The convergence of artificial intelligence (AI) and carbon nanotube (CNT) chemistry is accelerating innovations in the synthesis, functionalization, and advanced applications of carbon-based nanomaterials. This review highlights recent AI-driven methodologies, including neural networks, ensemble learning, metaheuristics, and hybrid frameworks that are redefining the design, surface engineering, and structure–property relationships of CNTs. Special attention is given to their roles in clean energy technologies, polymer nanocomposites, environmental systems, and nanoelectronics. Advances such as autonomous synthesis guided by deep learning, high-throughput experimentation, and AI-enabled property prediction are critically reviewed. Challenges including data fragmentation, class imbalance, and lack of benchmarking are addressed, alongside future directions such as physics-informed machine learning, robotics integration, and multi-objective optimization. This review positions AI as a disruptive catalyst in advanced CNT research, offering intelligent automation and predictive insights across diverse carbon-material applications.

Using pipes made of composite materials is to modify the performance of a fluid transporting system by combining materials with different properties to create lightweight, strong, corrosion-resistant, and durable devices. The wave propagation characteristics of composite pipes are of special interest when subjected to highly transient loads. However, transient loads can produce dynamic waves that travel through the pipe material. In such circumstances, composite pipes must show appropriate characteristics in managing the wave propagations generated by the applied loads. This paper attempts to study the wave propagation in composite pipes under the effects of internal flow velocity. The Hamilton principle and Euler-Bernoulli beam assumptions are used to derive the governing differential equations of pipes conveying fluids with clamped-free and clamped-clamped boundary conditions. The finite element method with the Newmark computational scheme is then utilized to discretize and solve the equations and find the time-dependent response of the system. The effects of boundary conditions and fluid flow velocity on the dynamic behavior of composite pipes will also be investigated. The results demonstrate that both fluid and boundary conditions significantly contribute to how composite pipes respond when subjected to highly transient impact loads.

The motivation for the present study comes from the appearance of fiber dissolution in industrial applications of composite pipes under different flowing fluids and operating conditions. To mitigate the consequences of glass fiber dissolution in glass fiber reinforced plastics (GRP) pipes, it is essential to investigate the dynamic characteristics of the pipes under internal fluid flow. This paper presents a novel time-dependent micromechanical model and examines the effects of glass fiber dissolution on the instability and vibrational behavior of a composite pipe conveying fluid. The Hamiltonian principle obtains the governing equations of the conveying fluid composite pipe system with fiber dissolution defects. The Finite Element Method (FEM) is then used to solve the eigenvalue problem for the natural frequencies, divergence, and flutter critical velocities of the composite pipe conveying fluid. The effects of different parameters, such as span and amount of dissolution, as well as the quality of the dissolved portion of the fibers, are highlighted on the instability and vibration characteristics of composite pipes. The results show that fiber dissolution significantly affects the behavior of composite pipes conveying fluid. This work also provides a better understanding of the above-mentioned "environmental aging" type in fiber-reinforced composites.

The global flexibility and local rigidity of corrugated pipes have made them a good candidate in many engineering applications such as aerospace, oil and gas industries, heat and cooling systems, compact heat exchangers, etc. In this study, dynamic responses of corrugated clamped-clamped pipes conveying fluid are investigated. The governing equations of the system are derived by using the Hamiltonian principle based on the Euler-Bernoulli beam hypothesis. Non-uniformity of the flow velocity profile is considered in the formulation for both laminar and turbulent fluid flow. So, the flow-profile-modification factor for laminar flow and space-dependent mean velocity for turbulent flow are proposed. For spatial discretization of these equations, the finite element method is used. The effects of several parameters including fluid velocity, the corrugation length, as well as corrugation amplitude on the stability of the pipe system are examined. Natural frequencies of the pipe in hydrostatic flow conditions and critical flow velocities are determined for a vast range of parameters. Numerical results show that the stability of the system is significantly affected by the corrugation length and amplitude.

