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Aims and Objective: The main objective of the kinetic investigation of the reaction between ethyl acetoacetate 1, ammoniumacetat 2, dimedone 3, and diverse substitutions of benzaldehyde 4-X, (X= H, NO2, CN, CF3, Cl, CH (CH3)2, CH3, OCH3, OCH3, and OH) for generating 4-substituted 1, 4-dihydropyridine derivatives (product 5) was to recognize the most realistic reaction mechanism. The layout of the reaction mechanism was studied kinetically via a UV-visible spectrophotometry approach. Materials and Methods: Among the various mechanisms, only mechanism1 (path1) involving 12 steps was recognized as a dominant mechanism (path1). Herein, the reactions between 1 and 2 (kobs= 814.04 M-1.min-1) and also between 3 and 4-H (kobs= 151.18 M-1.min-1) can be accepted as the first and second steps (step1 and step2) of the reaction mechanism, respectively. Amongst all steps, only step9 of the dominant mechanism (path1) comprised substituent groups (X) near the reaction center. Results and Discussion: Para electron-withdrawing or donating groups on the compound 4-X increased the rate of the reaction 4 times more or decreased 8.7 times less than the benzaldehyde alone. So, this step is sensitive for monitoring any small or huge changes in the reaction rate. Accordingly, step9 is the rate-determining step of the reaction mechanism (path1). Conclusion: The recent result is in agreement with the Hammett description of an excellent dual substituent factor (r = 0.990) and positive value of reaction constant (ρ= +0.9502), which confirms that both the resonance and inductive effects “altogether” contribute to the reaction center of step9 in the dominant mechanism (path1).

Experimental and numerical study regarding the uniaxial tensile test and the forming limit diagram are addressed in this paper for AL2024 with the face-centered cube structure. First, representation of a grain structure can be obtained directly by mapping metallographic observations via scanning electron microscopy approach. Artificial grain microstructures produced by Voronoi Tessellation method are employed in the model using VGRAIN software. By resorting to the finite element software (ABAQUS) capabilities, the constitutive equations of the crystal plasticity were utilized and implemented as a user subroutine material UMAT code. The hardening parameters were calibrated by a trial and error approach in order to fit experimental tensile results with the simulation. Then the effect of the changing grain size, the heterogeneity factor, and the grain aspect ratio were studied for a uniaxial tensile test to emphasize the importance of the microstudy behavior of grains in material behavior. Furthermore, the polycrystal plasticity grain distribution was employed in the Nakazima test in order to obtain the forming limit diagram. The crystal plasticity-driven forming limit diagram reveals more accurate strains, taking into account the involving the micromechanical features of the grains. An innovative approach is pursued in this study to discover the necking angle, both in tensile test or Nakazima samples, showing a good agreement with the experiment results.

Supramolecular carriers as a targeted drug delivery system have a significant role in managing the pharmacokinetics and pharmacodynamics of drugs. Therefore, in this project, we used cyclodextrin (CD) as a host molecule for tamoxifen (TMX) and methotrexate (MTX) to evaluate apoptosis mechanism and statistical patterns of release. The flow cytometry analysis showed that combination therapy by anticancer drugs was successful in apoptosis induction compared to free TMX and MTX. Also, real-time PCR and western blot analyses were performed to measure gene expression of Bak1, Bclx, and caspase-3 in estrogen and folate receptor-positive MCF-7 cell lines. All results confirmed that MNPs containing TMX and MTX can significantly increase Bak1/Bclx ratios plus the activity of caspase-3, while free MTX and free TMX showed no effects on triggering apoptosis after 24 h of exposure. According to results of pharmacokinetic studies onto TMX and MTX release, it is revealed that both models that consist of Sahlin-Peppas and Ritger-Peppas create the good fitting curves more than other statistical patterns at both low and high temperatures (37°C and 42°C). For this reason, activation parameters (ΔH‡, ΔS‡, and ΔG‡) were calculated to estimate the favorable model. The lower energy barrier indicates that the Sahlin-Peppas is the favorable model with both diffusion and relaxation process. Therefore, combination therapy by two anticancer drugs, TMX and MTX, utilizing cyclodextrin-based host–guest supramolecular magnetic nanoparticles (CD-MNPs) provided new results for induction of apoptosis and pharmacokinetic model.

This article is the first attempt to employ deep learning to estimate the frequency performance of the rotating multi-layer nanodisks. 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 current nanostructure is modeled as a nanodisk on the viscoelastic substrate. Due to rotation, the centrifugal and Coriolis effects are considered. Hamilton’s principle and generalized differential quadrature method (GDQM) are presented for obtaining and solving the governing equations of the high-speed rotating nanodisk on a viscoelastic substrate. The outcomes show that the number of layers viscoelastic foundation, angular velocity speed, angle of ply, nonlocal, and length-scale parameters have a considerable impact on the amplitude and vibration behavior of a laminated rotating cantilevered nanodisk. As an applicable result in related industries, in the initial value of radius ratio, damping of the foundation does not have any effect on the dynamics of the system, but when the outer radius is bigger enough, the effect of damping parameter on the frequency of the laminated nanostructure will be bold sharply.

