Multi-scale Hybrid Nanocomposite Research Articles

Effects of polymer’s viscoelastic properties and curved shape of the CNTs on the dynamic response of hybrid nanocomposite beams

Carbon nanotube (CNT)-reinforced polymer nanocomposites have excellent stiffness, strength and viscoelastic nature due to the time-dependent properties of the polymers. Hence, adequate knowledge about their rheological behavior is required to use such nanomaterials in designing aerospace structures. The present paper gives an account of the time dependency of the polymer and curvy shape of the CNTs while tracking the vibrational responses of multiscale hybrid nanocomposites. A combination of the modified Halpin–Tsai model and mixture’s rule is used for the homogenization process. According to the dynamic form of the virtual work’s principle, the governing equations will be attained based on a refined shear deformable beam theorem. In addition, Galerkin’s analytical solution is implemented to extract the system’s natural frequency for supported and clamped beams. The findings of this paper indicate that vibration suppression in the nanocomposite structures can be delayed if a high value is assigned to the polymer’s relaxation time. Besides, it is illustrated that hybrid nanocomposites consisting of wavy CNTs cannot provide ideal frequencies related to the nanocomposites manufactured from straight CNTs.

Modeling dynamic characteristics of the thermally affected embedded laminated nanocomposite beam containing multi-scale hybrid reinforcement

The current paper is devoted to investigate the free and forced vibrational responses of the multi-phase angle-ply laminated nanocomposite beam with focusing on the occurrence of resonance phenomenon. The influence of uniform thermal loading and three-parameter Kerr substrate which can affect the resonance behavior of the structure is surveyed. Utilizing a superior nanofiller with the name of Graphene Oxide (GO) together with the macro-scale Carbon Fibers (CFs) will constitute a novel multi-scale hybrid reinforcement for the polymer matrix. The combination of the Halpin–Tsai micromechanical model and extended rule of the mixture is implemented to estimate the effective properties of this multi-scale hybrid nanocomposite. Refined higher-order beam theory is employed to obtain the displacement fields and then with applying Hamilton’s principle, the governing equations are derived and analytically solved via Galerkin's exact solution method. Also, the presented results are validated with reputed works in open literature. Furthermore, some tabulated and graphical results are provided to reveal the effects of various parameters such as fibers’ orientation angle, weight and volume fractions of reinforcements, different boundary conditions, beam’s slenderness ratio, Kerr substrate parameters, excitation frequency and temperature change on the dynamic behavior of the proposed structure.

On energy absorption of the light-weight curved composite panel used in vehicle's roof

In this study, the dynamic stability and energy absorption of a novel type of sandwich panels with an extensive application in light vehicles are investigated. The curved panels are laminated multi-scale hybrid nanocomposites reinforced with carbon nanotubes. The whole panel is on a non-polynomial viscoelastic substrate to control the stability of the panel following vibrations. The 3D elasticity model is utilized for analyzing dynamic behavior and energy absorption. Moreover, a non-polynomial viscoelastic model is employed to take the effect of the viscoelastic substrate into account. The equivalent bulk properties of the nanocomposite are obtained using micromechanics and Halpin–Tsai relations. The nano-reinforcements are considered to have even distribution and random orientations in the epoxy matrix. The effects of material and loading conditions including viscoelastic parameters, compressibility, fiber’s volume and weight fractions, damping factor, and initial axially stress on the dynamic stability of the curved panels are evaluated. The most important outcome of this paper is that the change in parameters has a significant effect on dependency of energy absorption on radial stress. In application, the results suggest decreasing compressibility leads to increasing energy absorption of the shell structure.

