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The current investigation examines the vibrational properties of porous truncated conical structures made from a composite material consisting of polyvinylidene fluoride (PVDF) reinforced with Terfenol-D particles. The effective properties of the magneto-electro-elastic composite were determined using the Eshelby–Mori–Tanaka model. The governing equation of the system is obtained by applying the principles of minimal potential energy and Hamilton's principle to the first-order shear deformation theory. The equations are solved utilizing the generalized differential quadrature technique. This study aims to examine the interconnections among the volume percentage, vertex angle, shell length, boundary conditions, and porosity of Terfenol-D. Moreover, to validate the results, a comprehensive analysis was performed by comparing them with the existing body of literature, resulting in a favorable and accurate agreement. The results demonstrate a consistent decrease in the linear natural frequency as the vertex angle gradually increases. The findings derived from this study have the potential to serve as a reference point for future analyses. [ABSTRACT FROM AUTHOR]

This study aims to examine the dynamic characteristics of a sandwich composite nanoplate when exposed to a nano damper–spring–mass stimulator. The composite structure consists of a core layer composed of magnetostrictive material, accompanied by upper and lower facesheets made of functionally graded material (FGM). Moreover, the proposed framework is designed to be based on a visco-Pasternak medium. The governing equations of nanoplates are derived using the higher-order shear deformation theory (HSDT) and Hamilton's principle. In the end, Navier's solution is utilized to solve partial differential equations, while the Laplace transform is employed for solving ordinary differential equations. Subsequently, a thorough investigation is conducted with a primary focus on examining the impact of different parameters on the dynamic response of the continuous system. The findings indicate that the incorporation of the damper–spring–mass system into the nanoplate has a notable impact on its natural frequency. The results can serve as reference points for the effective development of nanosensors, nanoresonators, drug delivery systems, and biosensors. [ABSTRACT FROM AUTHOR]

The main goal of this study is to examine the buckling properties of a composite material that combines graphene-origami-enabled features with magnetostrictive facesheets. The nonlocal theory, as developed by Eringen, has been used for the purpose of quantifying the small-scale parameter. However, the system being presented is based on the theoretical framework established by Winkler and Pasternak, which incorporates the analysis of a deformable medium. The use of a theoretical framework referred to as higher-order sinusoidal shear deformation theory has been utilized to formulate the governing equation. The governing equation is then solved via the Galerkin solution approach, while considering various boundary conditions. In order to assess the precision and effectiveness of the present inquiry, the findings are juxtaposed with the prevailing scholarly publications in the academic literature. Furthermore, this study aims to examine the impact of several factors, including as the weight fraction, hydrogen atom coverage, aspect ratio, and temperature, on the critical buckling load. The findings of the present investigation indicate that an increase in the weight fraction of graphene-origami-enabled material leads to an increase in the buckling load. The main aim of this study is to improve the understanding and predictive capability of engineers and designers about the phenomenon of buckling response. The aforementioned data have the potential to provide advantages in the advancement of nanoscale systems, including highly sought-after technologies such as sensors and actuators. [ABSTRACT FROM AUTHOR]

The main aim of this study is to examine the buckling behavior of a composite material that has both magnetostrictive capabilities and functionally graded facesheets. The effective material parameters of the functionally graded layer are determined using the power-law model. Eringen's nonlocal theory has been used for the quantification of the small-scale parameter. In contrast, the suggested system is based on the theoretical framework established by Winkler and Pasternak, which incorporates the analysis of an elastic medium. The use of higher-order sinusoidal shear deformation theory has been employed to derive the governing equation. This governing equation is then solved analytically using the Galerkin solution method, considering various boundary conditions. In order to assess the precision and effectiveness of the ongoing inquiry, the findings are juxtaposed with the existing literature articles. Furthermore, this study examines the impact of many factors, including aspect ratio, velocity feedback gain, and foundation, on the critical buckling load. The findings of the present research indicate that there is a positive correlation between the porosity volume parameter and the buckling load of the structure. The current study aims to provide engineers and designers with a better understanding and predictive capability about buckling response. This knowledge may be advantageous in the design of nanoscale systems, including highly sought-after technologies like as sensors and actuators. [ABSTRACT FROM AUTHOR]

