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Antar K., Amara K., Besseghier A. / Физическая мезомеханика 27 3 (2024) 183-186 183
УДК 539.3
Исследование влияния тепловых воздействий на прохождение волн через стенки углеродных нанотрубок в полимерной матрице в рамках градиентных теорий упругости
12 3
K. Antar , K. Amara , A. Besseghier
1 Университетский центр Наамы, Наама, 45000, Алжир 2 Университет Айн-Темушента, Айн-Темушент, 46000, Алжир
3 Университет Тисемсильта, Тисемсильт, 38000, Алжир
В статье изучены колебательные свойства двустенных углеродных нанотрубок в полимерной матрице в рамках различных градиентных теорий упругости. Рассмотрено изменение механического поведения двустенных углеродных нанотрубок и полимерной матрицы в зависимости от температуры. Особое внимание уделено влиянию масштабных эффектов на распространение волн в двустенных углеродных нанотрубках. Показано, что изменение температуры оказывает влияние на определенные характеристики поперечных колебаний в нанотрубках. Получены согласованные определяющие уравнения для моделирования свободных поперечных колебаний двустенных углеродных нанотрубок с использованием нелокальной модели балки Эйлера-Бернулли с учетом влияния температуры и сил Ван-дер-Ваальса между внутренними и внешними нанотрубками.
Ключевые слова: плазматические мембраны, гормоны стресса, флуоресцентный анализ
DOI 10.55652/1683-805X_2024_27_3_183-186
Investigation of thermal impacts and different gradient elasticity theories on wave propagation through the polymer matrix incorporated
carbon nanotube walls
K. Antar1, Kh. Amara2,3, and A. Besseghier4
1 Faculty of Science and Technology, University Center of Naama, 45000, Algeria 2 Faculty of Science and Technology, University of Ain Temouchent, Ain Temouchent, 46000, Algeria 3 Engineering and Sustainable Development Laboratory, University of Ain Temouchent, Ain Temouchent, 46000, Algeria 4 Faculty of Science and Technology, Tissemsilt University, Tissemsilt, 38000, Algeria
This paper explores the vibrational properties of double-walled carbon nanotubes embedded in a polymer matrix within different gradient elasticity theories. The study considers how the mechanical behavior of double-walled carbon nanotubes and the polymer matrix changes with temperature. The research highlights the significance of scale effects on wave propagation in double-walled carbon nanotubes and shows that certain characteristics of transverse vibrations in double-walled carbon nanotubes are affected by temperature variations. In addition, the paper derives consistent governing equations for modeling free transverse vibrations of double-walled carbon nanotubes using the nonlocal Euler-Bernoulli beam model, considering the effects of temperature and Van der Waals forces between the inner and outer nanotubes.
Keywords: gradient elasticity theory, carbon nanotubes, wave propagation, thermal effects
1. Introduction
Carbon nanotubes (CNTs) are remarkable struc-
tures that have captured the imagination of scientists
and engineers worldwide. These cylindrical nanoma-
terials, composed of carbon atoms arranged in a unique hexagonal pattern, exhibit extraordinary mechanical, electrical and thermal properties. Research on the mechanical properties of carbon nanotubes has
© Antar K., Amara K., Besseghier A., 2024
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Antar K., Amara K., Besseghier A. / OusmecKan MesoMexanuKa 27 3 (2024) 183-186
been ongoing since their discovery by Iijima [1]. The results from this research demonstrate that CNTs possess superior mechanical properties. While there are various reports in the literature regarding the exact properties of CNTs, theoretical and experimental results consistently show an extremely high elastic modulus, exceeding 1 TPa (the elastic modulus of diamond is 1.2 TPa), for CNTs. The reported strengths of CNTs are 10-100 times higher than that of the strongest steel, all while being significantly lighter. Consequently, the mechanical behavior of CNTs has been the subject of numerous recent studies [2-12].