This paper presents the results of several numerical simulations of two flow configurations involving a pipe conveying fluid and simultaneously subject to an external axial flow, using a coupled two-way Fluid-Structure Interaction (FSI) computational approach. The computational model is made up of two parts: a finite volume-based computational fluid dynamics (CFD) code for the fluid domain, and a finite element-based computational solid mechanics code for the structural domain. This approach solves the fluid and structural domains simultaneously, accounting for both the structural deformation caused by fluid pressure and the changes in fluid pressure resulting from structural deformation. To achieve accurate results, the process involves exchanging data between the solid and fluid models. In this technique, the pressure is transferred from CFD to structural analysis, and the deformation is transferred from structural to CFD analysis. This update occurs with each iteration until both solutions converge. Additionally, the simulation results are compared to those obtained from experiments for further validation.

Isogeometric Analysis (IGA) employs B-Splines and Non-Uniform Rational B-Splines (NURBS) to construct approximating functions, establishing a numerical approach for solving governing differential equations related to elliptic diffusion. In this study, IGA is implemented to model groundwater flow in unconfined aquifer systems bearing different geometries. The proposed IGA methodology exploits its approximating functions to intricately delineate the problem’s geometry, achieving this precision with a minimal set of control points. A novel boundary-updating formula is introduced, dynamically repositioning fundamental points within each iteration to enhance accuracy. The efficacy of the improved IGA is verified through four numerical and benchmark simulations, including comparisons with analytical solutions. The IGA-derived results outperform the analytical solutions and closely align with the predicted heads of groundwater at the specified nodes using known numerical solutions (with less than 5% difference). Using IGA offers several benefits over analytical solutions, including enhanced continuity of the approximation solution and improved precision. The present formulation enables efficient simulation of groundwater flow, considering the exact aquifer domain geometry, while only requiring a small number of degrees of freedom. This innovative approach holds the potential to significantly expedite model creation, particularly in intricate structural scenarios, as it obviates the need for intricate meshing and enables the simultaneous development of geometry and computational models.

The nonlinear free vibrations and stability of pipes conveying fluid constructed of Functionally Graded Carbon Nano-Tube Reinforced Composite (FG-CNTRC) materials are studied in this paper. The material properties of FG-CNTRC are supposed to be graded within the thickness direction and estimated by the modified rule of mixtures. The equations of motion of the system are derived using the extended Hamilton’s principle for open systems based on Timoshenko beam theory. To consider nonlinear effects, large deformations-small strains hypothesis is adopted by applying the von Kármán geometric nonlinear theory. The nonlinear free vibration and the fluid flow effects in the pipe system are investigated numerically, employing the super convergent finite element method to discretize nonlinear coupled partial differential equations. This is a powerful method to accurately predict steady state response of a dynamical system. The Newmark and Newton-Raphson methods are also applied to solve the resulted set of ordinary nonlinear differential equations. The applicability of the proposed mathematical approach is then be studied through several numerical investigations with different parameters including nanotube volume fraction, mass ratio, CNT distributions, fluid velocity and pipe geometry.

Various types of pipelines and risers used in oil and gas industry undergo dynamic instabilities (buckling and flutter) due to the internal fluid flows. This paper aims to study the possibility of increasing pipeline stability by using pipes made of composite materials and reinforced by carbon nanotubes. Hamilton principle for open systems is used to derive the equations of motion of the pipe based on a higher order shear deformation theory. The rule of mixture is implemented to express the change of the material properties of the pipe through the pipe thickness. Finite element analysis with super convergent elements is used to solve the governing differential equations of the problem. Static equilibrium equations of the pipe without fluid are used to develop the shape functions of the elements. The results of the present study are compared with those available in the literature for dynamic behavior of pipes with Euler-Bernoulli and Timoshenko beam theories. The effects of different parameters on (i) vibration characteristics and (ii) stability limits of composite pipes conveying fluid are also examined.

