Search

This article is the first attempt to employ deep learning to estimate the mechanical performance of multi-phase systems. Features of the design-points are obtained with the aid of the fast-converging numerical method used to solve the governing motion equations developed according to the kinematics of shear deformable structures. The optimum values of the parameters involved in the mechanism of the fully-connected neural network are determined through the momentum-based optimizer. The strength of the method applied in this survey comes from the high accuracy besides lower epochs needed to train the multi-layered network. It should be mentioned that the mechanical characteristics of the structure are computed through a two-step micromechanical scheme including the Halpin–Tsai method. The accuracy of the employed approach is examined and verified through the comparison of the results with those published in the literature. The numerical results give the practical hint that increasing the content of the reinforcement phase not always equal to increasing the resistance of the composite structure toward static instability. Thus, designers must choose the weight content of nano or macro-scale reinforcements by considering the shape factors of these materials to boost the strength of the system appropriately.

This article presents the axial buckling analysis of polymer-CNT-fiber nanocomposite annular system (PCFCAS) resting on Winkler-Pasternak substrates under various temperature gradients. With the ai...

In this research, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid nano-composite reinforced disk in the thermal environment and subject to a harmonic external load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the viscoelastic disk subject to harmonic excitation. The fundamental and golden results of this paper could be that in the lower value of the external harmonic force, different FG patterns do not have any effects on the motion response of the structure. But, for the higher value of external harmonic force and all FG patterns, the chaos motion could be seen and for the FG-X pattern, the chaosity is more significant than other patterns of the FG. As a practical designing tip, it is recommended to choose plates with lower thickness relative to the outer radius to achieve better vibration performance.

In this research, we study the thermal buckling performance of multi-scale hybrid laminated nanocomposite (MHLC) disk (MHLCD) subjected hygro-mechanical loading. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macro-scale, respectively. The disk is modeled based on higher order shear deformation theory. We present a modified Halpin–Tsai model to predict the effective properties of the MHLCD. The minimum total potential energy principle is employed to establish the governing equations of the system, which is finally solved by the generalized differential quadrature method. To validate the approach, numerical results are compared with available results from the literature. Subsequently, a comprehensive parameter study is carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, moisture coefficient, stacking sequence of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio and inner radius to thickness ratio on the response of the plate. Some new results related to critical buckling of an MHLCD are also presented, which can serve as benchmark solutions for future investigations.

This is the first research on the vibrational analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate within the framework of higher order shea...

This is a fundamental study on the buckling temperature and post-buckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation. The matrix material is reinforced with graphene nanoplatelets (GPLs) at the nanoscale. The displacement–strain of thermal post-buckling of the FG-GPLRC disk via third-order shear deformation theory and using Von Karman nonlinear plate theory is obtained. The equations of the model are derived from Hamilton’s principle and solved by the generalized differential quadrature method. The direct iterative approach is presented for solving the set of equations that includes highly nonlinear parameters. Finally, the results show that the radius ratio of outer to the inner (Ro/Ri), the geometrical parameter of GPLs, nonlinear elastic foundation, externally applied voltage, and piezoelectric thickness play an essential impact on the thermal post-buckling response of the piezoelectrically FG-GPLRC disk surrounded by the nonlinear elastic foundation. Another important consequence is that, when the effect of the elastic foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the thermal post-buckling of the disk and this matter is true for both boundary conditions.

Modeling of viscoelastic behavior can be useful to accurate study of micro-shell vibration. In this study, influence of viscoelastic coefficient and material length scale parameter on frequency of ...

In this paper, the dynamics of a viscoelastic pipe conveying fluid attached to a nonlinear energy sink (NES) subjected to a sinusoidal flow is studied, aiming at performance improvement of such flu...

A pathway to the design of even more effective versions of the powerful anti-cancer drug Taxol is opened with the most detailed look ever at the dynamic and static behaviors of MAPs. Regarding this issue, the dynamic stability analysis of cantilevered microtubules in axons with attention to different size effect parameters based on the generalized differential quadrature method is presented. Supporting the effects of MAP Tau proteins and surrounding cytoplasm are considered as an elastic foundation. The better understanding modeled as a moderately thick curved cylindrical nanoshell. The real property of the living biological cells is presented as the Kelvin-Voight viscoelastic properties. Hamilton's principle is employed to establish the Clamped-Free boundary conditions and governing equations, which is finally solved by the Fourier-expansion based generalized differential quadrature method (FGDQM). Considering length scale and nonlocal parameters (

In the present study, based on 12-unknown higher order shear deformation theory (HSDT), buckling and vibration analysis of FG-CNTRC rectangular plate are investigated for various types of temperatu...