Modeling for the analytical analysis of CNTs is mainly classified into two categories. The first one is atomic modeling, including such techniques as classical molecular dynamics [13, 14], tight binding molecular dynamics [15], and density functional theory [16], which is limited only to systems with a small number of molecules and atoms and therefore applicable only to small-scale modeling. On the other hand, continuum modeling is useful in analyzing large-scale CNTs. Yakobson et al. [17] studied axial-ly compressed buckling of single-walled carbon na-notubes using molecular dynamics simulation. These authors compared their simulation results with a simple continuum shell model and found that all changes in the buckling pattern could be predicted using a continuum model.
Application of nonlocal continuum theory to na-notechnology was initially addressed by Peddieson et al. [18], who analyzed static deformation of beam structures based on a simplified nonlocal model obtained by Eringen [19]. Recently, nonlocal beam models have been further applied to the investigation of static and vibration properties of single-walled or multiwalled CNTs [20-28].
In the early investigations on transverse vibrations and wave propagation in CNTs, the effect of the initial stress in CNTs on the vibration frequency and wave velocity was not considered. More recently, the effect of initial loading on the vibration of CNTs has attracted attention [29]. Zhang et al [30] studied transverse vibrations of double-walled CNTs under axial compressive load and pointed out that the natural frequencies decreased with increasing axial load while the associated amplitude ratio of the inner to the outer tube were independent of the axial load. Wang and Cai [31] investigated the effect of the initial stress on noncoaxial resonance of CNTs. Their results showed that the influence of the initial stress in CNTs on their natural frequency was obvious, but
the influence on their intertube resonance frequency was not obvious. Sun and Liu [32] studied vibrational characteristics of CNTs under initial axial loading using the Donnell equations. According to the derived results, the resonance frequency is related to the tension or compression forms of the initial axial stress. Lu [33] developed a nonlocal Euler beam model with axial initial stress.
The investigation of the dynamic behavior of CNTs has been the subject of numerous experimental, molecular dynamics, and elastic continuum modeling studies. Since controlled experiments on the nanoscale are difficult, and molecular dynamics simulations are limited to systems with the maximum number of atoms about 109 by the scale and cost of computation, the continuum mechanics methods are often used to investigate some physical problems on the nanoscale [34-36]. Other studies use continuous elastic beam models to study vibrations [37, 38] and sound wave propagation [39-41] in CNTs. In the literature [42, 43], multiwalled carbon nanotubes (MWCNTs) was modeled as a single elastic beam, neglecting Van der Waals forces between two adjacent tubes [44-46]. The role of Van der Waals forces between two adjacent tubes in transverse vibrations and wave propagation in MWCNTs was studied in [47-52] using the multiple Euler beam model. Recently, Tien et al. [53] studied buckling and forced oscillation of organic nanoplates. Abouelregal et al. [54, 55] investigated thermal effects on the response of an isotropic cylinder and the effect of microscopic features in nonsimple materials. Nasri et al. [56] used aramid fibers as reinforcing agents within the highly porous aerogel matrix. To gain a deeper insight into free vibrations of functionally graded nanoplates and the nonlocal continuum model, several theoretical models were proposed [57-62].
The present paper investigates the thermal impact on wave propagation in double-walled carbon nano-tubes integrated into the polymer matrix. The effects of temperature and surrounding Van der Waals forces between the inner and outer nanotubes are taken into account. The effect of temperature variation on the mechanical properties of carbon nanotubes and the polymer matrix is investigated using different gradient elasticity theories.
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Received 24.12.2023, revised 25.03.2024, accepted 01.04.2024
This is an excerpt of the article "Investigation of Thermal Impacts and Different Gradient Elasticity Theories on Wave Propagation through the Polymer Matrix Incorporated Carbon Nanotube Walls". Full text of the paper is published in Physical Mesomechanics Journal. DOI: 10.1134/S102995992404012X
Сведения об авторах
Kamel Antar, Dr., University Center of Naama, Algeria, amrdel31@gmail.com
Khaled Amara, Dr., University of Ain Temouchent, Algeria, khaled.amara@univ-temouchent.edu.dz
Abderrahmane Besseghier, Prof., Tissemsilt University, Algeria, khaled314645@gmail.com
