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УДК 539.3
Характеристики затухания нелокальных волн градиента деформации в листах термовязкоупругого графена с учетом нелинейных эффектов подложки
1 12 R. Selvamani , T. Prabhakaran , F. Ebrahimi
1 Институт технологий и науки Карунья, Коимбатур, Тамил Наду, 641114, Индия 2 Международный университет имени Имама Хомейни, Казвин, 34148-96818, Иран
В работе изучены дисперсионные характеристики тепловых, вязкоупругих и механических волн в листах графена на вязком основании типа Пастернака при равномерной тепловой нагрузке. С помощью уточненной теории пластин высшего порядка с двумя переменными получены кинематические соотношения для листов графена. Моделирование эффектов затухания в вязкоупругой среде выполнено в рамках модели Кельвина-Фойгта. В работе детально изучена размерная зависимость поведения листов графена в рамках нелокальной теории градиента деформации. Нелокальные определяющие уравнения записаны на основе принципа Гамильтона, и их аналитическое решение позволяет получить значения волновых частот. Для подтверждения эффективности подхода проведен сравнительный анализ с результатами предыдущих исследований. Зависимости волновых характеристик листов гра-фена от различных параметров представлены графически.
Ключевые слова: распространение волн, графеновые листы, нелокальная теория градиента деформации, вязкое основание типа Пастернака, тепловое нагружение
DOI 10.55652/1683-805X_2024_27_3_173-177
Damping characteristics of nonlocal strain gradient waves in thermoviscoelastic graphene sheets subjected to nonlinear
substrate effects
R. Selvamani1, T. Prabhakaran1, and F. Ebrahimi2
1 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamilnadu, 641114, India 2 Department of Mechanical Engineering, Imam Khomieni International University, Qazvin, 34148-96818, Iran
The present study explores dispersion characteristics of thermal, viscoelastic and mechanical waves in graphene sheets subjected to uniform thermal loading and supported by the visco-Pasternak foundation. Kinematic relations for graphene sheets are deduced within two-variable refined higher-order plate theory. Damping effects of the viscoelastic medium are modeled using the Kelvin-Voigt model. The research extensively investigates the size-dependent behavior of graphene sheets by incorporating nonlocal strain gradient theory. Nonlocal governing equations are formulated under Hamilton's principle and solved analytically to determine wave frequency values. To validate the results, a comparative analysis is conducted, and the outcomes are tabulated to confirm the effectiveness of the approach. Finally, graphical representations are employed to depict the influence of each parameter on the wave propagation responses of graphene sheets.
Keywords: wave propagation, graphene sheets, nonlocal strain gradient theory, visco-Pasternak foundation, thermal loading
1. Introduction
In recent years, the enhanced quality properties of nanomaterials have caught the attention of numerous researchers. The significance of size effects becomes
pronounced as structures reach very small dimensions, as evidenced by atomistic modeling and experimental studies. Consequently, the size effect plays a crucial role in shaping the mechanical behavior of
© Selvamani R., Prabhakaran T., Ebrahimi F., 2024
micro- and nanostructures. There is a notable current trend within the scientific community towards exploring the mechanical behavior of structures using nanoscale elements. Given the substantial interest of a growing number of researchers in employing nanoscale beams and plates, it becomes imperative to acquire comprehensive knowledge about the size-dependent behavior of these diminutive elements. As a result, nonlocal continuum theories were developed to elucidate small-scale effects when investigating the mechanical characteristics of nanodevices. Eringen [1] proposed the first nonlocal theory, called nonlocal elasticity theory, which relates the stress state in a desired point not only to the strain of this particular point but also to the strain of all adjacent points. This theory was employed by an abundant range of authors, and it is worth demonstrating some of the previous works gaining nonlocal elasticity during their study on the mechanical response of nano-beams or nanoplates. Evaluations of the contact problem of functionally graded materials via various analytical and numerical methods were exposed by Yay-laci et al. [2-16]. Wang et al. [17] analyzed