Functionally Graded Materials Research Articles

Hygrothermal buckling analysis of thin rectangular FGM plate with variable thickness

PurposeThis paper aims to contribute novel insights into the analysis of thin functionally graded material (FGM) plates with variable thickness, considering both temperature-dependent and independent material properties, focusing on critical linear buckling temperature rise and the effect of critical linear moisture for various moisture concentrations.Design/methodology/approachThe study derives stability and equilibrium equations for thin rectangular FGM plates under hygrothermal loading, employing classical plate theory (CPT). Buckling behavior is examined using Galerkin’s method to obtain pre-buckling force resultants.FindingsThe findings highlight significant increases in critical buckling temperature with aspect ratio, distinct temperature sensitivity between materials and increasing moisture susceptibility with larger aspect ratios. These insights inform material selection and design optimization for FGM plates under hygrothermal loading, enhancing engineering applications.Research limitations/implicationsThis research primarily focuses on hypothetical scenarios and mathematical model development and analysis.Originality/valueThis paper presents original contributions in the field by addressing the hygrothermal buckling analysis of thin FGM rectangular plates with variable thickness, utilizing CPT, thereby enriching the understanding of structural behavior in varying environmental conditions.

Effect of interdiffusion layer of functionally graded Al–Cu composites fabricated by spark plasma sintering on mechanical and thermal properties

The effect of the microstructure of multi-layer Al–Cu functionally graded materials (FGMs) fabricated through spark plasma sintering (SPS) on the mechanical and thermal properties was systemically investigated. Uniformly mixed Al–25, 50, 75 Cu (vol%) powder samples were prepared by mechanical ball milling and used for fabricating two types of FGMs: FGM 1 with three layers (Cu/Al–50Cu/Al) and FGM 2 with five layers (Cu/Al–75Cu/Al–50Cu/Al–25Cu/Al). These FGMs were then sintered at 400 °C under a compressive pressure of 250 MPa for 5 min. The microstructures of the sintered FGMs exhibited gradual variations in the Al and Cu contents. An interdiffusion layer composed of Cu9Al4 and CuAl2 at the layer/layer interfaces was observed, the thickness of which was analyzed by energy-dispersive spectroscopy line mapping. The Vickers hardness of FGM 1 and FGM 2 were higher than that calculated by rule of mixture due to the formation of Al-Cu IC such as Cu9Al4 and CuAl2. The drastic enhancement in a Al-75Cu layer was obtained by dominant formation of Cu9Al4. On the other hand, the thermal conductivity of the prepared FGMs was lower than that of Al due to the formation of Al–Cu ICs, enhanced heat dissipation compared with the Al–Cu composite materials. The mechanical and thermal properties of Al-Cu FGMs can be controlled by designing the layer composition or the number of layers.

Effect of bi-directional material gradation on thermo-mechanical bending response of metal-ceramic FGM sandwich plates using inverse trigonometric shear deformation theory

PurposeThe purpose of this study is to investigate the bending analysis of metal (Ti-6Al-4V)-ceramic (ZrO2) functionally graded material (FGM) sandwich plate with material property gradation along length and thickness direction under thermo-mechanical loading using inverse trigonometric shear deformation theory (ITSDT). FGM sandwich plate with a ceramic core and continuous variation of material properties has been modelled using Voigt’s micro-mechanical model following the power law distribution method. The impact of bi-directional gradation of material properties over the bending response of FGM plate under thermo-mechanical loading has been investigated in this work.Design/methodology/approachIn this study, gradation of material properties for FGM plates is considered along length and thickness directions using Voigt’s micromechanical model following the power law distribution method. This type of FGM is called bi-directional FGMs (BDFGM). Mechanical and thermal properties of BDFGM sandwich plates are considered temperature-dependent in the present study. ITSDT is a non-polynomial shear deformation theory which requires a smaller number of field variables for modelling of displacement function in comparison to poly-nominal shear deformation theories which lead to a reduction in the complexity of the problem. In the present study, ITSDT has been utilized to obtain the governing equations for thermo-mechanical bending of simply supported uni-directional FGM (UDFGM) and BDFGM sandwich plates. Analytical solution for bending analysis of rectangular UDFGM and BDFGM sandwich plates has been carried out using Hamilton’s principle.FindingsThe bending response of the BDFGM sandwich plate under thermo-mechanical loading has been analysed and discussed. The present study shows that centre deflection, normal stress and shear stress are significantly influenced by temperature-dependent material properties, bi-directional gradation exponents along length and thickness directions, geometrical parameters, sandwich plate layer thickness, etc. The present investigation also reveals that bi-directional FGM sandwich plates can be designed to obtain thermo-mechanical bending response with an appropriate selection of gradation exponents along length and thickness direction. Non-dimensional centre deflection of BDFGM sandwich plates decreases with increasing gradation exponents in length and thickness directions. However, the non-dimensional centre deflection of BDFGM sandwich plates increases with increasing temperature differences.Originality/valueFor the first time, the FGM sandwich plate with the bi-directional gradation of material properties has been considered to investigate the bending response under thermo-mechanical loading. In the literature, various polynomial shear deformation theories like first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and higher-order shear deformation theory (HSDT) have been utilized to obtain the governing equation for bending response under thermo-mechanical loading; however, non-polynomial shear deformation theory like ITSDT has been used for the first time to obtain the governing equation to investigate the bending response of BDFGM. The impact of bi-directional gradation and temperature-dependent material properties over centre deflection, normal stress and shear stress has been analysed and discussed.

