Carbon Nanotube-reinforced Composites Research Articles

Trigonometric Higher‐Order Shear Deformation Theory on Exact Solution for Lateral and Longitudinal Dynamic Response of Magneto‐Electric Carbon Nanotube‐Reinforced Composite Beams Under Two Moving Loads Resting on Winkler–Pasternak Foundation

This paper aims to analyze the transverse and axial dynamic response of magneto‐electric carbon nanotube‐reinforced composite (CNTRC) beams under two moving constant loads resting on an elastic foundation. The governing equations of the magneto‐electric CNTRC beam are obtained based on Mantari’s shear deformation beam theory, Hamilton’s principle, and Laplace transforms to solve the derived differential equations. The beams, which include a Winkler spring and shear layer, are considered as resting on the elastic foundation. The boundary conditions for this work are simply supported. This marks the inaugural instance in which a precise analytical approach rooted in mathematical principles has been employed to examine these constructions. The drawback inherent in this technique lies in its reliance on a simply supported boundary condition, stemming from the challenge associated with performing Laplace inversion on the Coupled equations. A comparison with previous studies has been conducted, which is a valuable contribution. Several examples were used to analyze the magnetic, voltage, and spring constant factors, the volume fraction of carbon nanotubes (CNTs), the velocity of a moving constant load, and their influence on the transverse and axial dynamic responses and maximum deflections.

The free vibration of the MEE sandwich microplate with the FG-CNTRC core using the MSGT

This study deals with the free vibration of the sandwich microplate with the core made of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) and magneto-electro-elastic (MEE) face sheets. The governing equation of the microplates is derived by using the refined plate theory (RPT) with two variables and the modified strain gradient theory (MSGT). The Non-Uniform Rational B-Splines (NURBS) basis function of the isogeometric approach (IGA) is used for the approximation of the displacement and electric and magnetic fields of the microplates. The paper studies the effect of the length scale parameters (LSPs), CNTs distributions, CNTs volume fraction, magnetic and electric loads and geometry on the vibrational frequency of the MEE sandwich microplate.

Experimental and numerical buckling analysis of CNT reinforced polymer composite plates

A combined experimental and numerical buckling analysis is performed for Carbon nanotube-reinforced composite (CNTRC) laminates under uniaxial in-plane compressive load. A finite element simulation program is developed in MATLAB environment and the recorded buckling responses are verified with the experimental results. Closely aligned numerical and experimental results exhibits that inclusion of 0.3% CNT increases buckling strengths of CNTRC composite laminates, regardless of their geometrical parameters. Clamped edge laminates exhibit higher buckling mode shapes, influenced by aspect ratio and edge restraint. Microscopic analysis of CNTRC's fractured surface under compression shows enhanced buckling strength attributed to CNTs’ bridging and pullout effects in the matrix, suppressing crack initiation and propagation. Field Emission Scanning Electronic Microscope (FESEM) is utilized for this investigation.

Investigation of the Replication Quality of Microstructures on Injection Moulded Specimens Made from Recycled Polypropylene Composites Reinforced with Carbon Nanotubes

During the research, functional microstructures were created on the cavity surface of the injection moulding tool using femtosecond laser technology. Automotive-grade polypropylene (PP), as well as its recycled and carbon nanotube-reinforced composites, were used as the raw materials. The replicated structures were examined using confocal microscopy. It is expected that by optimizing the process parameters, the filling of the structured cavity surface with nanocomposite materials can reach a quality level comparable to plastic specimens made from non-reinforced raw materials. The aim is to provide results of scientific and industrial value to demonstrate the influence of the modified mould surface on the flow of the polymer melt and thus on the filling of the injection moulded products.

Active vibration control of rotating carbon nanotube reinforced composite cylindrical shells via piezoelectric patches

This paper addresses the active vibration control of rotating carbon nanotube reinforced composite (CNTRC) cylindrical shells via piezoelectric actuator and sensor pairs. Considering circumferential initial stresses and Coriolis forces induced by rotation, an electromechanical coupling model of a simply supported CNTRC cylindrical shell, covered with surface-bonded piezoelectric sensors/actuators is established using the Lagrange equations and the model validation is carried out through a comparative analysis with existing literature. To suppress vibrations of rotating CNTRC cylindrical shells over a range of speeds, an LQR (Linear Quadratic Regulator) closed-loop controller is designed and its effectiveness is analyzed and evaluated through dynamic response analysis. Furthermore, the optimization of piezoelectric patch layout is performed by analyzing the performance of the controller for rotating CNTRC shells with typical piezoelectric sensors/actuators distributions. This paper presents and validates a strategy for vibration control of rotating CNTRC cylindrical shells using piezoelectric patches. The findings derived can offer guidance for vibration suppression of rotating thin-walled structures in practical engineering applications.