The main point of the current study is that the frequency analysis of a graphene platelets–reinforced composite (GPLRC) imperfect panel covered with piezoelectric sensor and actuator (PISA) based on the 3D elasticity theory is investigated. Rule of mixture is employed to obtain varying mass density and Poisson’s ratio, while module of elasticity is computed by modified Halpin-Tsai model. The governing equations are obtained using the 3D elasticity theory. By using Fourier series expansion along the longitudinal and latitudinal directions for the stress and displacement fields, a closed form solution is derived. The novelty of the current study is the consideration of the GPLRC panel and PISA, as well as imperfection are implemented on the proposed model using theory of 3D elasticity. Due to perfect bonding between piezoelectric layers and core the compatibility conditions are derived. Finally, influences of PISA thickness, graphene platelet (GPL) distribution pattern, porosity, span angle of panel, number of layers and GPL weight function on the dynamic stability of the GPLRC smart imperfect panel are presented. Another important consequence is that the sandwich panels with lower span angle have better natural frequency. In other words, to obtain desirable frequency response using structures which their shape is similar to GPLRC plate is more recommended than those resemble to GPLRC cylindrical shell.

In this article, buckling analysis of a porous nanocomposite cylindrical shell reinforced with graphene platelets (GPLs) using first-order shear deformation theory is carried out. Internal pores and GPLs are scattered uniformly and/or nonuniformly in the thickness direction. The mechanical properties such as the effective modulus of elasticity through the thickness direction are computed by the modified Halpin–Tsai micromechanics approach, whereas density and Poisson ratio are in accordance with the rule of mixtures. The Rayleigh–Ritz method is employed to obtain a critical buckling load of the graphene-reinforced porous cylindrical shell. The accuracy of the obtained formulation is validated by comparing the numerical results with those reported in the available literature as well as with the software ABAQUS. Moreover, the effects of patterns of internal pores and GPLs distribution, GPLs weight fraction, density and size of internal pores, different boundary conditions, geometric factors such as mid-radius to thickness ratio and shape of graphene platelets on the buckling performance of the functionally graded graphene platelet-reinforced composite porous cylindrical shell are explored.

In this article, the thermal vibration of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plate resting on an elastic foundation under the mechanical load framework o...

Because of promoted thermomechanical performance of functionally graded graphene platelet–reinforced composite ultralight porous structural components, this article investigates bending and free vibration behavior of functionally graded graphene platelet–reinforced composite porous cylindrical shell based on the theory of elasticity. Effective elasticity modulus of the composite is estimated with the aid of modified version of Halpin–Tsai micromechanics. Rule of mixtures is used to obtain mass density and Poisson’s ratio of the graphene platelet–reinforced composite shell. An analytical solution is introduced to obtain the natural frequencies and static behavior of simply supported cylindrical shell by applying the state-space technique along the radial coordinate and Fourier series expansion along the circumferential and axial direction. In addition, differential quadrature method is used to explore the response of the cylindrical shell in the other cases of boundary conditions. Validity of the applied approach is examined by comparing the numerical results with those published in the available literature. A comprehensive parametric study is conducted on the effects of different combinations of graphene platelets distribution patterns and porosity distribution patterns, boundary conditions, graphene platelets weight fraction, porosity coefficient, and geometry of the shell (such as mid-radius to thickness ratio and length to mid-radius ratio) on the bending and free vibration behavior of the functionally graded graphene platelet–reinforced composite porous cylindrical shell. The results of this study provide useful practical tips for engineers designing composite structures.

Up to now, no studies have been yet reported to study the mechanical behaviors of three-dimensional functionally graded graphene platelets reinforced composite (FG-GPLRC) open-type panel. In this paper, the free vibration of FG-GPLRC open-type panel under multi-directional initially stressed using three-dimensional poroelasticity theory is investigated for the first time. Weight fraction of graphene open-type panel is assumed to be distributed either uniformly or functionally graded (FG) along the radial direction. Modified Halpin–Tsai model is used to compute effective Young’s modulus, whereas effective Poisson’s ratio and mass density are computed using the rule of mixture. State-space differential equations are derived from the governing equation of motion and constitutive relations in cylindrical co-ordinates. The accuracy of the obtained formulation is validated by comparing the numerical results with those reported in the available literature as well as with the finite-element modeling. The influences of several importance parameters, such as various directional initial stress, compressibility coefficient, porosity, and various type of sandwich open-type cylindrical panel, are investigated on the frequency of the structures. The results of the present study can be served as benchmarks for future mechanical analysis of cylindrical FG-GPLRC structures.

