Tsai Model Research Articles

On the wave propagation in a higher-order multi-phase curved porous system

The porosity affecting the vibrational characteristics of structures should be considered due to the fact that these porosities can happen during the manufacturing process. The solid body and the liquid or gas compose the porous materials. In this regard, for the first time, wave propagation corresponding to the curved panel made of reinforced porous composites is investigated. Higher-order shear deformable theory (HSDT) is employed in order to extract the formulation. The effective material is attained by employing the rule of the mixture as well as the modified Halpin–Tsai model. Also, equations of motions that are solved analytically are extracted via Hamilton’s principle. The impacts of radius-to-total thickness ratio, the weight fraction of carbon nanotubes (CNTs), porosity factor, that different composite patterns, the pattern of porosity, as well as carbon fibers on phase velocity behavior corresponded with a reinforced curved porous panel are studied. The presented results can be employed in ultrasonic inspection techniques as well as structural health monitoring.

Simulation of multi – field coupling damping characteristics of magnetorheological damper in ring system by artificial intelligence method

A new kind of smart material called Magnetorheological (MR) has attracted a lot of attention among designers due to its mechanical properties that can alter in a controlled fashion by an external magnetic field. Regarding this issue, in the current work, for the first attempt, the dynamic stability of a sandwich shell made of MR core and graphene nanoplatelets reinforced composite (GPLRC) face sheets is presented. Using the role of the mixture and modified Halpin–Tsai model, the effective material properties of GPLRC face sheets are presented. Via Hamilton’s principle and linear viscoelastic theory, the governing equations of the current sandwich structure are developed. Also, compatibility equations for accurate modeling of the sandwich structure are presented. The discrete singular convolution integration method (DSC-IM) for prediction of nth-order derivatives of a sufficiently smooth function via weighted linear sum function of the amounts at each separated point in the throughout allowable input range is presented. For more verification, a deep neural network as an artificial intelligence method is presented. Finally, the results show that GPL’s weight fraction, viscoelastic foundation, the geometry of GPLs, and geometry of the structure have an important role in dynamic stability and modal loss factor parameter of sandwich shells.

A dual‐scale homogenization method to study the properties of chopped carbon fiber reinforced epoxy resin matrix composites

AbstractIn this work, a dual‐scale homogenization (DSH) procedures including the representative volume element (RVE) and Unit cell (UC) with Halpin–Tsai models in the UC scale and space direction‐sensitive Hotelling expansion (SDSHE) models in RVE scale separately. These two methods are introduced and implemented to predict the response of effective elastic properties in chopped fiber reinforced epoxy matrix structures. A post‐processing scheme of subdomain in UC scale based on Gauss theorem is proposed in SDSHE method, which is used to extract the average strain and stress in UC three‐dimensional structure. In addition, the X‐ray computed tomography was used to determine the fourth order tensor orientation angle and the probability distribution information of chopped fiber length in testing samples. Homogenization properties in RVE scale, and inclusion volume fraction (VF), thickness of interface and orientation tensors are designed in UC scale and compared. The excellent correlations with experiments prove the effectiveness of the proposed models. Furthermore, the algorithm proposed in this paper realizes the homogenization of the two scales in the process of numerical analysis, and it will effectively take into account many problems that cannot be achieved by other algorithms, such as the path strain of the model, the thickness of the interface, and so on.

Stability/instability of magnetorheological core sector structure for mechanical control braking system by the intelligent computer method

ABSTRACT Due to the amazing mechanical properties of the magnetorheological (MR) materials, which can quickly transit from fluid to solid and vice versa, these materials have attracted a lot of attention among designers. So, for the first time, a dynamic stability analysis of a sandwich sector plate made of an MR core and two graphene nanoplatelets reinforced composite (GPLRC) face sheets has been presented. Using the role of mixture and Halpin–Tsai model, material properties of the GPLRC layers have been modeled. For modeling the MR core, shear stress and strain properties of MR fluids have been characterized into pre-yield and post-yield regions. Via first-order shear deformation theory, compatibility equations between the layers, and Hamilton’s principle, motion equations of the structure have been achieved. A generalized differential quadrature method with Chebyshev polynomials greed points has been applied for obtaining the responses of structure. The verification section has been separated into two parts. The first and second ones are verification between the current outcomes with the results of the published report and the machine learning method based on deep neural networks, respectively. Consequently, the results show that some geometrical and physical parameters have an important role in the dynamic stability of the current structure.