A comprehensive computer simulation for frequency analysis of the annular system with a honeycomb core and angle-ply multiscale hybrid nanocomposite face sheets

The honeycomb structures, due to minimal density, relative high out-of-plane compression properties, and out-of-plane shear properties, have attracted a lot of attention. Regarding this issue, in the current research, fundamental frequency analysis of the annular plate with two angle-ply multiscale hybrid nanocomposite face sheets and a honeycomb core is investigated. Halpin-Tsai as well as Hamilton’s principle, are presented for obtaining the effective material properties and governing equations of the presented composite system. For modeling the thermal environment, three-kind of thermal loading is presented. Also, the current structure is covered with the Kerr elastic foundation. The generalized differential quadrature method is presented for obtaining the exact fundamental frequency of the annular plate with two angle-ply multiscale hybrid nanocomposite face sheets and a honeycomb core. Finally, the result section is given to illustrate the influences of two angle-ply multiscale hybrid nanocomposite reinforcement, the geometry of honeycomb core, thermal loading, elastic foundation, the weight fraction of nanocomposites, and structural parameters of the annular plate on the fundamental frequency of the annular plate with two angle-ply multiscale hybrid nanocomposite face sheets and a honeycomb core. The outcomes of the current report show that for the clamped edge in the boundary conditions and each increasing is a reason for falling down the frequency of the annular plate with a honeycomb core. Another consequence is that the impact of temperature changes on the frequency of the disk is hardly dependent on the fiber angle.

Effect of viscoelastic properties of polymer and wavy shape of the CNTs on the vibrational behaviors of CNT/glass fiber/polymer plates

Carbon nanotube (CNT)-reinforced polymer nanocomposites possess marvelous stiffness and strength as well as viscoelastic nature due to the time-dependent properties of the polymers. Hence, adequate knowledge about their rheological behavior is required if it is aimed at using such nanomaterials in design of aerospace structures. Present manuscript is arranged to account for the time-dependency of the polymer as well as wavy shape of the CNTs while tracking the vibrational responses of multi-scale hybrid nanocomposites for the first time. To this purpose, a mixture of the modified Halpin–Tsai model and mixture’s rule is used for the homogenization process. According to the dynamic form of the virtual work’s principle, the governing equations of the problem will be attained based on a higher-order shear deformable plate theorem to consider for thick structures. In addition, the Navier’s analytical solution is implemented to extract the system’s natural frequency for simply-supported plates. The findings of this paper indicate on the fact that the vibration suppression in the nanocomposite structures can be delayed if a high value is assigned to the characteristic relaxation time of the polymer. Besides, it is illustrated that hybrid nanocomposites consisted of wavy CNTs (i.e., corresponding with more realistic case) cannot provide ideal frequencies related to the nanocomposites manufactured from straight CNTs.

Spider Web-like Flexible Tactile Sensor for Pressure-Strain Simultaneous Detection.

Multiparameter integrated sensors are required for the next generation of flexible wearable electronics. However, mutual interference between detected signals is a technical bottleneck for a flexible tactile sensor to realize pressure-strain monitoring simultaneously and sensitively. Herein, a flexible dual-parameter pressure-strain sensor based on the three-dimensional (3D) tubular graphene sponge (TGS) and spider web-like stretchable electrodes is designed and fabricated. As the pressure-sensitive module, the unique 3D-TGS with an uninterrupted network of tubular graphene and high graphitic degree demonstrates great robust compressibility, supporting compression to ∼20% without shape collapse. The spider web-like stretchable electrodes as the strain-sensitive module are fabricated by a spray-embedded process based on the hierarchical multiscale hybrid nanocomposite of Ag nanowires (NWs) and carbon nanotubes (CNTs) with an optimal mass ratio. By comparing the output signals of spider web-like flexible electrodes, the magnitude and direction of the applied force can be effectively monitored simultaneously. Moreover, the potential applications of the flexible dual-parameter pressure-strain device in human-machine interaction are also explored, showing great promise in artificial intelligence and wearable systems.

On the nonlinear dynamics of the multi-scale hybrid nanocomposite-reinforced annular plate under hygro-thermal environment

In this article, the nonlinear free and forced vibration analysis of multi-scale hybrid nano-composites (multi-scale HNC) annular plate (multi-scale HNCAP) under hygro-thermal environment and subjected to mechanical loading is presented. The material of matrix composite is enhanced by either carbon fibers (CF) or carbon nanotubes (CNTs) at the small or macro-scale. The multi-scale laminated annular plate’s displacement fields are determined using third-order shear deformation theory (third-order SDT) and nonlinearity of vibration behavior of this structure is taken into account considering Von Karman nonlinear shell model. Energy method known as Hamilton principle is applied to create the motion equations governed to the multi-scale HNCAP, while they are solved using generalized differential quadrature method (GDQM) as well as multiple scale method. The results created from finite-element simulation illustrates a close agreement with the semi-numerical method results. Ultimately, the research’s outcomes reveal that increasing value of the moisture change ( $$\Delta H$$ ) and orientation angle parameter ( $$\theta$$ ), and the rigidity of the boundary conditions lead to an increase in the structure’s frequency. Besides, whenever the values of the nonlinear parameter ( $$\gamma$$ ) are positive or negative, the dynamic behavior of the plate tends to have hardening or softening behaviors, respectively. Also, there are not any effects from $$\gamma$$ parameter on the maximum amplitudes of resonant vibration of the multi-scale HNCAP. Last but not least, by decreasing the structure’s flexibility, the plate can be susceptible to have unstable responses.

Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems

Honeycomb structures have the geometry of the lattice network to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multiscale hybrid nanocomposite (MHC) face sheets rested on an elastic foundation. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the effects of the orientation of fibers ( $$\theta_{{\text{f}}} /\pi$$ ) in the epoxy matrix, Winkler–Pasternak constants ( $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ ), thickness to length ratio of the honeycomb network ( $$t_{{\text{h}}} /l_{{\text{h}}}$$ ), the weight fraction of CNTs, value fraction of carbon fibers, angle of honeycomb networks, and inner to outer radius ratio on the frequency of the sandwich disk. The results show that it is true that the roles of $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ are the same as an enhancement, but the impact of $$K_{{\text{w}}}$$ could be much more considerable than the effect of $$K_{{\text{p}}}$$ on the stability of the structure. Additionally, when the angle of the fibers is close to the horizon, the frequency of the system improves.

On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method

This article presents the frequency responses of a sandwich disk with a lactic core (honeycomb), two middle layers containing SMA fiber, and two outer layers (multi-scale hybrid nanocomposite (MHC)). The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Compatibility equations are considered for modeling the interface between the layers of the sandwich disk. Afterward, a parametric study is done to present the effects of SMA fiber, boundary conditions, outer to inner radius ratio, honeycomb network angle, thickness to length ratio of the honeycomb, fibers angle, weight fraction of CNTs, honeycomb to face sheet thickness ratio on the frequency of the multi-phase sandwich disk. The results show that employing the honeycomb network as the core of the structure improves the dynamic response of the structure, impressively. Another consequence is that if there are C-C, C-S boundary conditions, by ever-increase in the θh/π, the dynamic response tends to decline.

Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework

Honeycomb structures are one type of structure that has the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multi-scale hybrid nanocomposite (MHC) face sheets. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method. Afterward, a parametric study is carried out to investigate the effects of the thickness to length ratio of the honeycomb core, honeycomb core thickness to inner radius ratio, value fraction of carbon fibers, radius ration of the disk, the angle of honeycomb network, the weight fraction of CNTs, and tensile and compressive in-plane force on the frequency of the sandwich disk with honeycomb core and MHC. The results show that the critical fiber angle is $$\theta_{{\text{f}}} /\pi =$$ 0.5 for C–C and C–S boundary conditions. Another consequence is that when the structure is fixed with S–S boundary conditions, for $$p =$$ 500 and $$p = 1000$$ , as well as the critical dimensionless angle for fibers is 0.5, there are two more range for critical fiber angle in which they are $$0.275 \le \theta_{{\text{f}}} /\pi \le 0.375$$ and $$0.23 \le \theta_{{\text{f}}} /\pi \le 0.39$$ , respectively. Additionally, the range of the critical dimensionless angle for fibers increases by increasing the applied load. Some new results related to dynamic behavior of an MHC are also presented, which can serve as benchmark solutions for future investigations.

Wave propagation response of agglomerated multi-scale hybrid nanocomposite plates

This paper aims to investigate the wave propagation analysis of multi-scale hybrid nanocomposite plates by considering the influences of the aggregation of the nanoparticles. For the constituent materials of the plate, a polymeric matrix is supposed to have macro- and nano-reinforcements dispersed in it. The well-known micromechanical methods, such as Eshelby-Mori-Tanaka model and the rule of the mixture, are exerted to compute the effective material properties of the nanocomposite plate. Also, a refined higher-order shear deformation theory is implemented to obtain the motion relations. Besides, the governing equations are derived by employing the principle of Hamilton. Then, the analytic method is used to solve the obtained governing equations of structure and finally wave frequency and phase velocity are calculated. The effects of the various parameters on the variation of phase velocity and wave frequency of the multi-scale nanocomposite plates are examined. The presented results demonstrate that the mechanical response of the system can be decreased, while the nanotubes are covered by clusters.