This paper aims to provide a new insight into the stability analysis of pipes/tubes conveying fluid with non-conventional cross sections that can be considered as an alternative design for traditional circular pipes used in a wide range of industrial applications. They provide the flexibility of being installed with major vertical or horizontal axes based on the desired hydraulic conditions and type of practical applications. However, the effects of non-uniformity of the flow velocity distribution need to be considered in the governing equations of pipes with non-conventional cross sections. In this paper, the influence of non-uniform flow velocity profile on dynamic behavior and instability of elliptical pipes made of functionally graded materials (FGMs) is studied. To achieve this goal, the traditional equation of motion for a circular pipe with an ideal fluid flow is modified through the recalculation of centrifugal and Coriolis forces for every differential element of the fluid. Timoshenko's beam theory is used to obtain the governing differential equations of motion and finite element method is utilized in the discretization process and solution of the governing equations of the problem. Consequently, critical flow velocities, divergence and re-stabilization behavior of the pipe are predicted using a modal analysis approach. The effects of power index and aspect ratio on the stability of FGM elliptical pipes are also investigated.

Dynamic behavior and instability of clamped-clamped pipes conveying fluid with longitudinal fins are studied in this paper. The analysis is done for pipes made of both homogeneous and functionally graded materials (FGM). In the FGM case, the materials of pipe and fins are assumed to be graded through the radial direction based on a power-law distribution. The Hamiltonian principle and Euler-Bernoulli beam assumptions are employed to derive the governing differential equations of the pipe system. Different fin configurations are investigated and the effects of several parameters including power‐law index, fluid velocity, number of fins, thickness and height of the fins are analyzed. Natural frequencies of the pipe and critical flow velocities are determined for various values of parameters. Numerical results show that the stability of the system is significantly affected by the power‐law index and fin dimensions. Among different fin configurations studied in this paper, the addition of non-horizontal fins provides significant improvement in the stability of both homogeneous and FGM pipes conveying fluid and consequently, can be considered as an effective "dynamic stabilizer" for the pipe system. In contrast to non-horizontal fins, the horizontal fins improve the stability of pipes conveying fluid, slightly.

Abstract This paper presents the results of a coupled two-way fluid–structure interaction (FSI) analysis of a slender flexible vertical cantilevered pipe hanging concentrically within a shorter rigid tube forming an annulus. The pipe is subjected to internal and annular flows simultaneously. This system has applications in brine production and salt-cavern hydrocarbon storage. In this study, the fluid–structure problem is solved with a finite volume based computational fluid dynamics (CFD) code for the fluid domain coupled to a finite element based computational solid mechanics code for the structural domain. The numerical results obtained for the free-end displacement of the central pipe versus the annular/internal flow velocity ratio Uo/Ui are presented and compared with those obtained from experiment. The capability of the numerical model to predict the onset of the experimentally observed flutter instability in the system is also examined. This study provides a better insight into the dynamics of the system.

In addition to the traditional hollow circular sections used in marine structures, other hollow sections have attracted the attention of architects and design engineers due to their mechanical characteristics such as torsional rigidity and local strength against impact loading. The purpose of this study is to investigate dynamic response of pipes conveying fluid with variable wall thickness through both circumferential and axial directions. Pipes with variable wall thickness have different flexural rigidities about two different principal axes. This property allows these pipes to be oriented efficiently, meet various design requirements and resist the applied loads. The results of this investigation provide a better insight into the physics and dynamic behavior of noncircular pipes conveying fluid. Two different geometries are studied, (i) the pipe is assumed with a general non-circular cross section with variable wall thickness along the circumferential direction, (ii) both inner and outer boundaries of the pipe cross section are assumed to be circles whereas the wall thickness of the pipe along axial direction is varied with a specified function. The governing differential equations of the problem are derived using Timoshenko beam theory with the effect of shear deformation included in the formulation. The discretization of the problem domain is done using the finite element method. Consequently, a modal analysis is employed to calculate the critical flow velocities of the pipe with clamped-clamped end conditions. The effects of different cross sections on the critical flow velocity are investigated. The importance of Coriolis forces on the presence of coupled-mode flutter and re-stabilization point are also discussed for different values of mass ratio.

