Generalized Differential Quadrature Method Research Articles

Nonlinear two-dimensional transient thermoelastic analysis of functionally graded composite plates subjected to localised cooling loads

In this study, for the first time, localized thermal cooling is considered for the transient thermoelastic response of an axisymmetric plate, addressing the underexplored area of localized low-temperature thermoelasticity. Functionally graded composite plates are analyzed which consist of a mixture of stainless steel (SUS304) and low-carbon steel (AISI1020). A two-dimensional transient heat conduction equation is employed to capture localized cooling effects, featuring various adaptive time-dependent thermal boundary conditions which mirror both loading and unloading scenarios, effectively simulating real-world phenomena. Novel parameters are introduced to facilitate a comprehensive understanding of various aspects of thermal load handling and their impact on thermoelastic responses. The heat conduction equations are solved using the Generalized Differential Quadrature Method (GDQM) and the Crank-Nicolson scheme. The nonlinear governing equations, incorporating geometrical nonlinearity through the von Kármán assumption within the First Shear Deformation Theory (FSDT) framework, are solved using the GDQM and the Picard's technique. The model is validated using Finite Element Method (FEM) through Abaqus. A comprehensive analysis is provided that considers influence of the ratio of thermally affected and unaffected plate surface, thermal load magnitude, rapidity of thermal loading and unloading, duration of the cooling load, geometrical nonlinearity, and temperature dependence of material. The study shows that the maximum von Mises stress within the structure remains consistent regardless of the duration of the cooling load, as long as the rate at which the cooling load is applied stays the same. Additionally, the findings reveal that even minor localized thermal loads can produce substantial stress, especially at the intersection of thermally affected and non-affected zones on the exposed surface in some situations.

Nonlinear vibration of porous truncated conical shell under unified boundary condition and mechanical load

The aim of this article is to research nonlinear vibration responses of a metal porous truncated conical shell undergoing mechanical harmonic loads in thickness direction. The artificial spring technique is employed to unify boundary condition which can arrive at arbitrary classical boundary condition in real-word by changing the stiffness of springs. Utilizing Hamilton's principle, theoretical formulations of the conical shell are developed in view of FSDT and von-Kármán geometric relation. Afterwards, by employing generalized differential quadrature method (GDQM), the governing equation of nonlinear vibration in the form of partial differential equation is truncated and discretized into an ordinary differential equation which is a high-dimensional nonlinear dynamic system described in physical space rather than the mode space. On this basis, the analysis of effect of exciting frequency on the amplitude is carried out for three different distributing types of porous truncated conical shells by numerical integration. The frequency-amplitude responses of the system are depicted utilizing the sweeping frequency. The bifurcation diagrams, time series and phase diagrams are utilized to analyze the nonlinear dynamics of the porous truncated conical shell under unified boundary condition. It is found that the multiple solutions high-incidence area is near the 1st primary resonance, and vibration amplitude is dominated by the 1st order primary resonance and the 3rd one. The hardening-spring nature decreases for Type3, Type2 and Type1 successively.

A comprehensive study on the free vibration of adhesive lap joint laminated conical–conical shells adherends

In this research, the free vibration analysis of lap joint laminated conical shell connected to laminated conical shell with adhesive layer for various boundary conditions are investigated. Based on the first-order shear deformation theory (FSDT), the main field equations of the analytical model are derived and the governing differential equations of laminated conical shell to laminated conical shell adherends lap joint are obtained for homogeneous and elasticity adhesive layers by using Hamilton principle method. Then, based on the generalized differential quadrature method (GDQM), the equilibrium equations of the structure adherends are investigated. The influence of the boundary conditions, the type of the composite materials and adhesive layer, the circumferential wave number, the length to radius ratio of the shell, and the length of overlap to length of shell ratio are studied. Furthermore, the thickness to radius ratio and the thickness of adhesive to thickness of shell ratio, as well as the various cone angles of conical shell on the natural frequency of laminated conical adherends shells connected to the conical shells with adhesive layer are investigated. For validation of the numerical results, the results are compared with the previous research and the comparisons show very good agreement. The numerical results show that with the increase of the internal shell and external shell of semi-angle, the non-dimensional frequency of lap joint connection of two laminated conical shells with adhesive layer decreased and increased, respectively. Furthermore, with the increase of the adhesive thickness to conical shell thickness ratio and lap joint length to length of conical shell ratio, the dimensionless natural frequency of the structure increased.