The main objective of this work is to examine the vibrational characteristics of a nanobeam exhibiting auxetic activity, achieved by the incorporation of a magnetostrictive material called Terfenol-D. The nanobeam is postulated to include three distinct layers, whereby the central layer is comprised of a magnetostrictive substance, while the outside layers are formed of auxetic material. On the other hand, the use of higher-order parabolic shear deformation beam theory is utilized to obtain the kinematic relations. Moreover, Eringen's nonlocal theory is used to include the impact of small-scale phenomena. The governing equations are derived by the application of Hamilton's principle and then solved using analytical techniques. This work presents a thorough analysis and elucidation of the influence of several parameters, such as auxetic inclination angle, auxetic rib length, and feedback gain, on the investigated system. Based on current research, evidence suggests that adding auxetic facesheets to magnetostrictive beam results in decreasing dimensionless natural frequency. In order to establish the accuracy and dependability of the present study, a comparison examination has been undertaken to juxtapose our results with the existing body of scholarly literature. The results obtained from the present study have the potential to provide a valuable contribution to the advancement and improved understanding of nano-systems, namely nano-sensors and nano-actuators. Furthermore, the conclusions acquired from this study might potentially serve as a fundamental framework for future research. [ABSTRACT FROM AUTHOR]

The objective of this research is to manipulate the vibrational characteristics of a graphene-origami auxetic beam via the use of magnetostrictive materials. The use of higher-order parabolic shear deformation beam theory is utilized to determine the kinematic relations. Moreover, Eringen's nonlocal theory is used to include the impact of small-scale phenomena. The governing equations are derived by the application of Hamilton's principle and then solved using analytical techniques. The results indicate that the integration of a graphene-origami auxetic core into a magnetostrictive beam results in an augmentation of the dimensionless natural frequency. Moreover, the results obtained might potentially serve as a preliminary stage for future research endeavors. In order to establish the accuracy and dependability of the present study, a comparison examination has been undertaken to juxtapose our results with the existing body of scholarly literature. The results of the present study have the potential to further the understanding and advancement of nanosystems, namely nanosensors and nanoactuators. Moreover, the results might perhaps serve as a preliminary stage for future inquiries. [ABSTRACT FROM AUTHOR]

This article analyzes the nonlinear vibrations of porous truncated conical polyvinylidene fluoride (PVDF) reinforced with Terfenol-D particles. The effective properties of the magneto-electro-elastic composite have been obtained using the Eshelby–Mori–Tanaka model. Also, the porosity in the composite is considered uniform. The governing equation of the system is derived based on the von Karman theory of nonlinear strains and the theory of first-order shear deformation by applying the principle of minimum energy potential and Hamilton's principle. These equations are solved using the generalized differential quadrature method. The effect of porosity, vertex angle, shell length, boundary conditions, and volume fraction of Terfenol-D will be discussed. Also, for validation, the obtained results were compared with those found in the literature, which was a good answer, along with the accuracy. Results show that the nonlinear to linear natural frequency ratio has a decreasing trend at the lower vertex angle. The present findings can serve as a reference point for subsequent assessments. [ABSTRACT FROM AUTHOR]

The functionalization of graphene aims at altering its material properties to encourage its use in various new applications. In the present research, an investigation on a functionalized graphene oxide (FGO) reinforced nanocomposite (NC) plate is performed once the plate is subjected to thermal loading. The reinforcement of the plate is done with multiple functionally graded (FG) distributions through the thickness, specifically, uniform (U), X, V, and O. This action is for the purpose of finding the most effective distributional strategy for functionalized graphene oxide with ameliorated vibrational characteristics. Also, the Winkler–Pasternak elastic substrate serves as the support for the plate construction. To describe the mechanical properties of the FG nanocomposite plate, the Halpin–Tsai model is employed and a more advanced higher order shear deformation model is used to take the impact of shear deformation into account. Next, Hamilton's principle is utilized to derive the governing equations of the plate structure. These governing equations are then solved for a simply supported functionalized graphene oxide-reinforced nanocomposite plate. Ensuing, several parametric studies are presented to better delineate the impact of numerous variants including FGO's weight fraction, distribution patterns, temperature raise, elastic substrate coefficients, and geometrical properties on the nanocomposite plates' fundamental frequency. Results of our study indicate that raising the temperature and aspect ratio can decrease the natural frequency of FGO-reinforced NC plates, while increase in the FGO's weight fraction and elastic foundation does the opposite. [ABSTRACT FROM AUTHOR]

