On the nonlinear forced vibration of nanoshells via nonlocal strain gradient theory

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Sayed Mohamad Mirfatah , Hamzeh Salehipour , Ömer Civalek
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引用次数: 0

Abstract

This paper investigates the nonlinear forced vibration of doubly curved sandwich nanoshells with auxetic honeycomb core having negative Poisson's ratio and nanocomposite-reinforced coatings. It is assumed that the nanoshell structure rests on Winkler-Pasternak foundation. The dynamic response is analyzed under various periodic and impulsive pressure excitations. The basic governing, compatibility, and constitutive equations are derived in the context of the non-classical nonlocal strain gradient elasticity theory to rigorously account for the size-dependent effects in nonlinear dynamic response at nanoscale. Utilizing the first-order shear deformation theory, representing the strain components in terms of the deformation field and its derivatives, the derived governing equations can be expressed in a system of three-dimensional nonlinear partial differential equations. To achieve a closed-form solution avoiding the complexities of the numerical iterative methods in presence of geometrical nonlinearities, the considered shallow nanoshell panels are taken as simply supported at their different fixed or moveable states. Further, assuming an appropriate approximation for the deformation field, utilizing the Galerkin method, the governing partial differential equations are reduced to an explicit formulation of the corresponding ordinary differential equation of motion which is numerically solved by the Runge-Kutta (RK) method. In numerical investigations, the accuracy and reliability of the proposed analytical-numerical approach are first validated by comparing the obtained results with benchmark solutions available in the literature. Subsequently, the influence of various parameters, including mechanical and geometrical properties, boundary conditions, and different periodic and impulsive external pressure excitations, on the geometrically nonlinear forced vibration behavior of the nanoshell panels is systematically analyzed using the developed solution methodology.
基于非局部应变梯度理论的纳米壳非线性强迫振动研究
研究了具有负泊松比的双弯曲蜂窝芯夹层纳米壳和纳米复合材料增强涂层的非线性强迫振动。假设纳米壳结构建立在温克勒-帕斯捷尔纳克基础上。分析了不同周期和脉冲压力激励下的动态响应。在非经典非局部应变梯度弹性理论的背景下,导出了基本的控制方程、相容性方程和本构方程,以严格地解释纳米尺度非线性动力响应中的尺寸依赖效应。利用一阶剪切变形理论,用变形场及其导数表示应变分量,推导出的控制方程可以用三维非线性偏微分方程组表示。为了避免几何非线性存在时数值迭代方法的复杂性,将所考虑的浅纳米壳板作为不同固定或移动状态下的简支板。进一步,假设变形场有适当的近似,利用伽辽金方法,将控制偏微分方程简化为相应的运动常微分方程的显式形式,并采用龙格-库塔(RK)方法进行数值求解。在数值研究中,首先通过将所得结果与文献中可用的基准解进行比较,验证了所提出的解析-数值方法的准确性和可靠性。随后,利用所建立的求解方法,系统分析了各种参数(包括力学和几何特性、边界条件、不同周期和脉冲外部压力激励)对纳米壳板几何非线性强迫振动行为的影响。
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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