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.

Free Vibration Analysis of Spinning Sandwich Annular Plates with Functionally Graded Graphene Nanoplatelet Reinforced Porous Core.

This paper conducted the free vibration analysis of a sandwich annular thin plate with whirl motion. The upper and lower faces of the annular plate are made of uniform solid metal, while its core is porous foamed metal reinforced by graphene nanoplatelets (GPLs). Both uniform and non-uniform distributions of GPLs and porosity along the direction of plate thickness which leads to a functionally graded (FG) core are taken into account. The effective material properties including Young’s modulus, Poisson’s ratio and mass density are calculated by employing the Halpin–Tsai model and the rule of mixture, respectively. Based on the Kirchhoff plate theory, the differential equations of motion are derived by applying the Lagrange’s equation. Then, the assumed mode method is utilized to obtain free vibration behaviors of the sandwich annular plate. The finite element method is adopted to verify the present model and vibration analysis. The effects of porosity coefficient, porosity distribution, graphene nanoplatelet (GPL) distribution, graphene nanoplatelet (GPL) weight fraction, graphene nanoplatelet length-to-thickness ratio (GPL-LTR), graphene nanoplatelet length-to-width ratio (GPL-LWR), spinning speed, outer radius-to-thickness ratio and inner radius-to-thickness ratio of the plate, are examined in detail.

Some improvements on the energy absorbed in composite plate resting on the viscoelastic substrate

The vibration, as well as energy of a reinforced three-phase hybrid composite plate resting on a viscoelastic foundation subjected to initial stress, is examined with the aid of three-dimensional elasticity theory. The two-parameter viscoelastic Winkler–Pasternak foundation is formulated. The multilayer plate with three, five, and seven layers are modeled with the aid of compatibility conditions. The state-space-based analytical method is utilized as the solution procedure to extract the results. To attain the composite material properties, the rule of the mixture alongside modified Halpin–Tsai model is incorporated. The distribution of the carbon nanotubes is supposed to be nonuniform. The parametric examination on the impacts of the sequence of the composite layers, initial stresses, foundation coefficients, and nanocomposite related constants on the vibration frequency as well as energy stored in the system is carried out. The extracted results indicate that the initial stresses and foundation parameters play a significant role in determining the frequency value along with the energy of the system.

Active Flutter Suppression and Aeroelastic Response of Functionally Graded Multilayer Graphene Nanoplatelet Reinforced Plates with Piezoelectric Patch

This paper investigates the aeroelastic flutter and vibration reduction of functionally graded (FG) multilayer graphene nanoplatelets (GPLs) reinforced composite plates with piezoelectric patch subjected to supersonic flow. Activated by the control voltage, the piezoelectric patch can generate the active mass and active stiffness that can accordingly increase the base plate’s stiffness and mass. As a result, it changes the GPLs reinforced plate’s dynamic characteristics. The motion equation of the plate-piezoelectric system is derived through the Hamilton principle. Based on the modified Halpin–Tsai model, the effects of graphene nanoplatelets weight fraction and distribution pattern on the dynamic behaviors of the plate are numerically studied in detail. The result illustrates that adding a few amounts of grapheme nanoplatelets can effectually enhance the aeroelastic properties of the plates. Two kinds of control strategies, including the displacement and acceleration feedback control, are applied to suppress the occurrence of the flutter of the plate. It shows that the displacement and acceleration feedback control can improve the critical flutter Mach number of the plate by attaching active stiffness and active mass, respectively. Furthermore, the combined displacement and acceleration feedback control has a better control effect than that of considering only one of them.

Hydrothermal Ageing Effect on Reinforcement Efficiency of Nanofibrillated Cellulose/Biobased Poly(butylene succinate) Composites.