The primary focus of this study is to analyze the vibrational properties of a nanobeam with a porous structure, which is composed of a functionally graded material. Additionally, the nanobeam comprises a magnetostrictive substance known as Terfenol-D. The nanobeam is postulated to include three distinct layers, whereby the central layer is comprised of a magnetostrictive material, while the outside layers are built of functionally graded material. On the other hand, the use of higher-order parabolic shear deformation beam theory is utilized to get the kinematic relations. Moreover, Eringen's nonlocal theory is used to include the impact of small-scale phenomena. The governing equations are derived by the application of Hamilton's principle and then solved using analytical techniques. This study presents a thorough examination and elucidation of the influence exerted by several elements, such as aspect ratio, feedback gain, and gradient index, on the system being studied. Based on extant research, empirical evidence indicates that increasing the feedback gain results in a decrease in the natural frequencies. In order to establish the accuracy and dependability of our present study, we have undertaken a comparison examination of our results in relation to the existing body of the literature. The results of the present study have the potential to advance the understanding and progress in the field of nano-systems, namely nano-sensors and nano-actuators. [ABSTRACT FROM AUTHOR]

This paper investigates the buckling problem of a multi-scale hybrid nanocomposite shell for the first time while the cylinder is supposed to be rested on an elastic substrate. The constituent material is considered to be made from a polymeric matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers' agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing the Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube-reinforced (CNTR) nanocomposite are coupled with those of carbon fibers (CFs) within the framework of a modified rule of the mixture. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the static form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin's method to obtain the buckling load of the structure for both simply supported and clamped boundary conditions. The results indicate on the fact that if the agglomeration effects are ignored, the designed nanocomposite system may fail under low static excitations. Also, it is better to avoid from the construction of a large number of small clusters to make the nanocomposite structure more powerful against buckling mode failure. [ABSTRACT FROM AUTHOR]

In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSDT) is implemented to take into account the influence of the shear deformation on the motion equations of the system. Then, the governing equations are achieved on the basis of the energy-based Hamilton's principle. Finally, the derived equations will be solved analytically for the purpose of extracting the natural frequency of the continuous system. A set of numerical examples are provided to cover the effects of various parameters on the wave dispersion characteristics of the plate. It can be declared that the hybrid nanocomposite system can achieve higher wave frequencies compared with other types of composite structures. Additionally, it is found that the selection of the lay-ups and length-to-diameter ratio plays a significant role in the determination of the sandwich plate's acoustic response. [ABSTRACT FROM AUTHOR]

Free oscillation analysis of shells consisted of multi-scale hybrid nanocomposites is carried out with regard to the destroying effect of the nanofillers' agglomeration on the system's dynamics. The equivalent material properties of the hybrid nanocomposite are obtained in the framework of a bi-level micromechanical procedure. The influence of existence of agglomerated carbon nanotubes (CNTs) on the stiffness of the nanocomposite is included with the aid of the Eshelby-Mori-Tanaka method. Thereafter, the first-order shear deformation theory (FSDT) of the shells will be combined with the dynamic form of the principle of virtual work to reach the Euler-Lagrange equations of the problem. Next, the governing equations will be extracted from the Euler-Lagrange ones by using the constitutive equations of the nanocomposite. To obtain the natural frequencies of the system for shells with clamped and simply supported ends, the Galerkin's method is hired. The validity check reveals that the utilized methodology is powerful enough to predict the frequency behaviors of nanocomposite shells. According to the results, it can be inferred that the hybrid nanocomposite shells may be involved in resonance phenomenon in low-range frequencies if the impact of the CNTs' aggregation is neglected. Obviously, the volume fraction of the CNTs inside the inclusions plays a magnificent role in the determination of the system's dynamic behavior. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the wave propagation analysis of multi-scale hybrid nanocomposite plates by considering the influences of the aggregation of the nanoparticles. For the constituent materials of the plate, a polymeric matrix is supposed to have macro- and nano-reinforcements dispersed in it. The well-known micromechanical methods, such as Eshelby-Mori-Tanaka model and the rule of the mixture, are exerted to compute the effective material properties of the nanocomposite plate. Also, a refined higher-order shear deformation theory is implemented to obtain the motion relations. Besides, the governing equations are derived by employing the principle of Hamilton. Then, the analytic method is used to solve the obtained governing equations of structure and finally wave frequency and phase velocity are calculated. The effects of the various parameters on the variation of phase velocity and wave frequency of the multi-scale nanocomposite plates are examined. The presented results demonstrate that the mechanical response of the system can be decreased, while the nanotubes are covered by clusters. [ABSTRACT FROM AUTHOR]