the wave dispersion characteristics of nanoplates within nonlocal elasticity. The studies conducted by Ebrahimi et al. [18-21] are notable for the dynamic analysis of nanomaterials via size effects. Eltaher et al. [22] described the vibrational properties of nanobeams in the framework of the finite element method and Eu-ler-Bernoulli beam theory. The bending vibration analysis of nanobeams was performed by Ghadiri and Shafiei [23] using the differential quadrature method. A few years later, researchers figured out that nonlocal elasticity theory was not powerful enough to completely estimate the behavior of small structures [24]. In other words, the stiffness-hardening behavior of nanostructures was neglected in nonlocal elasticity and only the stiffness-softening effect was included. This stimulated the development of a new nonlocal theory, called nonlocal strain gradient theory, to rectify the mentioned deficiency. Li and Hu [25] presented nonlocal strain gradient theory to highlight size effects while studying the buckling response of nanobeams. Examination of the thermome-chanical buckling properties of orthotopic nanoplates was performed by Farajpour et al. [26] in the framework of nonlocal strain gradient theory. The constitutive equation of classical continuum mechanics does not consider size effects [27-36]. This makes it difficult to accurately describe thermal and mechanical engineering properties of nanomaterials. Continuum mechanics was used to address this issue
as an alternative to small-scale investigations and molecular dynamics simulations. Narendar and Go-palakrishnan [37] dealt with surface effects on the wave propagation behavior of a nanoplate. Impact and reaction of thermal stresses on various functionally graded materials were discussed by Tounsi et al. [38-47] within different computational theories.
Graphene sheets possess some advantageous over other small structures made of different materials, such as higher elastic potential [48] and larger thermal conductivity [49]. According to the above information, it is necessary to obtain detailed results on the mechanical response of these types of nanostruc-tures. Thus, Murmu and Pradhan [50] tried to show the dynamic response of embedded monolayer gra-phene sheets employing Eringen's nonlocal theory. Ansari and Rouhi [51] presented an atomistic finite element model for vibration and axial buckling analysis of monolayer graphene sheets. Size-dependent mechanical characteristics of propagating waves in graphene sheets were exactly studied by Arash et al. [52] within nonlocal elasticity. Furthermore, magne-tomechanical vibration and stability analysis of mo-nolayer graphene sheets rested on the viscoelastic foundation is the issue of another research performed by Ghorbanpour Arani et al. [53]. Xiao et al. [54] presented nonlocal strain gradient theory to examine the wave propagation behavior of viscoelastic mono-layer graphene sheets.
The literature survey reveals that wave propagation characteristics of a graphene sheet on the visco-elastic medium under thermal loading has not yet been investigated. Henceforward, it is found necessary to survey this problem here for the first time. The graphene sheet is considered to rest on the visco-Pasternak substrate including a linear constant (Winkler coefficient), a nonlinear constant (Pasternak coefficient) and a damping constant. Shear deformation is taken into account using a higher-order two-variable shear deformation plate theory. Moreover, nonlocal strain gradient theory is utilized to consider small-scale effects. Once the nonlocal differential equations are completely derived, they will be solved analytically using an exponential function. The influence of each parameter is precisely explained at the end of the paper.
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Received 29.11.2023, revised 22.12.2023, accepted 26.12.2023
This is an excerpt of the article "Damping Characteristics of Nonlocal Strain Gradient Waves in Thermovisco-elastic Graphene Sheets Subjected to Nonlinear Substrate Effects". Full text of the paper is published in Physical Mesomechanics Journal. DOI: 10.1134/S1029959924040106
Сведения об авторах
R. Selvamani, Dr., Karunya Institute of Technology and Sciences Coimbatore, India, selvamani@karunya.edu T. Prabhakaran, Karunya Institute of Technology and Sciences Coimbatore, India, prabha251999@gmail.com F. Ebrahimi, Dr., Imam Khomieni International University, Iran, febrahimy@eng.ikiu.ac.ir