Free oscillations of porous multi-graded graphene oxide nanocomposites coupled hemispherical-cylindrical shell-configuration structures under various edge constraints

Quantitative investigations of the vibrational characteristics coupled hemispherical-cylindrical shells (CHSCSs) formed of three types, including of porous, nanocomposite, and porous nanocomposite, under various edge conditions are carried out here: (1) a matrix strengthened by graded graphene oxide powder (GOP), (2) a matrix with the effects of the porosity, and (3) a matrix strengthened by multi-graded GOP with the porosity characteristic. To modify the vibrational characteristics of the nanocomposite, nine different functionally graded models are evaluated for GOP distribution within the matrix and CHSCS thickness. The Halpin-Tsai homogenization formula is used to compute the GOP nanocomposite (GOPN) material's mechanical characteristics. Addedly, a functionally graded type of the effect of the porosity is used. The CHSCS equations may be derived from Donnell's theory as well as from the first shear deformation theory (FSDT). The governing equations of the CHSCSs are determined using variation calculation, named Hamilton's principle. After that, this equation system is built using the generalized differential quadrature method (GDQM). The frequencies used as benchmarks are compared to those produced here to test the system. Remarkably, the lowest frequencies of the CHSCS made of pure matrix and multi functionally graded GOPN were decreased for all BCs by extending the value of the porosity factor. In addition, by increasing the value of the porosity factor for all BCs, the porous FGÓ-GOPN CHSCS had the greatest variation related to decreasing the minimum frequencies.

Buckling analysis of sandwich plates reinforced with various loading of multi-walled carbon nanotubes

The current investigation aims to examine the buckling behavior of sandwich structures reinforced with faces containing varying weight percentages (wt.%) of multi-walled carbon nanotubes (MWCNT), through the combined employment of experimental and numerical analysis techniques. In particular, the numerical analysis is executed through the implementation of the generalized differential quadrature method (GDQM). The study first determines the mechanical properties of the pure and reinforced samples via experimental tests. The buckling equations of the sandwich plate are then derived using the Frostig approach and a high-order shear deformation theory (SDT) for the flexible core. The continuity conditions between the faces and the core are considered to obtain the structural equations of the system, and Lagrange coefficients are introduced to enhance the accuracy of the governing equations. Subsequently, the study investigates the impact of various parameters, such as core thickness, aspect ratio, different boundary conditions (BC), and the addition of MWCNT nanoparticles on the critical buckling load of the system, utilizing the mechanical properties obtained for the composite faces. The present investigation reveals that the incorporation of MWCNT into the composite matrix brings about notable enhancements in the mechanical characteristics of sandwich structures. Specifically, the elastic modulus and ultimate strength of the faces are found to increase following the addition of MWCNT. Additionally, the critical buckling load of the sandwich plates is observed to rise with an increase in aspect ratio and length-to-thickness ratio, while a decrease in axial load yields similar results. The clamped boundary condition has higher critical buckling loads than the simply supported boundary condition. The addition of MWCNT nanoparticles decreases the dimensionless critical buckling force as the b/a ratio increases. Finally, the reported results of the current investigation present noteworthy findings about the advancement and improvement of sandwich composite structures to meet various application requirements.

Bending Vibration and Buckling Analysis Of Nonhomogeneous Nanotubes Using Nonlocal Elasticity Theory and Gdq Method

In this paper structural analysis of nonhomogeneous nanotubes has been carried out using nonlocal elasticity theory. Governing differential equations of nonhomogeneous nanotubes are derived. Nonlocal theory of elasticity has been employed to include the scale effect of the nanotubes. Nonlocal parameter, elastic modulus, density and diameter of the cross sections are assumed to be functions of spatial coordinates. General Differential Quadrature (GDQ) method has been employed to solve the governing differential equations of the nanotubes. Various boundary conditions have been applied to the nanotubes. Present results considering nonlocal theory are in good agreement with the results available in the literature. Effect of various geometrical and material parameters on the structural response of the nonhomogeneous nanotubes has been investigated. Present results of the nonhomogeneous nanotubes are useful in the design of the nanotubes.