Nanofibrillated cellulose (NFC) is a sustainable functional nanomaterial known for its high strength, stiffness, and biocompatibility. It has become a key building block for the next-generation of lightweight, advanced materials for applications such as consumer products, biomedical, energy storage, coatings, construction, and automotive. Tunable and predictable durability under environmental impact is required for high performance applications. Bio-based poly (butylene succinate) (PBS) composites containing up to 50% NFC content were designed and aged in distilled water or at high relative humidity (RH98%). PBS/NFC composites are characterized by up to 10-fold increased water absorption capacity and diffusivity and the data are correlated with model calculations. Aged samples exhibited decreased crystallinity and melting temperature. Incorporation of NFC into PBS showed up to a 2.6-fold enhancement of the elastic modulus, although accompanied by a loss of strength by 40% and 8-fold reduction in the strain at failure of maximally loaded composites. Hydrothermal ageing had almost no influence on the tensile characteristics of PBS; however, there were considerable degradation effects in PBS/NFC composites. Altered reinforcement efficiency is manifested through a 3.7-fold decreased effective elastic moduli of NFC determined by applying the Halpin–Tsai model and a proportional reduction of the storage moduli of composites. The adhesion efficiency in composites was reduced by hydrothermal ageing, as measured Puckanszky’s adhesion parameter for the strength, which decreased from 3 to 0.8. For the loss factor, Kubat’s adhesion parameter was increased by an order. PBS filled with 20 wt.% NFC is identified as the most efficient composition, for which negative environmental degradation effects are counterbalanced with the positive reinforcement effect. The PBS matrix can be used to protect the NFC network from water.

Dynamic stability of CNTs-reinforced non-uniform composite beams under axial excitation loading

This paper presents an analytical study on the dynamic stability of carbon nanotubes (CNTs) reinforced functionally graded composite beams when subjected to axial excitation loading. The composite beams are functionally graded using a I-type CNTs reinforcement. The section properties of the non-uniform functionally graded composite beams are assessed using Halpin–Tsai model. The analysis of dynamic stability of the composite beams is performed by using Bolotin’s method. Analytical expressions of determining free vibration frequency, critical buckling load, and excitation frequency of the non-uniform functionally graded composite beams are derived, in which both the shear deformation and rotary inertia effects are considered. The study demonstrates that the dynamic stability of the beam can be improved significantly when it is functionally graded using the I-type CNTs reinforcement.

Hygrothermal wave dispersion analysis of metal foam microplates strengthened by graphene embedded in a viscoelastic medium under 2D magnetic field effect

An analytical approach is developed to investigate the influences of hygrothermal conditions on the wave dispersion in porous graphene platelets (GPLs)-reinforced microplate embedded in the visco-Pasternak foundation. The effect of a 2D magnetic field is also considered in the present analysis. The pores and GPLs weight fraction are assumed to be non-linearly varied based on various patterns of distribution along the microplate thickness direction. Following the nonlocal strain gradient theory (NSGT) and a refined plate theory (RPT) considering the thickness stretching effect, the governing equations are obtained. The GPLs material properties are calculated employing the extended Halpin–Tsai model. The equations of motion are deduced based on Hamilton's principle. These equations are then analytically solved to obtain the wave frequency and phase velocity of the waves in a microplate. The present wave frequency and phase velocity are compared with the published ones. The impacts of GPLs weight fraction, pore coefficient, temperature rise, moisture concentration, Lorentz magnetic force, and foundation stiffnesses on the wave dispersion in the FG porous-GPLs microplate are introduced and discussed.

A Bayesian Approach to the Eagar–Tsai Model for Melt Pool Geometry Prediction with Implications in Additive Manufacturing of Metals

A Bayesian Approach to the Eagar–Tsai Model for Melt Pool Geometry Prediction with Implications in Additive Manufacturing of Metals

Free vibration analysis of simply-supported graphene platelets reinforced laminated piezoelectric cylindrical micro-shells

In this study, the micro-scale vibration analysis of the graphene platelets reinforced cylindrical micro-shells with piezoelectric layers is discussed. By simultaneous use of Hamilton’s principle and size-dependent modified couple stress theory, the governing equations of motion and the boundary conditions are derived. The natural frequencies for graphene platelets reinforced cylindrical micro-shell with piezoelectric layers are determined by the Navier’s approach. Three different graphene platelets distribution pattern are modeled in this study. The material properties of every layer of micro composite shell reinforced by graphene platelets are evaluated by Halpin–Tsai model. The present findings are validated with the available data in the literature. In addition, a parametric study is conducted to demonstrate the effects of the weight fraction, the distribution pattern, the material length scale parameter, the thickness of the piezoelectric layers, the length to radius ratio, the thickness to radius ratio, temperature change and the applied voltage on the natural frequency of piezoelectric GPL cylindrical micro-shell.