On the Buckling Response of Functionally Graded Carbon Nanotube-reinforced Composite Imperfect Beams

The current inquiry aims to scrutinize the porosity's effect on the buckling response of carbon nanotube reinforced composite (CNTRC) imperfect beams. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. Single-walled carbon nanotubes (SWCNTs) are distributed and aligned in a polymeric matrix with various reinforcement patterns to create CNTRC porous beams. The material properties of the functionally graded beam determined using the mixture rule are assumed to vary according to the power law distribution of the volume fraction of the constituents. The mathematical models presented in this study are validated through numerical comparison with existing results. The new buckling results of carbon nanotube-reinforced porous beams are analyzed considering the influence of several parameters, including volume fraction, aspect ratios, degree of porosity, and types of reinforcement. The results stipulate that the above parameters play a significant role in the critical buckling load variation. It is proclaimed that the critical buckling load dwindled as porosity increased and that the X-CNT reinforced beam has a high resistance against buckling compared to other reinforcement types.

Vibration energy harvesting in an FG-CNTRC circular microplate with a surface-bonded piezoelectric layer

Piezoelectric energy harvesting using circular microplate has great potential to power microelectromechanical systems (MEMS). This paper studies vibrational energy harvesting by creating a model of a thin-walled circular microplate with a base layer of functional gradient carbon nanotube reinforced composites (FG-CNTRC) and a piezoelectric surface layer. Using the extended modified couple stress theory and the rule of mixture, the size effect and the effective Young's and shear moduli of the carbon nanotube reinforced composite (CNTRC) plate are established. Then, the governing equations are derived through the Lagrange's equations, and the analytical solutions of the relevant physical quantities are obtained. The specific examples are used to investigate the influence of length scale, carbon nanotube distribution, excitation frequency, and the ratio of the upper and lower plate radii on displacement, voltage, and power.

Buckling and post-buckling of anisogrid lattice-core sandwich plates with nanocomposite skins

This research offers an in-depth examination of the buckling and post-buckling responses observed in sandwich plates distinguished by the presence of an anisogrid lattice core and face layers composed of functionally graded carbon nanotube-reinforced composites (FG-CNTRC). To model this structure, a global continuous model for the lattice core is employed, while the displacement field is approximated using the First-Order Shear Deformation Theory (FSDT). Geometrically nonlinear strain relations based on the von-Kármán assumptions are incorporated to accurately capture the structural response. The homogenization of the FG-CNTRC skins is achieved through the modified rule of mixture, enabling estimations of effective material properties. To separate pre-buckling and post-buckling phases, we implement the adjacent-equilibrium criterion. Solving the linear (pertaining to buckling) and nonlinear (related to post-buckling) equations is based on the Generalized Differential Quadrature (GDQ) technique alongside an iterative method grounded in the displacement control strategy. Our analysis explores the influence of core and skin characteristics on the stability of these sandwich plates. By examining critical buckling thresholds, post-buckling equilibrium paths, and the underlying mechanisms driving these responses, we contribute insights into the structural stability and performance of such composite structures. This study not only enhances our understanding of buckling behavior in anisogrid lattice core sandwich plates but also holds promise for diverse engineering applications where structural stability is paramount.

Nonlinear bending examination of nanocomposite cylindrical shell exposed to mechanical loads using dynamic relaxation method

In the current context, the nonlinear bending examination of a carbon nanotube reinforced composite (CNTRC) shell exposed to mechanical loading using the first-order shear deformation shell model via the dynamic relaxation (DR) procedure, is perused. The composite shell is assumed to be reinforced in the longitudinal axis. The curved morphology distribution of CNTs is considered to be functionally graded (FG) or uniform along the shell thickness. Mechanical properties of the constituents are gathered based on the modified rule of the mixture. For verification, the present numeric outcomes are compared with available references and ABAQUS finite element package. Finally, the roles of effective items including carbon nanotubes (CNTs) distributions, thickness-to-radius and length-to-radius ratios, boundary conditions, and the volume fraction of CNTs are investigated on the maximum non-dimension deflection.