A new higher-order shear deformation theory for flutter instability of a hybrid sandwich panel resting on a viscoelastic foundation

Magnetorheological elastomers (MREs) are smart materials characterized by their ability to adjust mechanical properties through the manipulation of applied magnetic fields, facilitating rapid and reversible tunability. The incorporation of reinforcing fibers introduces distinctive materials termed Magnetorheological Elastomer Composites (MRECs), combining tunability with enhanced rigidity. This study delves into the flutter analysis of a sandwich panel with a mid-layer composed of laminated MRECs and face sheets composed of functionally graded materials (FGMs) featuring porosity. The sandwich panel is situated on a viscoelastic foundation and exposed to a supersonic air current. Employing a higher-order (hyperbolic) shear deformation theory (HSDT), the displacement field of the sandwich plate is estimated. This selection eliminates the requirement for shear correction factors. The mechanical characteristics of the three sheets are determined using the Halpin-Tsai micromechanical method and the rule of mixture. The First-order Piston theory is employed to evaluate the effect of aerodynamic pressure and airflow damping on the sandwich panel. The derivation of the motion equation is achieved through Hamilton's principle. In order to solve the motion equation of the structure, the Finite Element Method (FEM) is utilized. The investigation systematically explores the influence of diverse parameters on the flutter boundary of the sandwich panel.

Multilayer heterostructure inhomogeneous model for the functionally graded spherical shell with rotation effect for arbitrarily varying material properties

With the development of functionally graded materials (FGMs) composite technology, structural safety analysis related to FGMs has been widely concerned. An innovative multilayer heterostructure power-law inhomogeneous (MHPI) model is taken to solve the rotating FGMs hollow spherical shell with arbitrarily varying material properties (elastic modulus and density) along the radial direction. The basic idea of MHPI model is that the rotating FGMs spherical shell is divided into multiple sublayers, and two power functions approximate the elastic modulus and density of each sublayer respectively. For each single sublayer, the analytical solutions include two undetermined constants, which can be obtained from the boundary and continuity conditions. Many numerical examples of the rotating FGMs spherical shell are discussed, involving seven property profiles gradient laws assumptions, three boundary conditions, and nine volume fraction gradient models. Finally, this study further discusses the rotating FGMs spherical shell optimization design. The greatest advantage of this study is that the elastic response of the rotating FGMs spherical shell under various gradient assumptions is completely discussed. The numerical results show that the MHPI model can solve the problem of circumferential stress oscillation well and have good convergence and high accuracy. For many numerical examples, the error of the MHPI model results is about 5‰ when sublayer number reaches 15.

Thermoelastic analysis of disk with FEM for FGM variable parameters

Functionally graded materials (FGMs) using the finite element method (FEM) with C 0 elements, focusing on the examination of material variable parameters. The research advances the understanding of FGMs through a thermo-structural analysis of an FGM disk, assessing its response under thermal and mechanical loads. Thermal and thermo-mechanica analysis demonstrates the precision of the proposed approach in delineating the complex behavior of FGMs under diverse conditions. The research contributes to enrich the comprehension of FGM behavior using simple FEM models.

