonlocal strain gradient equations of motion are developed. After that, a numerical solving process using the generalized differential quadrature (GDQ) method together with the Galerkin technique is employed to obtain the nonlocal strain gradient frequency response and amplitude response associated with the nonlinear primary resonance of laminated FG-GPLRC microbeams. It is found that the nonlocality size effect leads to an increase in the peak of the jump phenomenon and the associated excitation frequency, while the strain gradient size dependency results in a reduction in both of them. Keywords Nanocomposites Multilayer functionally graded Nonlinear resonance Graphene platelets Size effect
1 Introduction The exceptional mechanical, electrical and thermal characteristics of graphene have led to attracting tremendous attention from the research community. Graphene-based nanocomposite materials can be one of the most promising applications of graphene nanosheets. Using graphene platelet (GPL) as composite nanofiller makes the enhancement of multifunctional property possible. Recently, some studies have been carried out to analyze the mechanical behavior of multilayer functional graded graphene plateletreinforced composite (FG-GPLRC) structures. Yang et al. [1] reported the buckling and postbuckling response of laminated FG-GPLRC Timoshenko beams using the differential quadrature method. Song et al. [2] predicted the & Qiannan Wu [email protected] 1
School of Science, North University of China, Taiyuan 030051, China
free and forced vibrations of multilayer FG-GPLRC firstorder shear deformable plates using the Navier solution. Feng et al. [3] investigated the nonlinear bending characteristic of laminated FG-GPLRC Timoshenko beams via the Ritz method. Wu et al. [4] examined the dynamic stability of l
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