This article aims to investigate buckling characteristics of a functionally graded magneto-electro-thermo-elastic nanoshell based on nonlocal strain gradient theory (NSGT). Accounting for nonlocal and strain gradient size-dependency, NSGT has two scale coefficients. The nanoshell is subjected to external electric, magnetic, mechanical, and thermal fields. The temperature distributions are considered as uniform and linear thorough the nanoshell thickness. All material properties including elastic, piezoelectric, and magnetic properties are defined based on a power-law distribution type. Seven coupled governing equations are derived for the nanoshell based on Hamilton's rule and then solved applying Galerkin's approach. The dependency of the buckling behavior of the nanoshell on applied thermal load, temperature distribution, electric voltage, magnetic potential, material gradient index, scale parameters, and shear deformation will be explored. [ABSTRACT FROM AUTHOR]

This paper describes the nonlinear vibration of a novel smart plate with an auxetic metamaterial core and piezoelectrically actuated multiscale hybrid nanocomposite porous layers (GPL/CF/PVDF) using Reddy's higher-order shear deformation theory (HSDT). Using the rule of mixture (ROM) and Halpin–Tsai model (HT), the current properties of electroelastic layers were determined. Smart plate equations are detected using Hamilton's principle, Maxwell's law, and von Karman nonlinearity terms. The generalized differential quadrature method (GDQM) is then employed to discretize the governing equations of a sandwich plate for various boundary conditions. In addition, the smart plate's nonlinear frequency ratio and nonlinear natural frequency are detected using the angle of auxetic cell, the electric voltage, and the graphene nanoplatelet weight fraction. In addition, the influence of the porosity constant, the thickness of the auxetic core, and the thickness of the smart graphene-reinforced hybrid nanocomposite layer on (ω nl / ω l) and ω nl were computed and presented in each figure. [ABSTRACT FROM AUTHOR]

In the present research, free vibration study of functionally graded (FG) nanobeams with graded nonlocality in thermal environments is performed according to the third-order shear deformation beam theory. The present nanobeam is subjected to uniform and nonlinear temperature distributions. Thermo-elastic coefficients and nonlocal parameter of the FG nanobeam are graded in the thickness direction according to power-law form. The scale coefficient is taken into consideration implementing nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of nonlocal Euler–Bernoulli and Timoshenko beam models, and it is revealed that the proposed modeling can accurately predict the vibration frequencies of the FG nanobeams. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio, and thermal loading in detail. The present study is associated to aerospace, mechanical, and nuclear engineering structures that are under thermal loads. [ABSTRACT FROM AUTHOR]

This paper proposes a four-variable shear deformation refined plate theory for free vibration analysis of embedded smart plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials. Magneto-electro-elastic properties of FG plate are supposed to vary through the thickness direction and are estimated through the modified power-law rule in which the porosities with even and uneven type are approximated. The governing differential equations and boundary conditions of embedded porous FG plate under magneto-electrical field are derived through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of embedded porous FG plate supposed to magneto-electrical field with various boundary condition. Influences of several important parameters such as material graduation exponent, porosity volume fraction, magnetic potential, electric voltage, various boundary conditions, elastic foundation parameters and plate side-to-thickness ratio on natural frequencies of embedded porous MEE-FG plate are investigated and discussed in detail. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates resting on elastic foundation. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases. [ABSTRACT FROM AUTHOR]

This article proposes a higher-order shear deformation beam theory for free vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in a thermal environment. The temperature-dependent material properties of functionally graded carbon nanotube-reinforced composite beams are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. The governing equations and boundary conditions are derived by using Hamilton's principle, and the Navier solution procedure is used to achieve the natural frequencies of the sandwich beam in a thermal environment. A parametric study is led to carry out the effects of carbon nanotube volume fractions, slenderness ratio, and core-to-face sheet thickness ratio on free vibration behavior of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Numerical results are also presented in order to compare the behavior of sandwich beams including uniformly distributed carbon nanotube-reinforced composite face sheets to those including functionally graded carbon nanotube-reinforced composite face sheets. [ABSTRACT FROM PUBLISHER]

In this article, the size-dependent and porosity-dependent vibrational behavior of magneto-electro-elastic functionally graded (MEE-FG) nanoscale beams on two-parameter elastic substrate is presented via a third-order shear deformation beam model. Porosity-dependent material coefficients of the nanobeam are compositionally graded throughout the thickness according to a modified power-law model. Incorporation of small size effect is carried out based on Eringen’s nonlocal elasticity theory. Through Hamilton’s principle, derivation of nonlocal governing equations is performed. After analytically solving these equations, the influences of porosity, elastic foundation, magnetic potential, applied voltage, scale coefficient, material gradation and slenderness ratio on the frequencies of the porous MEE-FG nanobeams are examined. [ABSTRACT FROM AUTHOR]