Achieving High-Temperature Stable Structural Color through Nanostructuring in Polymer-Derived Ceramics.

Structural colors offer a myriad of advantages over conventional pigment-based colors, which often rely on toxic chemical substances that are prone to UV degradation. To take advantage of these benefits in demanding environments, there is growing interest in producing structural colors from ceramics. Polymer-derived ceramics (PDCs) emerge as a compelling choice, presenting two distinct advantages: their enhanced shape ability in their polymeric state associated with impressive temperature resistance once converted to ceramics. This study pioneers the fabrication of noniridescent structural colors from silicon oxycarbide (SiOC) PDC, enabled by the nanostructuring of an inverse photonic glass within the PDC material. This design, a functionally graded material with an inverse photonic glass (FGM-PhG) structure, leverages the innate light-absorbing properties of SiOC, yielding a vivid structural color that maintains its saturation even in white surroundings. This study elucidates the process-structure-properties relationship for the obtained structural colors by investigating each layer of the functionally graded material (FGM) in a stepwise coating deposition process. To further emphasize the exceptional processing flexibility of PDCs, the three-step process is later transferred to an additive manufacturing approach. Finally, the FGM-PhG structural colors are demonstrated to have remarkable thermal stability up to 1000 °C for 100 h, possibly making them the most thermally stable ceramic structural colors to date.

Investigation on dual wire TIG Arc additive manufacturing of IN625 and SS316L FGM for continuous gradient and sandwich structures

Fabrication of functionally graded material (FGM) has been studied using dual wire WAAM-TIG (wire arc additive manufacturing - tungsten inert gas) process. The experimental research aims to perform the feasibility study of different designs of FGMs, including continuous gradient (CG-FGM) and sandwich structures (SW-FGMs). The weight percentage of two wire materials, SS316L and IN625, was precisely controlled using individual wire feeding systems. Process parameters were identified to obtain the defect-free deposition for the desired combination of weight percentage. The governing elements, i.e., Ni and Fe, showed a gradual variation in the case of CG-FGM and alternate peaks for SW-FGMs while examined using energy-dispersive X-ray spectroscopy (EDS). The alternate material distinction was noticeable with the increase in the number of individual layers for each set of SW-FGMs. The microstructure evolution of CG-FGM showed a smooth transition from equiaxed to columnar dendrites along the build direction, while SW-FGM showed heterogeneous behaviour. The hardness was steadily increasing in CG-FGMs and formed a wavy pattern in SW-FGMs. X-ray diffraction (XRD) analysis confirmed the formation of the austenitic phase, and variation in peak heights correlates to the change in microstructure and hardness. The conducted tribological study showed the specific wear rate gradually decreased with an increase of Ni content in CG-FGM, whereas in SW-FGM, it showed a strong dependency on the adopted design. The alloying effect in SW-FGM with different design modalities and its comparison with equal weight percentages were also studied in detail and presented.

Introducing ANN-GP algorithm to estimate transient bending of the functionally graded graphene origami-enabled auxetic metamaterial structures

This article presents a new method called the artificial neural networks-genetic programming (ANNs-GP) algorithm, which effectively predicts the bending behavior of functionally graded graphene origami-enabled auxetic metamaterial (FG-GORAM) structures under transient conditions. Functionally graded materials (FGMs) display spatial heterogeneity in their composition and microstructure, resulting in distinctive mechanical characteristics that make them well-suited for a wide range of engineering applications. The objective of this study is to create a prediction model that can accurately capture the intricate transient bending behavior of FGM structures. To do this, the researchers have used the ANN-GP technique, which combines ANNs with GP. The ANN component acquires knowledge from a dataset including actual or simulated bending data, while the GP component fine-tunes the structure and parameters of the neural network to improve its ability to make accurate predictions. The proposed algorithm combines the strengths of ANNs and GP to accurately predict the bending behavior of FG-GORAM structures. This algorithm is robust and efficient, allowing designers and engineers to optimize the performance and reliability of these structures in various applications. The effectiveness of the ANN-GP method is proved by comparing it to experimental or simulated data. This shows that the algorithm has the potential to be a useful tool for designing and analyzing sophisticated materials and structures.