Vibration analysis of multi-scale hybrid nanocomposite shells by considering nanofillers’ aggregation

Free oscillation analysis of shells consisted of multi-scale hybrid nanocomposites is carried out with regard to the destroying effect of the nanofillers’ agglomeration on the system’s dynamics. The equivalent material properties of the hybrid nanocomposite are obtained in the framework of a bi-level micromechanical procedure. The influence of existence of agglomerated carbon nanotubes (CNTs) on the stiffness of the nanocomposite is included with the aid of the Eshelby-Mori-Tanaka method. Thereafter, the first-order shear deformation theory (FSDT) of the shells will be combined with the dynamic form of the principle of virtual work to reach the Euler-Lagrange equations of the problem. Next, the governing equations will be extracted from the Euler-Lagrange ones by using the constitutive equations of the nanocomposite. To obtain the natural frequencies of the system for shells with clamped and simply supported ends, the Galerkin’s method is hired. The validity check reveals that the utilized methodology is powerful enough to predict the frequency behaviors of nanocomposite shells. According to the results, it can be inferred that the hybrid nanocomposite shells may be involved in resonance phenomenon in low-range frequencies if the impact of the CNTs’ aggregation is neglected. Obviously, the volume fraction of the CNTs inside the inclusions plays a magnificent role in the determination of the system’s dynamic behavior.

RETRACTED ARTICLE: Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM

In this research, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid nano-composite reinforced disk in the thermal environment and subject to a harmonic external load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the viscoelastic disk subject to harmonic excitation. The fundamental and golden results of this paper could be that in the lower value of the external harmonic force, different FG patterns do not have any effects on the motion response of the structure. But, for the higher value of external harmonic force and all FG patterns, the chaos motion could be seen and for the FG-X pattern, the chaosity is more significant than other patterns of the FG. As a practical designing tip, it is recommended to choose plates with lower thickness relative to the outer radius to achieve better vibration performance.

Chaotic oscillation of a multi-scale hybrid nano-composites reinforced disk under harmonic excitation via GDQM

In the presented computational approach, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid Nano-composites reinforced disk (MHCD) embedded in a viscoelastic media and subject to a harmonic load. UsingHamilton's principle and Von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the viscoelastic disksubject to harmonic excitation. The golden results of this paper is that the chaotic motion and nonlinear frequency of the disk is hardly dependent on the value of the outer to inner radius ratio (Ro/Ri) and viscoelastic parameters and it means that by increasing the value of Ro/Ri parameter and taking into account the viscoelastic foundation, the motion of the system tend to show the chaotic motion. Moreover, at the lower value of the Ro/Ri parameter, quasi-harmonic and chaotic responses can be seen for the conditions with and without considering the effect of viscoelastic foundation and at the higher value of the parameter, the chaosity of the system decreases.

Effect of agglomeration of the nanotubes on the vibration frequency of the multi-scale hybrid nanocomposite conical shells: a GDQ-based study

In the present manuscript, the generalized differential quadrature method (GDQM) will be employed in order to solve the free vibration problem of three-phase carbon fiber/nanotube/polymer hybrid nanocomposite conical shells, rested on a two-parameter elastic medium, regarding for the influence of the agglomeration of the carbon nanotubes (CNTs) on the dynamic responses of the shell for the first time. The equivalent material properties of the multi-scale hybrid nanocomposite will be derived according to a two-step homogenization procedure including the Eshelby-Mori-Tanaka method incorporated with the modified form of the rule of the mixture. Afterward, the strain-displacement relationships of the continuous system will be obtained using the classical shell theory for thin-walled conical shells. Extending the Hamilton’s principle for the conical shell, the motion equation of the problem will be enriched. At the end, the associated boundary condition will be used in associated with the GDQ discretization for the purpose of extracting the natural frequency of the continuous system. The verification tests reveal that the presented mathematical framework is powerful enough to estimate the dynamic response of the system. The results of this study show that existence of agglomeration phenomenon can dramatically affect the dynamic behaviors of the nanocomposite structure.