A unified local-nonlocal integral formulation for dynamic stability of FG porous viscoelastic Timoshenko beams resting on nonlocal Winkler-Pasternak foundation

We present a study on the nonlocal dynamic stability of functionally graded (FG) porous viscoelastic Timoshenko beams resting on a Winkler-Pasternak foundation. The porosity distributions are assumed to be symmetric or antisymmetric about the mid-plane of the beams, and the Kelvin-Voigt viscoelastic model is considered to depict the beams’ viscoelastic properties. Unlike most studies on this topic, we consider both the beam’s bending deformation and the foundation reaction as nonlocal, simultaneously, by uniting the equivalently differential forms of two well-posed local-nonlocal integral models (i.e., strain-driven (ε-D) and stress-driven (σ-D) strategies) which are strictly equipped with a set of constitutive constraint conditions, through which both the softening and hardening effects on the stiffness of structures due to size reduction can be addressed. The generalized differential quadrature method (GDQM) is utilized for discretizing variables presented in the differential problem formulation, from which the numerical solution of the dynamic instability region (DIR) of different bounded beams can be obtained. After conducting comparative studies to validate the proposed model, the effects of nonlocal parameters, static force factor, porosity distribution and viscoelastic property on the DIR are investigated. Moreover, the influence of incorporating the nonlocality of the foundation is also presented.

General boundary conditions implementation for the static analysis of anisotropic doubly-curved shells resting on a Winkler foundation

In the present work an Equivalent Single Layer (ESL) formulation is proposed for the static analysis of doubly-curved anisotropic structures of arbitrary geometry and variable stiffness resting on a Winkler elastic foundation. In-plane and out-of-plane general distributions of linear elastic springs are provided for the implementation of general external constraints along the edges of the structure. The structure is geometrically described accounting for the principal curvatures of the shell object of analysis. A generalized set of blending functions based on Non-Uniform Rational Basis Spline (NURBS) curves is adopted so that arbitrary shaped structures can be modelled with the same approach. The fundamental governing equations are obtained in terms of displacement field unknowns, which has been effectively described accounting for a unified formulation based on the minimum potential energy principle. General anisotropic lamination schemes are considered, setting a general orientation of each lamina, as well as all possible material symmetries. The numerical implementation is performed by means of the Generalized Differential Quadrature (GDQ) method, thus allowing a strong formulation of the structural problem. A series of validation examples is performed on shells with zero, single and double curvatures in which the static structural response provided with the proposed formulation has been compared to that obtained from a refined three-dimensional finite element model, showing a great accordance between these different approaches. The research shows that the employment of higher order theories, together with the GDQ method, allows to obtain very accurate results with a reduced computational cost, compared to finite element simulations.

Vibration Analysis of a Unimorph Nanobeam with a Dielectric Layer of Both Flexoelectricity and Piezoelectricity.

In this study, for the first time, free and forced vibrational responses of a unimorph nanobeam consisting of a functionally graded base, along with a dielectric layer of both piezoelectricity and flexoelectricity, is investigated based on paradox-free local/nonlocal elasticity. The formulation and boundary conditions are attained by utilizing the energy method Hamilton's principle. In order to set a comparison, the formulation of a model in the framework of differential nonlocal is first presented. An effective implementation of the generalized differential quadrature method (GDQM) is then utilized to solve higher-order partial differential equations. This method can be utilized to solve the complex equations whose analytic results are quite difficult to obtain. Lastly, the impact of various parameters is studied to characterize the vibrational behavior of the system. Additionally, the major impact of flexoelectricity compared to piezoelectricity on a small scale is exhibited. The results show that small-scale flexoelectricity, rather than piezoelectricity, is dominant in electromechanical coupling. One of the results that can be mentioned is that the beams with higher nonlocality have the higher voltage and displacement under the same excitation amplitude. The findings can be helpful for further theoretical as well as experimental studies in which dielectric material is used in smart structures.

Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core

PurposeThe purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.Design/methodology/approachThe FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.FindingsA series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.Originality/valueThis paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

On the energy absorption of the reinforced sandwich curved beam equipped with piezoelectric layers through ANN and MCS analyses

The aim of this research is to investigate the impact of a viscoelastic foundation on the vibration of a curved beam structure with clamped and simply-supported boundary conditions. The structure considered is a micro-scale laminate composite beam made up of two piezoelectric face layers and a carbon nanotube-reinforced composite core. The study employs non-classical elasticity theory and nonlocal strain gradient theory to account for both nano-scale and microscale effects. The equations of motion are derived using the energy terms of the beam and a variational principle, with boundary conditions assumed to be clamped at one end and simply supported at the other end. A semi-analytical method of general differential quadrature method is used to solve the equations due to their nonlinear terms. To capture the effects of various parameters on the in-plane vibration of sandwich arches, an artificial neural network is designed and implemented. The study analyzes the impact of nonlocal and gradient parameters, geometrical aspect ratios, and substrate constants of the structure on the natural frequency and amplitude of vibration of the laminate beam. Results show that increasing nonlocal and gradient parameters have different effects on the amplitude and frequency of vibration of the beam.

Nonlinear large amplitude vibrations of higher-order functionally graded beams under cooling shock

In this paper, thermally induced vibrations of beams made of functionally graded materials (FGMs) subjected to cooling shocks are investigated. It is considered that the beam has been made of a mixture of stainless steel (SUS 304) and low-carbon steel (AISI 1020). To model the displacement field, the third-order beam theory, known as the Reddy beam theory (RBT), is used. Material properties depend on temperature and distribution of materials, and this dependence is modeled through the temperature and the location of materials along the thickness direction. Considering the uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and the equations of motion governing the higher-order beam are derived utilizing Hamilton's principle. Solving the equations is done numerically; the generalized differential quadrature method (GDQM) is employed to approximate the spatial derivatives, and the Newton-Raphson scheme is applied to linearize the equations. In addition, for approximation of the time derivatives, the Newmark method is utilized. Subsequently, the effects of various parameters on the non-dimensional lateral deflection of the higher-order beam considering two different types of thermal loading are investigated. A comprehensive parametric study is conducted to study the effects of important parameters including beam thickness, thermal load rapidity time, the amount of applied load, and the FG parameter.

Vibrational features of graphene oxide powder nanocomposite coupled conical-cylindrical shells applicable for aerospace structures under various boundary conditions

Overcoming the challenging circumstances encountered in aerospace components has led to the widespread use of small-scale reinforcements to improve structure-related performance. Accordingly, the vibrational properties of coupled conical-cylindrical shells (CCCSs) made of a matrix material reinforced by functionally graded graphene oxide powder (FGGOP) are numerically investigated under various boundary conditions (BCs) in this paper. To enhance the vibrational feature of the CCCS reinforced by graphene oxide powder (GOP), three models are measured regarding distribution related to this small-scaled material within the polymer along with the thickness related to the CCCS. The Halpin-Tsai homogenization form is also employed to develop the mechanical values associated with the GOP-nanocomposite materials. The main equations related to the CCCSs are obtained by joining Donnell's theory and the first shear deformation theory (FSDT). Additionally, using variation calculation (Hamilton's principle), the motion equations (MEs) of the CCCS reinforced by FGGOP are determined. Then, the generalized differential quadrature method (GDQM) is utilized to produce the system related to the MEs. Next, standard eigenvalue determination obtains the frequencies of the CCCS made of the FGGOP-nanocomposite. Finally, the frequencies of various benchmarks are compared with those determined here to validate the proposed scheme. Also, more than a few new and interesting samples are designed and solved numerically to indicate the impacts of the GOP, geometrical values, and various BCs on the vibration responses of the CCCS made of GOP-nanocomposite. Remarkably, this paper is the first evaluation related to the free vibration of the coupled conical-cylindrical shells reinforced by FGGOP under different BCs.