Nonlinear vibration control of interconnected functionally graded fluid-conveying pipeline

In this study, an exploratory vibration experiment is established and an interconnected functionally graded material (FGM) pipeline system is installed. This experiment represents the first time that NiTiNOL-steel wire ropes (NiTi-ST) are applied to FGM pipeline system. And the experimental results demonstrate that the NiTi-ST has a practical vibration damping effect. Based on the experiment, a further theoretical pipeline system model is created. The effects of fluid velocity, temperature difference, and clamp stiffness on the modal and response of the pipeline system are added. The modal analysis part is solved through the implementation of the Rayleigh-Ritz approach using a set of modified orthogonal polynomials. In order to verify the accuracy of the Raylei-Ritz calculations, the finite element method (FEM) is also used. The response analysis part is solved through the Galerkin truncation method (GTM) and harmonic balance method (HBM). To match the harmonic balance solutions, the Runge-Kutta method (RK) are adopted. The results of the response analysis reveal that NiTi-ST demonstrates significant nonlinear vibration control capabilities to the interconnected FGM pipeline system under various conditions.

Effect of Three Layered Centrifugal Casting on Tribological and Microstructural Characteristics of Mg Based Functionally Graded Material Alloy

Objectives: The aim of this study is to examine the tribological properties and microstructural of functionally graded material (FGM) composites based on magnesium (Mg) base material. Magnesium alloys are commonly employed in the development of biomaterials for implant applications owing to their favorable corrosion properties. The research objective is to produce Zn/Mo reinforced functionally graded magnesium composites using the centrifugal casting. Methods: A centrifugal process was employed to fabricate a functionally graded material (FGM) consisting of three layers with a cylindrical shape. The base material used for this FGM was Magnesium, which was alloyed with 10% of Zn and 10% of Mo. The developed FGMs have been analyzed for their mechanical and microstructural characteristics. The microstructure of the samples were analyzed via the Optical Microscope (OM). It is identified that denser particle molybdenum (Mo) have influenced the mechanical and microstructural characteristics of the FGM composites. Findings: Results recommend that, all the three layered testing’s, Mg (80%) +Zn (10%) + Mo (10%) composite exhibited favorable mechanical and microstructural properties. It is identified that denser particle of Mo which is influenced the microstructural characteristics. The alteration in micro hardness in the direction of centrifugal force is observed, and it is observed that the minimum wear loss for sliding wear samples A, B & C of Mg based FGM alloy were found to be 0.0018 g, 0.028 g and 0.031 g respectively, while the maximum wear loss for sliding wear samples A, B & C of FGM alloy were found to be 0.0021 g, 0.41 g and 0.31 g respectively. Novelty: In this study, a novel three-layered centrifugal casting technique was devised. Owing to its rapid degradability, the anticipated duration of the implants within the human body would be significantly shorter in comparison to alternative biomaterials such as Titanium and Stainless steel. Furthermore, the findings from the conducted tests strongly advocate for the utilization of this technique in biomedical implantations. Keywords: Functionally graded material (FGM), Centrifugal casting, Tribological characteristics, microstructural behavior, and bio­implants

Machine learning-based prediction of heat transfer performance in annular fins with functionally graded materials

This paper presents a study investigating the performance of functionally graded material (FGM) annular fins in heat transfer applications. An annular fin is a circular or annular structure used to improve heat transfer in various systems such as heat exchangers, electronic cooling systems, and power generation equipment. The main objective of this study is to analyze the efficiency of the ring fin in terms of heat transfer and temperature distribution. The fin surfaces are exposed to convection and radiation to dissipate heat. A supervised machine learning method was used to study the heat transfer characteristics and temperature distribution in the annular fin. In particular, a feedback architecture with the BFGS Quasi-Newton training algorithm (trainbfg) was used to analyze the solutions of the mathematical model governing the problem. This approach allows an in-depth study of the performance of fins, taking into account various physical parameters that affect its performance. To ensure the accuracy of the obtained solutions, a comparative analysis was performed using guided machine learning. The results were compared with those obtained by conventional methods such as the homotopy perturbation method, the finite difference method, and the Runge–Kutta method. In addition, a thorough statistical analysis was performed to confirm the reliability of the solutions. The results of this study provide valuable information on the behavior and performance of annular fins made from functionally graded materials. These findings contribute to the design and optimization of heat transfer systems, enabling better heat management and efficient use of available space.