Due to important role of composite materials in broad spectrum of applications, this article focused on bending and frequency characteristics of a functionally graded graphene platelet (GPL) reinfo...

In this paper, three-dimensional static and free vibration analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) truncated conical shells, cylindrical shells and annula...

Due to superior characteristics added to composite structures by using graphene-platelets (GPLs) as nanofillers, this article investigates torsional buckling analysis of functionally graded graphen...

This article analyzes critical voltage and frequency information of functionally graded graphene nanoplatelets-reinforced composite (FG-GPLRC) porous cylindrical microshell embedded in piezoelectric layer, subjected to temperature gradient. The current non-classical model is capable of capturing the size dependency in the microshells by using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. To satisfy temperature boundary conditions, the Fourier series solution is extracted. In addition, for the first time, thermal conductivity coefficients regarding each GPL’s distribution pattern are presented. The thermally equations are solved via Heun’s differential equation. The mechanical properties of FG-GPLRC layer are estimated based on modified Halpin–Tsai micromechanics and rule of mixtures. Hamilton’s principle is utilized to develop governing equations of motion and boundary conditions. Finally, an analytical solution is carried out based on Navier method to obtain critical voltage and frequency in the case of simply supported shell, whereas a semi-analytical solution is proposed based on differential quadrature method (DQM) for other boundary conditions. The results show that piezoelectric layer, graphene nanoplatelets’ (GPLs) distribution pattern, porosity distribution, difference gradient thermal, length scale parameter and GPL weight function play important roles on the natural frequency and critical voltage of the GPL porous cylindrical microshell coupled with piezoelectric actuator. The results of the current study are useful suggestions for the design of materials science, micro-electromechanical systems and nano-electromechanical systems such as nano-actuators and nano-sensors.

This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing equations of motion, which is finally solved by generalized differential quadrature method (GDQM) and perturbation method (PM). Finally, the results show that FG patterns, different orientation angle of the fiber, the VF and WCNT parameters, axial load, nonlinear temperature gradient, and applied temperature of the top surface play an essential impact on the linear and nonlinear dynamic responses of the MHCD. The more significant outcome of this research is that the effects of the VF, WCNT, $$\theta$$ , and β parameters on the nonlinear frequency of the MHCD can be considered at the higher value of the large deflection parameter and the effect of negative axial load on the dynamic responses of the structure is more intensive. As an applicable result show that the best functionally graded (FG) pattern for serving the highest nonlinear dynamic response of an MHC reinforced annular plate is FG-A.

This survey addresses the non-polynomial framework for bending responses of three-phase multi-scale hybrid laminated nanocomposite (MHLNC) reinforced circular/annular plates (MHLNCRCP/ MHLNCRAP) based upon the three-dimensional theory of elasticity for various sets of boundary conditions. The sandwich structure with two, three, five, and seven layers is modeled using compatibility conditions. The state-space based differential quadrature method (SS-DQM) is presented to examine the bending behavior of MHLNCRCP/ MHLNCRAP by considering various boundary conditions. Halpin–Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale composite. Singular point is investigated for modeling the annular disk. The carbon nanotubes (CNTs) are supposed to be randomly oriented and uniformly distributed through an epoxy resin matrix. Afterward, a parametric study is done to present the effects of various symmetric cross-ply laminated layers, various types of sandwich circular/annular plates, and various types of pressure on the bending characteristics of the MHLNCRCP/ MHLNCRAP. Numerical results reveal that sinusoidal load is the best pressure for improving the nanocomposite circular/annular plates’ deformation resistance and stress.

In this work, we study the vibration and bending response of functionally graded graphene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different substrates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element predictions performed in the commercial COMSOL code, and similar outcomes available in the literature. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the reinforcing phase, as well as the surrounding environment and boundary conditions, with very interesting insights from a scientific and design standpoint.

