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The purpose is to explore the free vibration behaviour of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The goal of this study is to gain a better knowledge of the dynamic response of nanoscale structures made of functionally graded materials and porous features. The Rayleigh-Ritz approach is used in this study to generate realistic mathematical models that take elastic foundation support into account. This research can contribute to the design and optimization of advanced nanomaterials with potential applications in engineering and technology by providing insights into the influence of material composition, porosity and foundation support on the vibrational properties of nanoplates.

A systematic methodology is proposed to evaluate the free vibration characteristics of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The study began by developing the mathematical model, adding material properties and establishing governing equations using the Rayleigh-Ritz approach. Numerical approaches to solve the problem are used, using finite element methods. The results are compared to current solutions or experimental data to validate the process. The results are also analysed, keeping the influence of factors on vibration characteristics in mind. The findings are summarized and avenues for future research are suggested, ensuring a robust investigation within the constraints.

The Rayleigh-Ritz technique is used to investigate the free vibration properties of elastic foundation-supported porous functionally graded nanoplates. The findings show that differences in material composition, porosity and foundation support have a significant impact on the vibrational behaviour of nanoplates. The Rayleigh-Ritz approach is good at modelling and predicting these properties. Furthermore, the study emphasizes the possibility of customizing nanoplate qualities to optimize certain vibrational responses, providing useful insights for engineering applications. These findings expand understanding of dynamic behaviours in nanoscale structures, making it easier to build innovative materials with specific features for a wide range of industrial applications.

The novel aspect of this research is the incorporation of elastic foundation support, porous structures and functionally graded materials into the setting of nanoplate free vibrations, utilizing the Rayleigh-Ritz technique. Few research have looked into this complex combo. By tackling complicated interactions, the research pushes boundaries, providing a unique insight into the dynamic behaviour of nanoscale objects. This novel approach allows for a better understanding of the interconnected effects of material composition, porosity and foundation support on free vibrations, paving the way for the development of tailored nanomaterials with specific vibrational properties for advanced engineering and technology applications.

The purpose of the study is to perform elastic stress and deformation analysis of a functionally graded hollow disk under different conditions (rotation, gravity, internal pressure, temperature with variable heat generation) and their combinations.

The classical method of solution, Navier's equation, is used to solve the governing equation. The analysis considers thermal and mechanical boundary conditions and takes into account the variation of material properties according to a power law function of the radius of the disk and grading parameter.

The findings of the study reveal distinct trends and behaviors based on different grading parameters. The influence of gravity is found to be negligible, resulting in similar patterns to the pure rotation case. Variable heat generation introduces non-linear temperature profiles and higher displacements, with stress values influenced by grading parameters.

The study provides valuable insights into the behavior of displacement and stresses in hollow disks, offering a deeper understanding of their mechanical response under varying conditions. These insights can be useful in the design and analysis of functionally graded hollow disks in various engineering applications.

The originality and value of this study lies in the consideration of various loading combinations of rotation, gravity, internal pressure and temperature with variable heat generation. Furthermore, the study of effect of various angular rotations, temperatures and pressures expands the understanding of the mechanical behavior of such structures, contributing to the existing body of knowledge in the field.

When the temperature of an air conditioning unit’s fin surface goes below its dew point temperature, condensation forms on the unit’s surface. As a result, the cooling coil’s performance is compromised. By altering the cross-section and heat conductivity of the fins, the performance of such systems can be improved. This study aims to analyze the thermal performance of longitudinal fins made up of a variable thickness (assuming constant weight) and functionally graded material.

Different grading parameters are considered for an exponential variation of thermal conductivity. The humidity ratio and the corresponding fin temperatures are assumed to follow a cubic relationship. The Bvp4c solver in MATLAB^® is used to solve the differential heat transfer equation resulting from balancing heat transfer in a small segment.

Validation of the methodology is provided by previous research presented in this area. For different combinations of grading parameters, geometry parameters and relative humidity, the normalized temperature distribution along the fin length and fin efficiency contours are plotted, and the results are very promising.

When compared to the efficiency of an isotropic homogenous rectangular longitudinal fin with optimal geometry and grading parameters, a 17% increase in efficiency under fully wet conditions is measured. When it comes to fin design, these efficiency contour plots are extremely useful.

The purpose of this study was to introduce three-dimensional printing (3DP) of functionally graded sandwich foams (FGSFs). This work was continued by predicting the mechanical buckling and free vibration behavior of 3DP FGSFs using experimental and numerical analyses.

Initially, hollow glass microballoon-reinforced high-density polyethylene-based polymer composite foams were developed, and these materials were extruded into their respective filaments. These filaments are used as feedstock materials in fused filament fabrication based 3DP for the development of FGSFs. Scanning electron microscopy analysis was performed on the freeze-dried samples to observe filler sustainability. Furthermore, the density, critical buckling load (P_cr), natural frequency (f_n) and damping factor of FGSFs were evaluated. The critical buckling load (P_cr) of the FGSFs was estimated using the double-tangent method and modified Budiansky criteria.