A cantilevered pipe conveying fluid is a non-conservative system and loses its stability for a sufficiently high flow velocity. When a fluid-conveying pipe is involved as a structural element in a mechanical system (e.g., in oil and gas industry), it is often preferred to maximize the critical flow velocity in the pipe. This study focuses on the possibility of increasing the critical flow velocity of horizontal and vertical pipes conveying fluid by considering one or more additional masses and/or springs at various locations along the pipe. Galerkin method is used to solve the equation of motion of the problem derived based on the linear theory of elasticity and a plug flow model assumption. The results of the present study are compared with those available in literature. The results show a possibility of increasing the critical fluid velocity for horizontal and vertical cantilevered pipes. It is observed that the critical flow velocity can be significantly increased by adding a spring and a point mass at specific positions depending on the mass ratio β of the system.

Micropolar theory constitutes extension of the classical field theories. It is based on the idea that every particles of the material can make both micro rotation and volumetric micro elongation in addition to the bulk deformation. Since this theory includes the effects of micro structure which could affect the overall behaviour of the medium, it reflects the physical realities much better than the classical theory for the engineering materials.In the micropolar theory, the material points are considered to possess orientations. A material point carrying three rigid directors introduces one extra degree of freedom over the classical theory. This is because in micropolar continuum, a point is endowed with three rigid directors only. A material point is then equipped with the degrees of freedom for rigid rotations, in addition to the classical translational degrees of freedom. In fact, the micropolar covers the results of the classical continuum mechanics. The micropolar theory recently takes attentions in fluid mechanics and mathematicians and engineers are implementing this theory in various theoretical and practical applications.In this paper the fluid-structure analysis of a vibrating micropolar plate in contact with a fluid is considered. The fluid is contained in a cube which all faces except for one of the lateral faces are rigid. The only non-rigid lateral face is made of a flexible micropolar plate and therefore, interacts with the fluid. An analytical approach is utilized to investigate the vibration characteristics of the aforementioned fluid-structure problem. The fluid is non-viscous and incompressible. Duplicate Chebyshev series, multiplied by boundary functions are used as admissible functions and the frequency equations of the micropolar plate are obtained by the use of Chebyshev-Ritz method.Also the vibration analysis of the plates modeled by micropolar theory has been done. This analysis shows that some additional frequencies due to the micropolarity of the plate appears among the values of the frequencies obtained in the classical theory of elasticity, as expected. These new frequencies are called micro-rotational waves. We also observed that when the micropolar material constants vanish, these additional frequencies disappear and only the classical frequencies remain. Specially, we observed that these additional frequencies are more sensitive to the change of the micro elastic constants than the classical frequencies. The frequencies and mode shapes of the coupled fluid structure interaction problem are obtained in the present study based on the micropolar and classical modeling. The numerical results for the problem are compared with those obtained by the analytical method for their differences and to confirm the proposed method. The microrotatinal wave frequencies and mode shapes are also developed. The results show that the natural frequencies and mode shapes for the transverse vibrations of the problem are in good agreement with the classical one and our knowledge from the physical nature of the problem.

Dynamic analysis and design of light-weight structures subject to different types of applied forces is of considerable practical interest in engineering applications. Porous structures are a novel class of weight-efficient engineering materials with optimized mechanical properties and improved structural performance. Porous materials with functionally graded porosity are achieved by tailoring the size and density of the internal pores in one or more directions that leads the desired mechanical properties. In this paper, the dynamic response of poroelastic pipes made of a closed–cell porous material with functionally graded porosity subjected to influences induced by fluid flow is investigated. Three different porosity distributions through the pipe thickness are introduced. The finite element formulation of dynamic equations of pipeline conveying fluid are presented based on Timoshenko theory by considering the fluid–structure interaction and the effect of shear deformation. The complex modal analysis is employed to estimate the natural frequencies of a clamped-clamped pipe with different velocities. Finally, the effects of fluid velocity on the dynamic response of a poroelastic pipe are studied.