Vibrational characteristic simulations regarding connecting two different semi-spheroidal shells and a full-spheroidal shell with a conical shell categorized in underwater structures

Recently, the related structures of marine, underwater, and ocean structures, covering, ice-breaking devices, riser pipes, ballast water gears, gliders, and underwear noise migrations, can be counted by Connected Shells (CSs). Accordingly, for the first time, the investigation related to vibration outputs associated with connecting two different semi-spheroidal shells and a full-spheroidal shell with a conical shell, namely Connected Spheroidal-Conical Shell Assembly (CSCSA) organized in three assembly groups is examined here. In detail, General Shell Hypothesis (GSH) and the First Shear Deformation Theory (FSDT) are connected to find the main formulations of the CSCSAs' shell elements. Addedly, the Motion Governing Differential Equations (MGDEs) associated with each shell element related to the CSCSAs are identified as implementing Hamilton's principle. Addedly, the MGDEs associated with the CSCSA components are discretized, realizing the Generalized Differential Quadrature Method (GDQM). Thereafter, the Natural Frequency Factors (NFFs) of the CSCSAs are determined by implementing the eigenvalue determination. Also, the NFFs measured by the suggested context are linked to the NFFs determined using classical FEM-constructed commercial software to validate the provided approach since previous research has not been conducted on these structures in the literature (except one type related to the CSCSAs). More importantly, the largest observed inaccuracy is less than 1%. Consistent with this, the responses of this investigation may be operated as the benchmark. Finally, the impacts of the geometrical parameters connected to the CSCSAs on the NFFs of the structure are identified via the design and solution of original cases.

Application of GDQ method to large amplitude response of FGM joined spherical-conical shells under rapid surface heating

Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) joined spherical-conical shells are analyzed in the current research. Thermo-mechanical properties of the shells are assumed to be temperature and position dependent. The system of joined spherical-conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and Crank-Nicolson methods. This equation is non-linear since the thermo-mechanical properties of the shells are temperature dependent. The total functional of the shells is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β-Newmark time approximation technique. Numerical results are well-validated with the available data for the case of single FGM spherical shell. Parametric studies are conducted to examine the influences of conical and spherical shell geometries, material composition, temperature dependence, in-plane and out-of-plane mechanical boundary conditions, various configuration of conical/spherical shell system, and thermal boundary conditions. It is highlighted that thermally induced vibrations indeed exists.

Free-damped vibration tangential wave responses of FG-sandwich merged hemispherical-cylindrical shells under effects of artificial springs at merging and boundary conditions

This article is formed to extract the frequencies with free-damped vibration characteristics of the tangential waves related to the Functionally Graded (FG) sandwich Merged Hemispherical-Cylindrical Shells (MHCS) under elastic springs. The wall of the MHCS contains three layers of embodied Functionally Graded Material (FGM). The material characteristics of the structure change functionally along the thickness of each layer. Equivalent Single Layer (ESL) and Rule of Mixture (RM) are applied to determine the mechanical features of the materials. In addition, eight sandwich types are examined here. Moreover, both merging and support conditions are assumed to be flexible. Artificial transitional and rotational springs are modeled to apply the effect of a semi-rigid merging between hemispherical and cylindrical parts and the support’s flexibility. Further, Donnell's hypothesis and Hamilton's scheme are utilized to acquire the kinetic differential equations related to the MCHS. A recognized semi-analytical method, labeled the Generalized Differential Quadrature Method (GDQM), is being implemented to discretize the kinetic equations. In addition, the tangential wave frequencies are determined by solving the eigenvalue problem. The available results in the submitted framework are compared with the outputs of the FE-based software to validate the proposed procedure. Several innovative parametric studies will be implemented to illustrate the impacts of different general boundary conditions, semi-rigid connections, and material features on the vibrational behavior of MHCS.

Generalized differential quadrature element solution, swarm, and GA optimization technique to obtain the optimum frequency of the laminated rotary nanostructure

Optimization of the fiber angle in the laminated composite material to achieve the highest strength or stability has great importance in structural design. In the present study, we aim to utilize genetic algorithm (GA) and particle swarm optimization (PSO) together to find the best angle of composite layers in a multilayer cylindrical shell structure. To this aim, a detailed formulation of the composite cylindrical structure is presented using nonlocal strain gradient theory (NSGT), zigzag theory, and Hamilton's principle for a shear deformable shell displacement field. The modal equations of motion are further solved using the general differential quadrature element method (GDQEM). Having the route of obtaining the resonance frequency of the cylindrical composite structure, GA-PSO is engaged to obtain the optimal angle of the laminate composite to achieve the highest frequency. It is revealed that angle θ = 37.5° provides the highest frequency for a single-layer cylindrical shell. Using this angle, stacking sequences for 3, 5, and 7 layers’ composite are optimized to have the highest frequency. In the end, a detailed parametric study is presented using optimum condition shell composite. The results show that after 30 composite layers, changing the number of layers seems to be not effective on the resonance frequency of the cylinder for both simply supported and clamped boundary conditions.