In this study, frequency simulation and critical angular velocity of a size-dependent laminated rotary microsystem using modified couple stress theory (MCST) as the higher-order elasticity model is undertaken. The centrifugal and Coriolis impacts due to the spinning are taken into account. The size-dependent thick annular microsystem's computational formulation, non-classical governing equations, and corresponding boundary conditions are obtained by using the higher-order stress tensors and symmetric rotation gradient to the strain energy. By using a single material length scale factor, the most recent non-classical approach captures the size-dependency in the annular laminated microsystem. Furthermore, by ignoring the length scale element of the material, an annular microsystem’s mathematical formulation based on the classical model can be retrieved from the current model. Ultimately, the governing equations, which are non-classic, have been solved for various boundary conditions (BCs) using the two-dimensional generalized differential quadrature (2D-GDQ) approach. The effects of Young's modulus ratio the, rotating speed, radius ratio, laminated layers’ number, length scale element, and laminated types on the critical rotating speed and frequency responses of the laminated spinning microdisk are then investigated using MCST. The outcomes reveal that the negative influence from spinning velocity on the system’s dynamics is more significant than the negative influence from radius ratio, and the mentioned problem is more considerable for the vertical laminated pattern. Finally, the critical radius ratio and rotating speed increase by changing the laminated pattern from vertical to longitudinal.

In the current paper, vibrational and critical circular speed characteristics of a functionally graded (FG) rotary microdisk is examined considering a continuum nonlocal model called modified couple stress (MCS) model, for the first time in the literature. The generalized differential quadrature (GDQ) approach and variational method are used for deriving and solving the non-classical final relations. The FG size-dependent micro-sized disk’s final relations and corresponding boundary conditions (BCs) are achieved on the basis of the higher-order shear deformation (HSD) model. Then, a parametric analysis has been conducted to analyze the influences of the length scale factor, circumferential, radius ratio and radial mode number, FG material’s configuration, and BCs on the FG micro-scaled disk’s frequency by taking into account the MCST. The outcomes reveal that, at the initial value of the FG index (β), the negative impact from rotating speed on the dynamic stability of the system becomes bold. Furthermore, at the β factor’s lower amount and spinning velocity’s higher amount, there is instability in the responses of the system. Additionally, it is indicated that the negative effect from radius ratio on the frequency responses of the rotary FG microdisk becomes considerable at the length scale factor’s higher amount.

In this article, critical angular velocity, critical velocity of fluid flow and vibration control analysis of a rotating multi-hybrid nanocomposite reinforced (MHCR) cylindrical microshell covered with a piezoelectric layer as sensor and actuator (PLSA) are presented. The current non-classical model is capable of capturing the size dependency in the microshells 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. This structure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. In addition, the current structure rotates around its axial direction. The Coriolis and centrifugal effects due to the rotation are considered. For semi-numerical method, the strains and stresses can be determined through via the first-order shear deformable theory (FSDT). For accessing to various mass densities, thermal expansion as well as Poisson ratio, the rule of mixture is applied, although a modified Halpin–Tsai theory is used for obtaining the module of elasticity. The external voltage is applied to the sensor layer, while a Proportional-Derivative (PD) controller has been utilized for controlling output of sensors. The boundary conditions are derived through governing equations of the MHCR cylindrical microshell using energy method known as Hamilton’s principle and finally are solved using generalized differential quadrature method (GDQM). The outcomes show that the angular velocity, velocity of fluid flow, external force, PD controller, external voltage and MHC’s weight fraction have a considerable impact on the amplitude, and vibration behavior of a spinning MHCR cylindrical shell conveying fluid flow.

Honeycomb structures have the geometry of the lattice network to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multiscale hybrid nanocomposite (MHC) face sheets rested on an elastic foundation. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the effects of the orientation of fibers ( $$\theta_{{\text{f}}} /\pi$$ ) in the epoxy matrix, Winkler–Pasternak constants ( $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ ), thickness to length ratio of the honeycomb network ( $$t_{{\text{h}}} /l_{{\text{h}}}$$ ), the weight fraction of CNTs, value fraction of carbon fibers, angle of honeycomb networks, and inner to outer radius ratio on the frequency of the sandwich disk. The results show that it is true that the roles of $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ are the same as an enhancement, but the impact of $$K_{{\text{w}}}$$ could be much more considerable than the effect of $$K_{{\text{p}}}$$ on the stability of the structure. Additionally, when the angle of the fibers is close to the horizon, the frequency of the system improves.