The density of FGSFs decreased with increasing filler percentage. The mechanical buckling load increased with the filler percentage. The natural frequency corresponding to the first mode of the FGSFs exhibited a decreasing trend with an increasing load in the pre-buckling regime and an increase in post-buckled zone, whereas the damping factor exhibited the opposite trend.

The current research work is valuable for the area of 3D printing by developing the functionally graded foam based sandwich beams. Furthermore, it intended to present the buckling behavior of 3D printed FGSFs, variation of frequency and damping factor corresponding to first three modes with increase in load.

Hoping to uncover the physical principles of the vibration of the functionally graded material (FGM) microplate, by which the authors can make contributions to the design and manufacturing process in factories like micro-electro-mechanical system (MEMS) and other industries.

The authors design a method by establishing a reasonable mathematical model of the physical microplate composed of a porous FGM.

The authors discover that the porosity, the distributions of porosity, the power law of the FGM and the length-to-thickness ratio all affect the natural frequency of the vibration of the microplate, but in different ways.

Originally proposed a model of the micro FGM plate considering the different distributions of the porosity and scale effect and analyzed the vibration frequency of it.

This study aimed to analyze the free vibration of a radially graded Ni-Al2O3-based functionally graded (FG) disk with uniform thickness.

Using the energy method, natural frequencies of rotating and non-rotating disks were determined at the limit elastic angular speed. Material properties were estimated using a modified rule of mixture. Both even and uneven porosity variation effects were considered in the material modeling. Finite element analysis validated the analytical approach.

The study explored limit angular speeds and natural frequencies across various grading indices, investigating the impact of porosity types and grading indices on these parameters.

Insights from this research are valuable for researchers and design engineers involved in modeling and fabricating porous FG disks, aiding in more effective design and manufacturing processes.

This study contributes to the field by providing a comprehensive analysis of free vibration behavior in radially graded Ni-Al2O3-based FG disks. The incorporation of material modeling considering both even and uneven porosity variation adds originality to the research. Additionally, the validation through finite element analysis enhances the credibility of the findings.

The purpose of this study is a numerical simulation and an analytical analysis about the low-velocity impact on a functionally graded porous plate with porosity distribution in the thickness direction. In this article, polymethyl methacrylate is used for matrix, and single-walled carbon nanotube (CNTs) (10,10) with consideration agglomeration sizes and lumping of CNT inside the agglomerations is applied for reinforcement.

In analytical formulation, the non-linear Hertz contact law is applied for interaction between projectile and plate surface. High-order shear deformation plate theory is developed, and energy of the system for impactor and plate is written. The governing equations are derived using Ritz method and Lagrange equations and are solved using the fourth-order Runge–Kutta method. Also, ABAQUS finite element model of functionally graded porous plate with all edges simply supported and reinforced by CNT under low-velocity impact is simulated and is compared with those is achieved in the present analytical approach.

In parametric studies, the influence of porosity distribution patterns include uniform, non-uniform symmetric and non-uniform asymmetric on the histories of contact force and impactor displacement of simply supported plate reinforced by CNT are presented. Eventually, the effects of porosity coefficient, impactor initial velocity, impactor radius and CNTs lumping inside agglomerations for non-uniform symmetric distribution patterns are discussed in impact event in detail.

In this paper, the effect of combination of polymethyl methacrylate and CNTs with consideration agglomeration sizes and lumping of CNTs inside the agglomerations in the form of a functionally graded porous plate is studied in the problem of low-velocity impact analysis.

The paper aims to the size-dependent analysis of functionally graded materials in thermal environment based on the modified couple stress theory using finite element method.

The element formulation is developed within the framework of the penalty unsymmetric finite element method (FEM) in that the C¹ continuity requirement is satisfied in weak sense and thus, C⁰ continuous interpolation enhanced by independent nodal rotation is employed as the test function. Meanwhile, the trial function is designed based on the stress functions and the weighted residual method. Besides, the special Gauss quadrature scheme is employed for integrals of matrices in accordance with the graded variation of the material properties.

The numerical results reveal that in thermal environment, functionally graded materials exhibit better bending performance compared to homogeneous materials, Moreover, the findings also indicate that with an increase in MLSP, the natural frequencies of out-of-plane modes gradually increase, while the natural frequencies of in-plane modes show much less variation, leading to a mode switch phenomenon.

The work provides an efficient numerical tool for analyzing and designing the functionally graded structures in thermal environment in practical engineering applications.

This 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.

The 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.

The 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.

This research primarily focuses on hypothetical scenarios and mathematical model development and analysis.

This 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.

The 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.

In 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.

The 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.

For 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.