This paper explores the high-accuracy analysis of bending and frequency response of the sandwich cylindrical shell with functionally graded (FG) carbon nanotubes reinforced composite (FG-CNTRC) face-sheets and polymeric core under the effect of initial axial stress and various mechanical loading based upon the three-dimensional theory of elasticity for various sets of boundary conditions. The sandwich structure is composed of multilayers with uniformly dispersed carbon nanotubes (CNT) in each fictitious layer of face-sheets, but its weight fraction changes layer-by-layer along the thickness direction. With the aid of compatibility conditions, the sandwich structure with three layers is modeled. Analytical bending and frequency solutions are obtained for simply supported shells. Also, the state-space based differential quadrature method (SS-DQM) is employed to determine the bending and frequency response of the sandwich cylindrical shell by considering various boundary conditions. The bending response of the sandwich cylindrical shell is obtained under the impact of various mechanical loadings. The influences of several parameters, such as initial stress and various mechanical loadings are investigated on the bending and frequency of the structures. The results of the presented study can be served as benchmarks to assess the validity of the conventional two-dimensional theory.

This article presents a non-polynomial framework for bending responses of functionally graded-graphene nanoplatelets composite reinforced (FG-GPLRC) disk based upon three-dimensional refined higher-order shear deformation theory (3D-RHOSDT) for various sets of boundary conditions. By employing Hamilton’s principle, the structure's governing equations are derived and solved with the aid of the differential quadrature method (DQM). The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. Afterward, a parametric study is done to present the effects of weight fraction of GPLs, three kinds of FG patterns, shape mode, three kinds of boundary conditions, and different patterns of applied load on bending characteristics of the FG-GPLRC disk. The results show that in the outer and inner layers of the GPLRC disk, the structure with GPL-X and GPL-O patterns has the highest and lowest value of the shear stress, while in the middle layer, the mentioned relation between GPL patterns and shear stress changes to reverse. Another consequence is that the GPLRC disk has the best bending and static behavior against the sinusoidal pattern of applied load, and the structure shows weaker behavior against the uniform pattern. It is also observed that as the radius ratio increases, the buckled nodes are concentrated along the circumferential direction, and the mentioned issue is more considerable at the higher mode numbers.

In this article, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency, and chaotic responses of the graphene nanoplatelet (GPL) reinforced composite (GPLRC) doubly-curved panel subject to an external harmonic load. Using Hamilton's principle and the Von-Karman nonlinear theory, the nonlinear governing equations are derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. The results show that GPL's pattern, radius to length ratio, harmonic load, and thickness to length ratio have important role in the chaotic motion of the doubly-curved panel. The fundamental and golden results of this paper is that the chaotic motion and nonlinear frequency of the panel is hardly dependent on the value of the smaller radius to length ratio ( R 1 / a parameter) and viscoelastic foundation. It means that by increasing the value of R 1 / a parameter, and taking into account the viscoelastic foundation, the motion of the system tends to show the chaotic motion. Moreover, for GPL-A, GPL-V, and GPL-UD patterns, when the value of the R 1 / a parameter or the curvature shape of the doubly-curved panel increases, the chaoticity in motion response improves while for the GPL-O pattern, this matter reverses.

In the presented computational approach, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid Nano-composites reinforced disk (MHCD) embedded in a viscoelastic media and subject to a harmonic load. Using Hamilton's principle and Von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the viscoelastic disk subject to harmonic excitation. The golden results of this paper is that the chaotic motion and nonlinear frequency of the disk is hardly dependent on the value of the outer to inner radius ratio ( R o / R i ) and viscoelastic parameters and it means that by increasing the value of R o / R i parameter and taking into account the viscoelastic foundation, the motion of the system tend to show the chaotic motion. Moreover, at the lower value of the R o / R i parameter, quasi-harmonic and chaotic responses can be seen for the conditions with and without considering the effect of viscoelastic foundation and at the higher value of the parameter, the chaosity of the system decreases.

This is the first research on the free vibration analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate resting on the visco-Pasternak foundation and subjected to the nonlinear temperature gradient and mechanical loading within the framework of higher-order shear deformation theory (HSDT). Hamilton's principle is employed to establish governing equations within the framework of HSDT. In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Generalized differential quadrature method (GDQM) is applied to obtain a numerical solution. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of the stiffness of the substrate, patterns of temperature rise, axial load, damper and viscoelasticity coefficient, weight fraction and distribution patterns of GPLs and geometric dimensions of GPLs on the frequency response of the structure. The results revealed that applying sinusoidal temperature rise and locating more square-shaped GPLs in the vicinity of the top and bottom surfaces have important effect of the highest natural frequency and buckling load of the FG-GPLRC viscoelastic structure.