On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk

This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing equations of motion, which is finally solved by generalized differential quadrature method (GDQM) and perturbation method (PM). Finally, the results show that FG patterns, different orientation angle of the fiber, the VF and WCNT parameters, axial load, nonlinear temperature gradient, and applied temperature of the top surface play an essential impact on the linear and nonlinear dynamic responses of the MHCD. The more significant outcome of this research is that the effects of the VF, WCNT, $$\theta$$, and β parameters on the nonlinear frequency of the MHCD can be considered at the higher value of the large deflection parameter and the effect of negative axial load on the dynamic responses of the structure is more intensive. As an applicable result show that the best functionally graded (FG) pattern for serving the highest nonlinear dynamic response of an MHC reinforced annular plate is FG-A.

Thermal buckling analysis of agglomerated multiscale hybrid nanocomposites via a refined beam theory

Application of a newly developed refined higher-order beam theory in the thermal buckling problem of a multiscale hybrid nanocomposite beam is shown here with respect to effect of nanofillers aggregation for the first time. In this research, a mixture of macro and nanoscale fillers will be utilized to be dispersed in an initial matrix to possess a multiscale hybrid nanocomposite. The equivalent material properties are seemed to be calculated coupling the Eshelby-Mori-Tanaka model with the rule of mixture to consider the effects of CNTs inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy based approach is implemented to obtain the governing equations of the problem utilizing a refined higher-order plate theorem. Next, the derived equations will be solved in the framework of Galerkin’s well-known analytical method to reach the critical buckling load. It is worth mentioning that influence of various boundary conditions is included. Once the validity of presented results is proven, a set of numerical examples are presented to explain how each variant can affect the buckling behaviors of the structure.

Frequency Characteristics of Multiscale Hybrid Nanocomposite Annular Plate Based on a Halpin–Tsai Homogenization Model with the Aid of GDQM

In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler–Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. The annular plate is modeled based on higher-order shear deformation theory (HSDT). We present a modified Halpin–Tsai model to predict the effective properties of the MHCAP. Hamilton’s principle was employed to establish the governing equations of motion, which is finally solved by the generalized differential quadrature method (GDQM). In order to validate the approach, numerical results were compared with available results from the literature. Subsequently, a comprehensive parameter study was carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, outer temperature, volume fraction and orientation angle of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio, and inner radius to thickness ratio on the response of the plate. The results show that applying a sinusoidal temperature rise and locating more CNTs in the vicinity of the bottom surface yielded the highest natural frequency.

Static stability analysis of agglomerated multi-scale hybrid nanocomposites via a refined theory

Present paper is proposed to capture the influences of carbon nanotubes’ agglomeration on the stability behaviors of multi-scale hybrid nanocomposite beams within the frameworks of refined higher order beam theories for the first time. In this research, a mixture of macroscale and nanoscale fillers will be utilized to be dispersed in an initial matrix to possess a multi-scale hybrid nanocomposite. The equivalent material properties are seemed to be calculated coupling the Eshelby–Mori–Tanaka model with the rule of the mixture to consider the effects of carbon nanotubes inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy-based approach is implemented to obtain the governing equations of the problem utilizing a refined higher order beam theorem. Next, the derived equations will be solved in the framework of Galerkin’s well-known analytical method to reach the critical buckling load. It is worth mentioning that influence of various boundary conditions is included, too. Once the validity of presented results is proven, a set of numerical examples are presented to explain how each variant can affect the structure’s stability endurance.

Vibration analysis of fluid-conveying multi-scale hybrid nanocomposite shells with respect to agglomeration of nanofillers

The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution. The consistent material is considered to be made from an initial matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers’ agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube reinforced (CNTR) nanocomposite are coupled with those of CFs within the framework of a modified rule of mixture. On the other hand, the influences of viscous flow are covered by extending the Navier-Stokes equation for cylinders. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the dynamic form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin’s method to reach the natural frequency of the structure for both simply supported and clamped boundary conditions. Presenting a set of illustrations, effects of each parameter on the dimensionless frequency of nanocomposite shells will be shown graphically.