Buckling behavior of nonlocal Functionally Graded Piezoelectric (FGP) beams on elastic substrate via a higher order beam model is examined. The present beam model takes into consideration the shear deformation effects needless of any shear correction factor. Employing power-law function, the gradation of material properties of the beam is described. Incorporation of small scale parameter is carried out using nonlocal elasticity theory. Implementing an analytical approach which satisfies simply-supported boundary conditions, the governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. It is indicated that the buckling behavior of piezoelectric Nanobeams is significantly influenced by elastic foundation parameters, external voltage, scale parameter, power-law index and slenderness ratio. [ABSTRACT FROM AUTHOR]

In this article, an analytical model for the wave propagation analysis of inhomogeneous functionally graded (FG) nanobeam in thermal environment is developed based on nonlocal strain gradient theory, in which the stress accounts for not only the nonlocal elastic stress field but also the strain gradients stress field. The nanobeam is modeled through a higher order shear deformable refined beam theory which has a trigonometric shear stress function. The temperature field supposed to have a nonlinear distribution across the nanobeam thickness. Temperature-dependent material properties of nanobeams are spatially graded based on Mori–Tanaka model. The governing equations of the temperature-dependent functionally graded (FG) nanobeam are derived using the Hamilton’s principle. Numerical examples show that the characteristics of the wave propagation of FG nanobeam are influenced by various parameters such as nonlocality parameter, length scale parameter, gradient index, and temperature changes. [ABSTRACT FROM AUTHOR]

Free vibration analysis is presented for a simply supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third-order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher-order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design. [ABSTRACT FROM AUTHOR]

In this study, the thermal effect on the free vibration characteristics of embedded Single-walled carbon nanotubes (SWCNTs) based on the size-dependent Reddy higher order shear deformation beam theory subjected to in-plane thermal loading is investigated by presenting a Navier-type solution and employing a semi-analytical Differential transform method (DTM) for the first time. In addition, the exact nonlocal Reddy beam theory solution presented here should be useful to engineers designing nanoelectromechanical devices. The smallscale effect is considered based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle, and they are solved by applying DTM. Numerical results reveal that the proposed modeling and semi-analytical approach can provide more accurate frequency results of the SWCNTs compared to analytical results and some cases in the literature. The detailed mathematical derivations are presented, and numerical investigations are performed, whereas emphasis is placed on investigating the effect of several parameters such as small-scale effects, boundary conditions, mode number, thickness ratio, temperature change, and Winkler spring modulus on the natural frequencies of the SWCNTs in detail. The vibration behavior of SWCNTs is significantly influenced by these effects. Results indicate that the inclusion of size effect results in a decrease in nanobeam stiffness and leads to a decrease in natural frequency. Numerical results are presented to serve as benchmarks for future analyses of SWCNTs. [ABSTRACT FROM AUTHOR]

In this paper, free vibration and buckling analysis of functionally graded cylindrical shells subjected to combined static and periodic axial forces is presented considering the effect of transverse shear and rotary inertia. Material properties of functionally graded cylindrical shells are considered as temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results for silicon nitride-nickel cylindrical shells are presented based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on free vibration and buckling of functionally graded cylindrical shells subjected to combined static and periodic axial forces is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters. [ABSTRACT FROM AUTHOR]

This is the first research on the smart control and frequency analysis of a cylindrical sandwich nanoshell in the framework of the numerical-based generalized differential quadrature method (2D-GDQM). The current sandwich smart nanostructure is made of a honeycomb core and piezoelectric face sheets as sensor and actuator (PFSA). For modeling the size-dependent nanoshell, nonlocal stress-strain gradient theory (NSGT) is presented. Also, this nanostructure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. Also, the current structure rotates around its axial direction. The stresses and strains are obtained using the higher-order shear deformation theory (HSDT). The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. Governing equations and boundary conditions of the cylindrical sandwich nanoshell are obtained by implementing Hamilton's principle. The results show that the geometry of honeycomb core, PD controller, velocity of fluid flow, length to radius ratio (L/R), and applied voltage and have a significant influence on the frequency characteristics of a cylindrical sandwich nanoshell. Another important consequence is that applying the PD controller leads to an increase in the critical velocity of fluid flow in the smart nanostructure. [ABSTRACT FROM AUTHOR]