Nonlinear combined harmonic resonances of composite cylindrical shells operating in hygro-thermo-electro-magneto-mechanical fields

By considering the effects of the hygro-thermo-electro-magnetic environments, von Karman nonlinear terms, and multi-harmonic excitations, a coupled nonlinear vibration modeling of composite cylindrical shells comprising a carbon nanotube-reinforced composite (CNTRC) core and two piezoelectric/magnetic composite (PEMC) skins is developed, and the nonlinear dynamic behaviors of such cylindrical shells under primary, super/sub-harmonic, and combined resonance states are investigated. In the theoretical modeling process, the effective mechanical properties of the CNTRC core are first determined using the mixing and Schapery laws, and the hygro-thermo-electro-magneto-mechanical constitutive relations of the PEMC skins are then formulated. Within the framework of Reissner-Mindlin shell theory, the Lagrangian of the system containing Green-Lagrange and von Karman nonlinear terms is derived, and solution techniques based on the multiscale method are provided to obtain nonlinear frequencies, dynamic responses, and phases of CNTRC-PEMC cylindrical shells under multi-physics fields. Consequently, comparison studies are conducted to validate the correctness of the proposed model from different aspects. Based on this, various resonance and chaos behaviors of such structures subjected to multiple load components are revealed and compared, and the influences of environmental factors and structure composition on the amplitude-frequency curves, time-history responses, and phase planes are explored, with several recommendations and findings being drawn.

Natural frequency analysis of sandwich plate with auxetic honeycomb core and CNTRC face sheets using analytical approach and artificial neural network

In this paper, an analytical investigation is presented on the natural frequency analysis of sandwich plate resting on Winkler-Pasternak type elastic foundations in thermal environment. The sandwich plate consists of an auxetic honeycomb core with negative Poisson's ratio, which is assumed to perfectly bond to two carbon nanotube reinforced composite (CNTRC) face sheets to ignore potential interface effects or imperfections in bonding. The material properties of CNTRC are assumed to be temperature dependent. The volume fraction of carbon nanotube (CNT) varies through the thickness dimension according to linear functions with five different distribution patterns of CNT including UD, FG-O, FG-V, FG-Λ and FG-X. The governing equations of motion are derived based on the Reddy's first order shear deformation plate theory and Hamilton's principle, and the expression of the natural frequency is performed via Galerkin method. Artificial neural network (ANN) model is established to accurately predict the natural frequency of the sandwich plate on the basis of 1450 data points collected from analytical results. The effects of various material and geometrical parameters on the natural frequency of the sandwich plate are investigated in details.

A NURBS-based IGA using zig-zag plate theory for nonlinear passive/semi-active damping analysis of laminated FG-CNTRC plates

This study introduces an efficient and versatile numerical approach for simulating passive/semi-active damping treatments on laminated structures composed of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) plates. This novel approach integrates an isogeometric finite element formulation that leverages basic functions generated from Non-Uniform Rational Basis Spline (NURBS) with the Murakami zig-zag theory, Von Kármán’s nonlinear strain–displacement model, and the electro-mechanical coupling properties of the constraining layers. The proposed isogeometric formulation can be transformed into the Laplace domain using the Golla–Hughes–McTavish model to successfully simulate the time-dependent passive/semi-active damping mechanism of viscoelastic materials. Subsequently, results obtained in the Laplace domain are reconverted into the time domain using inverse techniques. The validation of the proposed model through two numerical examples showcases its high reliability and demonstrates the feasibility of simulating and controlling FG-CNTRC plates with various geometries within a Computer-Aided Design-Computer-Aided Engineering (CAD-CAE) analysis framework.