Recent advances in the development of new engineering materials have led to the creation of different types of porous materials. These materials can be used to remove harmful compounds from soil, air, and water as a method of environmental remediation. This paper aims to study the mechanical behavior of Functionally Graded (FG) porous materials. In terms of engineering applications, these weight-efficient materials may allow for an improvement in the structural performance of certain mechanical systems. In this analysis, the effects of porosity distribution in curved thick panels made of FG porous materials are numerically investigated using the Differential Quadrature Method (DQM). Two types of porous materials, including both open-cell and saturated closed-cell panels with three symmetric, non-symmetric, and uniform porosity distributions, are considered. Elasticity theory is used to develop the governing differential equations of the curved panel. The physical behavior of a curved panel and the influences of porosity distribution, boundary conditions, and geometrical characteristics (i.e., angle, length, radius, and thickness) of the panel are investigated.

In this paper, the effect of different profile variations on vibrational properties of non-uniform beams made of graded porous materials is studied. Timoshenko beam theory is used to present the mathematical formulation of the problem including shear deformation, rotary inertia, non-uniformity of the cross-section, and graded porosity of the beam material. Three different variations of porosities through the thickness direction are introduced. The beam is assumed with the clamped condition at both ends. To obtain a numerical solution, finite element formulations of the governing equations are presented. The non-uniform beam is approximated by another beam consisting of n elements with piecewise constant thickness to keep the volume and hence the total mass unchanged for each element. The beam response has been calculated for the first three modes of vibration. In each case, the results for different types of thickness variation and porosity distribution are compared with those obtained for a beam with uniform thickness. The effects of non-uniformity, taper parameters, and porosity distribution on the frequencies and mode shapes are investigated. It is observed that a considerable change in frequencies and mode shapes can be achieved by selection of different thickness variation and porosity distribution.

Stability analysis of curved pipes conveying fluid is of significant interest in many engineering aplications such as floating and moored system dynamics. The aim of this paper is to develop a new formulation based on the Isogeometric Analysis (IGA) for vibration and stability analyses of curved pipes conveying fluid. Both divergence and flutter instabilities of curved pipes are investigated. IGA uses B-Splines and Non-Uniform Rational B-Splines (NURBS) as basis functions. The main feature of IGA, as required in dynamic analysis of curved structures, is the ability of the NURBS functions to represent the exact geometry of the problem with fewer control points. This method provides several advantages including high-order continuity of the solution and better accuracy. The governing differential equations of the problem are obtained using the Hamiltonian's principle. The effects of rotary inertias of both pipe and fluid are also included in the mathematical formulation. It is shown that the present formulation can provide accurate results with small number of degrees of freedom. It is concluded that IGA can be used efficiently to predict the instability of curved pipes conveying fluid with the advantage of considering the exact curvature of the pipe.

The incapability of classical elasticity theory of accurately modeling the deformation behavior of structures at micro- and nanoscales has necessitated the development of more advanced theories. The strain gradient theory, being one of such theories, involves higher-order spatial derivatives of the field variables. However, except for few cases, there exists no analytical solution based on the strain gradient theory. This paper proposes a novel meshfree method with modified point interpolation functions possessing the Kronecker delta property; it is proposed to incorporate the strain gradient formulation into the Euler–Bernoulli beam theory. In the present method, the continuity of the shape function and its higher derivatives, appearing in the general form of the strain gradient theory, can be much more conveniently accommodated compared to the FEM. In addition, the present approach is based on the global weak form which is computationally less costly as compared to meshfree methods based on local weak form. The validity of the method is demonstrated by comparing the results with both analytical and experimental results for beams at macro- and microscales for static and dynamic loadings.

The fluid-elastic instability of hanging cantilevered pipes subject to internal and external flows is studied. Flow-induced vibrations cause these flexible tubular cantilevers to experience dynamic divergence (flutter) as well as static divergence (buckling) at high enough flow velocities. Specifically, the system studied consists of a flexible tubular hanging cantilever, which hangs concentrically within an outer rigid tube. Fluid flows internally from the clamped end of the cantilever to the free end and flows in the opposite direction in the annular region between the cantilever and the outer tube. For the system investigated, flow discharges radially from the free-end of the cantilever through the use of an end-piece. A linear model is derived in which series solutions are employed using Euler-Bernoulli beam comparison functions and is compared with experimental results. The effects of end-piece mass, confinement, pipe length, and comparisons between radial and axial flow have also been studied.