Hygro-thermal vibration study of nanobeams on size-dependent visco-Pasternak foundation via stress-driven nonlocal theory in conjunction with two-variable shear deformation assumption

This article presents a hygro-thermal-damping vibration analysis of two-variable shear deformation beams supported by a visco-Pasternak foundation. In contrast to the majority of the literature on this subject, the hygro-thermal load, and external foundation are simultaneously presented as nonlocal, by employing the well-posed stress-driven local/nonlocal mixture formulation with a set of constitutive constraints. The Generalized Differential Quadrature Method (GDQM) is adopted to solve the complex eigenvalue problem at hand. In the numerical simulation section, we first conduct comparison studies to validate the accuracy of the present formulation and results. Then, a series of benchmark results for the vibration frequency of different bounded higher-order shear deformation beams supported by the elastic foundation are presented. Subsequently, the effects of simultaneously applying stress-driven nonlocal assumptions on the foundation and hygro-thermal load in the undamped and damping vibration of the shear deformation beams are examined.

A generalized differential quadrature algorithm for the Sutterby nanofluid flow capturing irreversibility analysis and activation energy aspects

It is well known that the dissipation of energy in each mechanism can be assessed by scrutinizing entropy generation. It is a dominant tool permitting energy wastage minimization or optimal utilization for strengthening system functioning. In this study, we considered Sutterby nanofluid in the presence of activation energy subjected to a convectively heated surface. The Sutterby nanofluid model contains Brownian and thermophoresis movement features. Moreover, the role of magnetic field and mixed convection on Sutterby nanofluid heat transfer is observed. The relation between Entropy generation and the Bejan number is also expressed. Furthermore, the set of nonlinear PDEs is changed into non-linear ODEs by using some appropriate similarity transformations. Then these coupled ODEs are solved numerically by applying GDQM (generalized differential quadrature method). The results of the existing model for the velocity field, temperature profile, concentration distribution, entropy generation, and the Bejan number are exhibited pictorially and tabularly. The graphical analysis shows that nanofluid temperature intensifies for larger Eckert numbers, whereas it deteriorates for greater. Moreover, it discloses that entropy generation represents deteriorations for diffusive variables. Furthermore, graphical exploration of the Bejan number boosts for enlarged values of radiation parameters.

Natural frequency investigation of graphene oxide powder nanocomposite cylindrical shells surrounded by Winkler/Pasternak/Kerr elastic foundations with a focus on various boundary conditions

For the first time, the present research examines the free vibration responses, Natural Frequencies (NFs), of Graphene Oxide Powder (GOP) nanocomposite cylindrical shells surrounded by three types of elastic foundations considering different Boundary Conditions (BCs). To support this, the effects of various BCs are examined on the NFs related to the GOP Nanocomposite Cylindrical Shells (GOPNCS). In addition, elastic foundations are characterized by three factors: Winkler, Pasternak, and Kerr. Addedly, First-order Shear Deformation Theory (FSDT) and Donnell's shell theory are combined to discover the fundamental formulations related to the GOPNCS structures. Then, the equations of motion related to the GOPNCS are formulated employing Hamilton's principle. In subsequent, the equations associated with the previous step are discretized by implementing the Generalized Differential Quadrature Method (GDQM), counted as the mesh reduction method. Afterward, the standard eigenvalue determination is employed to determine the NFs associated with the GOPNCS. Ultimately, multiple benchmarks are answered to authenticate the scheme recommended for determining the NFs of the GOPNCS. Further, numerous original problems are arranged and highlight the effects of changes in material and geometrical features, various BCs, and three types of elastic foundations on the NFs related to the GOPNCS.