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

This study analyzes the nonlinear dynamic stability of carbon nanotube reinforced composite (CNTRC) piezoelectric viscoelastic nano/micro plate under time dependent harmonic compressive biaxial mechanical loading. The nano/micro plate is single-layer with a uniform and rectangular cross section. Polyvinylidene fluoride (PVDF) is the material used for the nano/micro plate. Also, it is located on a nonlinear viscoelastic piezoelectric foundation made of Zinc Oxide (ZnO). Single-walled carbon nanotubes (SWCNTs) have been used to strengthen nano/micro plate. Using Kelvin-Voigt model, the material properties of the system are assumed to be viscoelastic. Nano/micro plate is subjected to 2D magnetic field and electric potential. Magnetic field effects are incorporated using Maxwell’s relations. An alternating and direct voltage is applied to the nano/micro plate and also smart foundation in thickness direction. Eshelby-Mori-Tanaka approach is used to estimate the effective elastic properties. Additionally, follower force and uniform thermal gradient is applied to nano/micro plate in this study. The nonlinear strain–displacement relations are based on the Von-Kármán theory. According to classical, first order, third order, sinusoidal, parabolic, hyperbolic and exponential shear deformation plate theories, a new formulation is proposed incorporating surface stress effects through the Gurtin-Murdoch elasticity theory. In order to consider small scale parameters, this research is based on modified strain gradient theory (MSGT). Using the energy method and Hamilton’s principle, the non classical governing equations are derived. For nano/micro plate, simply supported boundary conditions are considered. For the purpose of solving differential equations, an analysis based on Galerkin procedure and finally the Bolotin method will be used to obtain the dynamic instability region (DIR). It is the objective of this study to investigate the impact of such parameters as small-scale parameters, alternating and direct applied voltage, intensity of magnetic field, surface effects, thermal environment and static load factor on the DIR. This study revealed that taking into account the smart foundation reduces the area of dynamic instability region by more than 60% for a constant intensity of magnetic field. The stability responses are also more convergent with the smart foundation. Additionally, the range is moved toward higher excitation frequencies and greater system stability. Validation of answers based on reliable scientific articles is one of the final stages of this research. These results can be used to design nano/micro electromechanical systems.

Nonlinear parametric excitation and dynamic stability of auxetic honeycombs core with CNTRC face sheets sandwich plate

This study aims to analyze the Nonlinear vibration and instability of a sandwich plate with an Auxetic Honeycomb core and a Carbon Nanotube Reinforced Composite (CNTRC) face layer on a viscous elastic foundation under parametric excitation. In the analytical model, the Hamilton principle and nonlinear strain-displacement relations determined by Von Karman theory and the first shear deformation plate theory (FSDT) are used. The governing equations are solved using the Galerkin method, which involves expanding the displacement field based on orthogonal functions. Once the displacement field has been expanded, a multiple-scale method is used to solve the equation of motion. The results show that the bifurcation diagrams and stability of sandwich plates depend on several parameters, including the geometric dimension of the honeycomb core, the material properties of the CNTRC face layer, and the temperature increment. The results of this study will likely be helpful in optimizing the design of sandwich plates for engineering applications, including the aerospace and automotive industries, where sandwich structures are widely utilized because of their high strength-to-weight ratios and excellent energy absorption capabilities.

Propagation characteristics of guided waves in CNTRCs plates resting on elastic foundations in a thermal environment

This paper investigates the wave propagation behavior of carbon nanotube-reinforced composites (CNTRCs) plates resting on elastic foundations in a thermal environment. The first-order shear deformation plate theory is applied to establish the mathematical model for the CNTRC plates. The effective material properties are calculated using the rule of mixture. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the CNTRC plates are derived using Hamilton’s principle. Then, the equations of motion are discretized by the Galerkin method and solved analytically by the eigenvalue method. Finally, the effects of various parameters including the temperature variations, the volume fraction of carbon nanotubes (CNTs), elastic foundations and the CNTs’ distribution patterns on the dispersion relations are investigated, it can be found that these parameters have significant effects on the wave propagation of CNTRCs plates.

Thermal Buckling and Vibrational Analysis of Carbon Nanotube Reinforced Rectangular Composite Plates Based on Third-Order Shear Deformation Theory

In this paper, thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) are investigated within the framework of third-order shear deformation theory (TSDT). CNT distribution along the thickness direction of the plate is uniformly or functionally graded. The equivalent properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations of motion are derived using the Hamilton principle. Obtained governing differential equations are analyzed by utilizing Fourier series expansion along the longitudinal and latitudinal direction for simply supported edges boundary conditions whereas for other edges boundary conditions we used the differential quadrature method (DQM) to solve numerically. Validation of the present formulation is assessed by comparing the results with those reported in the open literature. The effect of CNT volume fraction, the different patterns of CNT distribution, temperature difference, aspect ratio, and thickness-to-length ratio on buckling and vibration behavior of carbon nanotube-reinforced composite (CNTRC) plate is studied. The numerical illustration reveals that in the FG-X pattern of CNT distribution natural frequency and thermal buckling load is more significant compared with the other patterns of CNT distribution.