On the Hardness and Elastic Modulus of Phases in SiC-Reinforced Al Composite: Role of La and Ce Addition.

The use of silicon carbide particles (SiCp) as reinforcement in aluminium (Al)-based composites (Al/SiCp) can offer high hardness and high stiffness. The rare-earth elements like lanthanum (La) and cerium (Ce) and transition metals like nickel (Ni) and copper (Cu) were added into the matrix to form intermetallic phases; this is one way to improve the mechanical property of the composite at elevated temperatures. The α-Al15(Fe,Mn)3Si2, Al20(La,Ce)Ti2, and Al11(La,Ce)3, π-Al8FeMg3Si6 phases are formed. Nanoindentation was employed to measure the hardness and elastic modulus of the phases formed in the composite alloys. The rule of mixture was used to predict the modulus of the matrix alloys. The Halpin–Tsai model was applied to calculate the elastic modulus of the particle-reinforced composites. The transition metals (Ni and Cu) and rare-earth elements (La and Ce) determined a 5–15% increase of the elastic modulus of the matrix alloy. The SiC particles increased the elastic modulus of the matrix alloy by 10–15% in composite materials.

Free vibrational characteristics of GNP-reinforced joined conical–conical​ shells with different boundary conditions

The current study is devoted to analyzing the free vibration characteristics of joined conical–conical shells made of epoxy enriched with graphene nanoplatelets (GNPs). The mathematical modeling of the shell is performed utilizing the first-order shear deformation theory (FSDT) to incorporate the effects of shear deformations and rotational inertia. The effective modulus of elasticity is estimated using the Halpin–Tsai model and other effective mechanical properties are evaluated utilizing the rule of mixture. The set of the governing equations, associated compatibility conditions at the intersection of two shell segments, and boundary conditions are obtained using Hamilton’s principle. These equations are solved in the circumferential direction using trigonometric functions and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). Through this semi-analytical solution, the natural frequencies of the shell and corresponding mode shapes are determined and the validity of the presented solution is confirmed via the benchmark results reported by the other authors. The effects of various parameters on the natural frequencies of the GNP-reinforced joined conical–conical​ shells are examined including the circumferential wave number, the boundary conditions, the length-to-small radius ratio and semi-vertex angle in two shell segments, thickness-to-small radius ratio of the shell, and also mass fraction, aspect ratio, and dispersion pattern of the GNPs.

Design of Laminated Composite Plates with Carbon Nanotube Inclusions against Buckling: Waviness and Agglomeration Effects.

In the present study, a buckling analysis of laminated composite rectangular plates reinforced with multiwalled carbon nanotube (MWCNT) inclusions is carried out using the finite element method (FEM). The rule of mixtures and the Halpin–Tsai model are employed to calculate the elastic modulus of the nanocomposite matrix. The effects of three critical factors, including random dispersion, waviness, and agglomeration of MWCNTs in the polymer matrix, on the material properties of the nanocomposite are analyzed. Then, the critical buckling loads of the composite plates are numerically determined for different design parameters, such as plate side-to-thickness ratio, elastic modulus ratio, boundary conditions, layup schemes, and fiber orientation angles. The influence of carbon nanotube fillers on the critical buckling load of a nanocomposite rectangular plate, considering the modified Halpin–Tsai micromechanical model, is demonstrated. The results are in good agreement with experimental and other theoretical data available in the open literature.