Active layer damping of bi-directionally tapered functionally graded sandwich plates with 1-3 piezoelectric composites

This article investigates the effect of smart damping on bi-directionally tapered functionally graded sandwich plates. The substrate comprises FG material on both sides of the core of either soft herex or ceramic material. The viscoelastic layer of ALD is restrained, while the compelling layer consists of 1-3PZC. The finite element formulation developed incorporates layer-wise and first-order-shear-deformation theory. The plate’s damping is actively controlled using velocity feedback control incorporating piezoelectric patches. The effects of various parameters of taper ratio and patch positions on vibration control are investigated. The efficacy of the ALD in improving the structural performance of plates is investigated.

Three-dimensional nonlinear stress analysis of functionally graded shells subjected to displacement-dependent loads

The nonlinear geometrically exact (GeX) hybrid-mixed four-node solid-shell element under non-conservative loading, developed in the companion paper, is here extended to the stress analysis of functionally graded material (FGM) shells. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms can be taken exactly at element nodes. The FGM solid-shell element formulation is based on the choice of N sampling surfaces (SaS) parallel to the middle surface and located at Chebyshev polynomial nodes within the shell as well as on the outer surfaces, to introduce the displacements of these surfaces as basic unknowns. The use of Lagrange polynomials of degree N–1 in the distributions of displacements, strains, stresses, and elastic coefficients through the thickness of the shell leads to an efficient 3N-parameter shell formulation. To develop the FGM four-node solid-shell element based on the hybrid-mixed method, in which strains and stresses are utilized as primary variables, the Hu-Washizu variational principle is applied. Due to the analytical integration used to evaluate the tangent stiffness matrix, the developed FGM solid-shell element subjected to displacement-dependent loads shows superior performance in the case of coarse meshes and allows the use of only one load step in most of the considered benchmark problems. It has been established that the difference between the second Piola-Kirchhoff and Cauchy stress tensors in non-conservative problems for FGM shells undergoing moderately large strains can be significant.

Characteristics of 3D Printed Functionally Graded Material for Replacement of Dissimilar Metal Weld in Nuclear Reactor

The dissimilar metal welds in the most of the reactors are connections between low alloy steel parts and stainless steel piping. There is a high possibility of primary water stress corrosion cracking (PWSCC) damage attributed to residual stress caused by the difference in material properties in the dissimilar metal weld joints. A number of accidents such as leakage of radioactive coolant due to PWSCC have been reported around the world, posing a great threat to nuclear safety. The objective of this study is to develop a technology that can fundamentally remove dissimilar metal welds by replacing the existing dissimilar metal parts with the functionally graded material (FGM) manufactured by metal 3D printing consisting of low alloy steel and austenitic stainless steel. A powder production, mixing ratio calculation, and metal 3D printing were performed to fabricate the low alloy steel-stainless steel FGM, and microstructure analysis, mechanical properties, and coefficient of thermal expansion (CTE) measurement of the FGM were performed. As a result, it is observed that CTE tended to increase as the austenite content increased in FGM. The gradual change of coefficient of thermal expansion in a FGM showed that the additive manufacturing using 3D printing was effective for preventing an abrupt change in thermal expansion properties throughout their layers.

Symplectic superposition method for the free-vibrating problem of sigmoid functionally graded material rectangular thin plates clamped at four edges

The symplectic superposition method (SSM) is implemented to investigate the free vibration problem of sigmoid functionally graded material (FGM) rectangular thin plates clamped at four edges. Firstly, the vibration equation of the sigmoid FGM rectangular thin plate is transformed into Hamiltonian canonical equations. Then based on the analysis of boundary conditions of the plate, the vibration problem of the sigmoid FGM rectangular thin plate clamped at four edges is decomposed as two sub-problems simply supported on two opposite edges. And then based on the symplectic elasticity method (SEM), the series expansion solutions for the two sub-vibrating problems are obtained. Afterward, by superposing the series expansion solutions for the two sub-vibrating problems, a symplectic superposition solution of the freely vibrating sigmoid FGM rectangular thin plates clamped at four edges is obtained. Finally, we apply the obtained symplectic superposition solution to research the frequencies and vibration mode functions of some specific sigmoid FGM rectangular thin plates, and the impact of the aspect ratio a/b and material gradient index k on the vibration frequencies of the sigmoid FGM rectangular thin plates is studied.