Concurrent topology optimization design for CNT orientation and CNTRC layout

In this study, the topology optimization (TO) design of carbon nanotube (CNT) orientation and material layout for carbon nanotube-reinforced composites (CNTRCs) is performed for the first time. The equivalent performance of CNTRCs is calculated by the extended easy-to-implement rule of mixtures. Then, by considering two independent angle variables, a 3-dimensional (3D) concurrent optimization model for CNT orientation and material layout is constructed. To decrease the possibility of falling into local optimal solutions, a discrete interval method is proposed to divide the search space into specific subintervals, and thus the original optimization problem is changed into material selection and subinterval angle optimization problems. In addition, different from conventional fiber-reinforced composites, CNTRCs employ nanoscale filler as reinforcement, which makes it more beneficial to achieve local material strengthening. Therefore, to decrease the possibility of local optimal solutions and achieve local structural strengthening, a concurrent TO model involving CNTRCs and isotropic materials under the volume constraint is proposed to achieve the optimal balance between structural stiffness and economy. Subsequently, the sensitivities of structural compliance with respect to design, selection, and angle variables are derived. Also, the effectiveness of the proposed method is verified by 2D and 3D examples.

Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Higher Order Refined Composite Beams Using Differential Quadrature Finite Element Method

Present paper deals on the free vibration investigation of carbon nanotube-reinforced composite (CNTs) beams, based on refined third order shear deformation finite element beam theory. The particularity of this model is that, it can capture shear deformation effect without using of any shear correction factor by satisfying shear stress free at free edges. The carbon nanotubes are supposed to be immersed in a polymeric matrix with functionally graded pattern across the thickness direction of the beam, and their material properties are evaluated using the rule of mixture. The differential equations of motion and related boundary conditions are extracted using Lagrange’s principle and solved employing a robust numerical tool called, Differential Quadrature Finite Element Method (DQFEM) for the first time, with high convergence speed, fast calculus performance as well as a good numerical stability. The obtained results have been validated with those available in literature, in order to show the correctness of the present model. Afterwards, a deep parametric study is performed to examine the effects of various geometrical and material parameters on the vibration behavior of FG-CNTs beams.

Using Laurent’s series in the theoretical solution to estimate the stress resultants of FG-CNTRC plates weakened by a central cutout at different temperatures

Conventional ordinary materials have many weaknesses when exposed to extreme loadings. Hence, scientists develop novel engineered materials to address these weaknesses. Functionally Graded Carbon Nanotube Reinforced Composites (FG-CNTRCs) are a modern group of materials that have recently flourished thanks to their excellent and unique mechanical properties. One common loading condition is subjecting FG-CNTRC plates containing cutouts to in-plane loadings. The presence of an opening disturbs the stress field, especially in the proximity of the cutout, and creates stress concentration. This study estimates the stress and moment resultants on the edge of elliptical cutouts in asymmetric FG-CNTRC plates under various loading conditions using a new analysis based on Lekhnitskii’s complex variables method, mapping function, and Laurent series. Unlike previous studies on perforated asymmetric plates, which were based on numerical methods or the Schwartz formulations, this study presents a new solution using Laurent’s series to represent the holomorphic function. In calculating the stress and moment components around the opening, the effect of determining variables is studied. This approach can be generalized to solve different anisotropic body problems (FG_CNTRC, FGM, Laminate composites). Thus, stress and moment components in perforated anisotropic plates can be determined simply and systematically using this method.

Thermal vibrations of complex-generatrix shells made of sandwich CNTRC sheets on both sides and open/closed cellular functionally graded porous core

This article investigates dynamical characteristics of complex-generatrix cylindrical shells (CGCS) made of advanced composite with profiles defined by mathematical functions. The sandwich composite consists of an open/closed cellular functionally graded porous core, which is assumed to perfectly bond to two thin carbon nanotube-reinforced composite (CNTRC) face-sheets at two sides of the CGCS. Three different kinds of porosity distribution, as well as three CNT reinforcement configs variating through the thickness dimension are considered. By utilizing the classical shell theory and Von Karman–Donnell’s geometrical nonlinearity assumption, the displacement system of equations is established and then Galerkin’s method is utilized to solve the nonlinear governing differential equation, therefore fundamental frequencies and nonlinear dynamic behaviors are achieved. The effects of geometrical parameters, material distribution, thermal environment, and the elastic foundation are demonstrated in numerical tables and graphical figures. This paper is expected to contribute knowledge for science and technology of materials and structures.