This is the first research on the buckling and free vibration analysis of functionally graded graphene platelets reinforced composite annular plate resting on elastic substrate and subjected to nonlinear temperature gradient and mechanical load within the framework of higher order shear deformation theory (HSDT). Governing equations and boundary conditions are established by employing Hamilton’s principle. Generalized differential quadrature method is applied to obtain numerical solution. Considering nonlinear temperature gradient instead of the linear one and also the effects of elastic substrate besides describing the kinematics on the basis of HSDT makes the results closer to real condition. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of stiffness of the substrate, patterns of temperature rise, temperature gradient, axial load, weight fraction and distribution patterns of GPLs, outer radius to inner radius ratio, inner radius to thickness ratio of the plate and geometric dimensions of GPLs on the response of the structure. This study provides essential information to engineers seeking innovative ways to promote the composite structures in a practical way.

In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler&ndash, Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. The annular plate is modeled based on higher-order shear deformation theory (HSDT). We present a modified Halpin&ndash, Tsai model to predict the effective properties of the MHCAP. Hamilton&rsquo, s principle was employed to establish the governing equations of motion, which is finally solved by the generalized differential quadrature method (GDQM). In order to validate the approach, numerical results were compared with available results from the literature. Subsequently, a comprehensive parameter study was carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, outer temperature, volume fraction and orientation angle of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio, and inner radius to thickness ratio on the response of the plate. The results show that applying a sinusoidal temperature rise and locating more CNTs in the vicinity of the bottom surface yielded the highest natural frequency.

This is the first research on the vibration and buckling analysis of a graphene nanoplatelet composite (GPLRC) microdisk in the framework of a numerical based generalized differential quadrature method (GDQM). The stresses and strains are obtained using the higher-order shear deformable theory (HOSDT). Rule of the mixture is employed to obtain varying mass density, thermal expansion, and Poisson’s ratio, while the module of elasticity is computed by modified Halpin–Tsai model. Governing equations and boundary conditions of the GPLRC microdisk are obtained by implementing Extended Hamilton’s principle. The results show that outer to inner ratios of the radius ([Formula: see text], ratios of length scale and nonlocal to thickness [Formula: see text] and [Formula: see text], and GPL weight fraction [Formula: see text] have a significant influence on the frequency and buckling characteristics of the GPLRC microdisk. Another necessary consequence is that by increasing the value of the [Formula: see text], the distribution of the displacement field extends from radial to tangent direction, especially in the lower mode numbers, this phenomenon appears much more remarkable. A useful suggestion of this research is that, for designing the GPLRC microdisk at the low value of the [Formula: see text], more attention should be paid to the [Formula: see text] and [Formula: see text], simultaneously.

Free vibrational and bending behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular and annular plate with various boundary conditions is studied using the differential quadrature method (DQM). The weight fraction differs gradually across the thickness direction. Effective elasticity modulus of the nanocomposite has been estimated by the modified Halpin–Tsai model. Using equations of motion in the framework of the elasticity theory and constitutive relation, the state-space first-order differential equation along the thickness direction is derived. A semi-analytical solution is carried out based on the application of DQM along the radial direction and the state-space technique across the thickness of the plate. The present approach is validated by comparing the numerical results with those reported in the literature. Effect of graphene platelets (GPLs) weight fraction, different GPL distribution patterns, thickness-to-radius and outer-to-inner radius ratios and edge boundary conditions on the static and vibrational behavior of GPLs reinforced composite circular/annular plates are examined. The results implied that GPLs can improve the composite strength against different loading and GPLs could have an extraordinary reinforcing influence on the static and vibrational behavior of the circular/annular plates.

This paper aims at studying the vibrational behavior and dynamical stability of small-scale axially moving beams resting on the viscoelastic-Pasternak foundation in a hygro-thermal environment, according to a nonlocal strain gradient Rayleigh beam model. The Galerkin procedure is applied to determine the eigenvalues of the dynamic system of equations together with the stability regions of the system. A comparison study of the proposed method is performed, first, against the available literature. Thus, we examine the effect of the rotary inertia, flexural stiffness, boundary conditions, scale parameters, foundation conditions, and environmental loads, on the vibrational frequencies and stability boundaries of the system. Based on the numerical results, an increased flexural stiffness and strain gradient parameter enhance the vibrational frequencies of the system. It is also demonstrated that the destructive effects of hygro-thermal conditions can be alleviated by a fine-tuning of the foundation characteristics. The outcomes of the present research can represent a useful benchmark for optimization design purposes of moving nanosystems in complex environmental conditions.