Thermo-elastic Characteristics of Thermal Barrier Coating in a Gas Turbine Combustion Chamber with an Intermediate FGM Layer

This study is focused on the analysis of thermos-elastic characteristics of a gas turbine combustion chamber, where the inner surface experiences a higher temperature while the outer region of the wall should be thermally conductive to dissipate the heat of combustion. Using a single material is not suitable to ensure the above two requirements simultaneously. Instead of using a single material, a layered combustion chamber with high-temperature material at the inner region and thermally conductive material at the outer region can be a solution. This produces the problem of a sharp interface where disbonding occurs due to high thermal stresses. The problem of sharp interface can be eliminated by using a functionally graded material (FGM) layer in between the inner and outer layers of the combustion chamber. The present study considers a gas turbine combustion chamber consisting of three layers: the inner layer is used as a thermal barrier coating, the intermediate layer is a smooth transition from the inner layer to the outer layer, and the outer layer is a thermally conductive material. ANSYS simulation is used for the analysis of thermos-elastic characteristics of the combustion chamber with homogeneous and FGM intermediate layers. The effect of linear and nonlinear material distributions in the FGM layer on the thermos-elastic characteristics is studied. A comparison of results reveals that thermal stress smoothly changes from the inner layer to the outer layer in the case of the FGM intermediate layer compared to the homogeneous intermediate layer. This suggests that a combustion chamber with an FGM intermediate layer is more reliable than a homogeneous intermediate layer.

Discovery of microsegregation-aided transformation and twinning-induced plasticity in low Mn steel through directed energy deposition of functionally graded materials

Functionally graded materials (FGMs) combining two dissimilar steels, stainless steel 316 L and high-strength low-alloy steel, were additively manufactured using directed energy deposition. High-throughput characterization of the dissimilar steel FGM led to the discovery of a low Manganese (Mn<1 wt.%) TRIP (transformation-induced plasticity) and TWIP (twinning-induced plasticity) steel with a metastable microstructure enabled by additive manufacturing. Microsegregation from non-equilibrium solidification caused phase stability and stacking fault energy heterogeneity, leading to TRIP and TWIP effects in the as-built condition without heat treatment. Tensile testing of the new as-built TRIP and TWIP steel resulted in ultimate tensile strength of 960 MPa, yield strength of 415 MPa, total elongation of 26 %, and a unique strain hardening rate that increases after yielding. We compare experimental measurements of microsegregation with thermodynamic modeling to discuss the impact of microsegregation on phase stability, stacking fault energy, and solidification cracking susceptibility in additively manufactured FGMs. The highlights of this work include the discovery of a novel pathway for achieving TRIP and TWIP effects in additively manufactured steels without heat treatment. This work also shows that the TWIP effect can be introduced without high Manganese content playing a critical role in adjusting stacking fault energy.

Vibration analysis of Timoshenko microbeams made of functionally graded materials on a Winkler-Pasternak elastic foundation

In this work, the free vibration analysis of Timoshenko microbeams made of the Functionally Graded Material (FGM) on the Winkler-Paternak elastic foundation based on the Modified Coupled Stress Theory (MCST) is investigated. Material characteristics of the beam vary throughout the thickness according to the power distribution and are estimated through Mori–Tanaka, Hashin-Shtrikman and Voigt homogenization techniques. The Timoshenko microbeam model considering the length scale parameter is applied. The free vibration differential equations of FGM microbeams are established based on the Finite Element Method (FEM) and Kosmatka’s shape functions. The influences of the size-effect, foundation, material, and geometry parameters on the vibration frequency are then analyzed. It is shown that the study can be applied to other FGMs as well as more complex beam structures.

Advanced frequency of thick FGM cylindrical shells with fully homogeneous equation

The effects of shear deformation theory and improved shear correction factors on the advanced computation of frequencies by using the fully homogeneous equation for thick functionally graded material (FGM) circular cylindrical shells are studied. It is quite reasonable to consider the extra advanced effect of third-order shear deformation theory (TSDT) of displacements on the varied shear correction coefficient. The values of advanced nonlinear shear correction coefficient are usually functions of the nonlinear coefficient term in TSDT, power-law exponent parameter, and environment temperature. The main achievements in the nonlinear case of displacements and with the varied value of shear correction coefficients, the non-dimensional fundamental frequencies are estimated, investigated, and compared with the values in the linear case. This paper aims to study the fundamental frequencies of very thick FGM cylindrical shells under the advanced effects of shear deformation theory and improved shear correction factors.