Nonlinear dynamic analysis of FG carbon nanotube/epoxy nanocomposite cylinder with large strains assuming particle/matrix interphase using MLPG method

In this paper, a first known study on the large deformation dynamic behavior of functionally graded carbon nanotube-reinforced (CNTR) nanocomposite cylinder considering the particle/matrix interphase property is presented. The geometrically nonlinear dynamic analysis is carried out using the meshless local Petrov–Galerkin (MLPG) method based on the total Lagrangian approach. The obtained nonlinear time dependent equations are solved using the incremental-iterative Newmark/Newton–Raphson technique. The effective properties of CNTR cylinder is evaluated by employing the three-phase Halpin–Tsai model and rule of mixture. In these models, three constituent phases including nanoparticle, interphase and matrix is considered. It is assumed that CNTs is dispersed in the resin matrix with four different function along the radial direction to obtain the optimum grading pattern. The effects of interphase properties, CNT's weight fraction, CNT distribution pattern and volume fraction exponent on the dynamic characteristics of the cylinder are discussed in details. Numerical results demonstrated the high performance of the proposed MLPG method for geometrically nonlinear dynamic analysis of functionally graded carbon nanotube/epoxy nanocomposites due to its advantage in eliminating the mesh distortion and high capability in FG material modeling. Moreover, it is found that the interphase properties may dramatically affect the dynamic behavior of nanocomposite cylinder especially at the higher CNT volume fractions. So, it is important to consider the interphase properties to correctly model the nanocomposite structures.

The effects of thermal loadings on wave propagation analysis of multi-scale hybrid composite beams

This research is concerned with the analysis of wave propagation of multi-scale hybrid composite beams subjected to various types of thermal loading. Carbon fiber (CF) and carbon nanotube (CNT) are assumed as reinforcements that are distributed in the matrix. The homogenization process is performed exerting the Halpin–Tsai model and the rule of mixture. Different types of temperature rise, namely, uniform, linear and sinusoidal temperature rise are presumed to present a more trustworthy thermal analysis. The beam is rested on Winkler–Pasternak foundation. A refined trigonometric shear deformable beam theory is used to compute the kinetic relations without any external shear correction coefficient. Governing equations are derived implementing Hamilton’s principle and then solved analytically. Eventually, the effects of different parameters, such as CNT’s weight fraction, the volume fraction of CF, elastic foundation, different types of temperature rise, etc., on wave frequency and phase velocity. are provided numerically in the framework of a set of illustrations.

Vibration analysis of graphene nanoplatelets’ reinforced composite plates integrated by piezo-electromagnetic patches on the piezo-electromagnetic media

A new model of microplate is used to evaluate the vibrational response of a size-dependent three-layered sandwich structure, including functionally graded (FG) composite core by sinusoidal shear deformation plate theory. Also, this FG core is reinforced by graphene nanoplatelets (GPLs) and embedded between piezo-electromagnetic (PEM) face sheets. The matrix of the core is made of Epoxy and the extended rule of mixture (ERM) besides Halpin–Tsai model is chosen to predict the mechanical properties of the nanocomposite core. Moreover, BaTiO3-CoFe2O4 composition is considered as constituting material of PEM face sheets. Furthermore, the visco-Pasternak substrate is used to carry the whole structure. The aforementioned theories are employed efficiently to obtain motion equations. Finally, the vibrational response of the described model due to the different parameters’ variations is presented in tables and figures. Based on the results, temperature difference leads the structure to become stiffer and accordingly reduces the frequency. Moreover, using a square basis for a sandwich structure makes the lowest frequency and consequently stiffness.

Studying nonlinear vibrations of composite conical panels with arbitrary-shaped cutout reinforced with graphene platelets based on higher-order shear deformation theory

In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced composite for various functionally graded distribution patterns of graphene platelets. The governing equations are derived by a variational approach and represented in matrix-vector form for the computational purposes. Moreover, attributable to using higher-order shear deformation theory, a mixed formulation approach is presented to consider the continuity of first-order derivatives on the common boundaries of elements. In the numerical results, the nonlinear free vibration behaviors of functionally graded graphene platelet–reinforced composite conical panels including square/circular/elliptical hole and with crack are studied. The effects of boundary conditions, graphene platelet reinforcement, and other important parameters on the vibrational response of panels are comprehensively analyzed.