This composition investigates the frequency analysis of sandwich imperfect viscoelastic disks with graphene nano-platelets (GPLs)-reinforced viscoelastic composite (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum because of its high stiffness and low weight. The modified Halpin–Tsai model and rule of the mixture have been utilized to provide the effective material constant of the composite layers. Through employing Hamilton’s principle, the governing equations of the structure are accordingly discerned and resolved by utilizing the Generalized Differential Quadrature Method (GDQM). Throughout this investigation, viscoelastic properties have been modeled in accordance with Kelvin–Voigt viscoelasticity. The deflection as the function of time is capable of being resolved through employing the fourth-order Runge–Kutta numerical method. Afterwards, a parametric study is conducted to discern the effects of the FG patterns, outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the GPLs, the weight fraction of GPLs, FG face sheet thickness ratio, the thickness of honeycomb core to inner radius ratio, tensile, imperfect coefficient, and in-plane force on the frequency of the sandwich viscoelastic disk with honeycomb core and FG-GPLRVC face sheet.

In this study, the vibrational characteristics of a rotating multi-hybrid nanocomposite reinforced (MHCR) cantilevered disk (MHCRCD) are presented. The centrifugal and Coriolis effects due to the r...

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...

Mechanical systems especially annular disks have many applications in different fields such as engineering, agriculture, and medicine. In this regard, the large amplitude vibrations of multi-scale hybrid nanocomposite annular system (MHCAS) under hygrothermal environment and subjected to mechanical loading. Also, the structure is covered with elastic foundation. The matrix material is reinforced with carbon nanotubes or carbon fibers at the nano- or macro-scale, respectively. The displacement strain of nonlinear vibration of the multi-scale laminated disk via thirdorder shear deformation theory and using von Karman nonlinear shell theory is obtained. Hamilton's principle is employed to establish the governing equations of motion, which is solved by the generalized differential quadrature method and perturbation method. Finally, the results show that increasing the value of the DH and h parameters and the rigidity of the boundary conditions lead to increase in the frequency of the structure. Besides, when the value of the nonlinearity parameter (c) is positive and negative, the dynamic behavior of the system tends to have hardening and softening behaviors, respectively, and could not be seen any effects from c parameter on the maximum amplitudes of resonant vibration of the MHCAS. The last but not the list by increasing the rigidity of the structure, the system can be susceptible to have unstable responses. The presented outputs can be used in the structural health monitoring.

This research presents bending responses of FG-GPLRC plates based upon higher order shear deformation theory (HSDT) for various sets of boundary conditions. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the differential quadrature method (DQM). Afterward, a parametric study is done to present the effects of three kinds of FG patterns, weight fraction of the GPLs, radius ratio, and thickness to inner radius ratio on the bending characteristics of the FG-GPLRC disk. Numerical results reveal that in the initial value of the $$Zt/h$$ , using more GPLs for reinforcing the structure provides an increase in the normal stresses but this matter is inverse for the higher value of the $$Zt/h$$ . The results show that considering the smaller radius ratio is a reason for boosting the shear stresses of the structure for each $$Zt/h$$ . Another consequence is that for the negative value of $$Zt/h$$ , it is true that by increasing $$h/{R}_{i}$$ , the normal stresses increases but if there is positive value for $$Zt/h$$ , the radial and circumferential stresses fall down by having an increase in the $$h/{R}_{i}$$ .

In this article, amplitude, and vibrational characteristics of a rotating fiber metal laminated microdisk are presented. The current microstructure is modeled as a flexible microdisk surrounded by ...

Wave propagation simulation in a multi-hybrid nanocomposite (MHC)-reinforced doubly curved open shell covered with piezoelectric actuator is examined for the first time. The third-order shear deformation theory (third-order SDT) is applied to formulate the stress–strain relations. Rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constants of the MHC-reinforced open shell. By employing Hamilton’s principle, the governing equations of the structure are derived. Via the compatibility rule, the bonding between the smart layer and sandwich open shell is modeled. Also, with the aid of Maxwell's equation, the mechanics of the piezoelectric layer are formulated. Afterward, a parametric study is carried out to investigate the effects of the CNTs’ weight fraction, various FG face sheet patterns, small radius to total thickness ratio, the thickness of the smart layer, externally applied voltage, and carbon fiber angle on the phase velocity of the MHC-reinforced open shell. Another necessary consequence is that as the externally applied voltage to the piezoelectric layer of the smart open shell increases, there will be seen an enhancement on the phase velocity or wave response of the system and without a doubt this issue is much more substantial at the lower wave number. It is also observed that when the applied voltage is more than zero, we can find a range for the fiber angle that these values are the critical fiber angle and this critical range will expand by increasing the external electrical load. The useful suggestion of this study is that for designing the structure, we should attention to the FG pattern and higher value of the wavenumber, simultaneously. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

For the first time, the nonlinear forced vibration analysis of graphene nanoplatelets reinforced composite (GPLRC) annular plate under hygro-thermal environment and subjected to mechanical loading ...

The analysis of the wave propagation behavior of a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets is carried out in the framework of the higher-order shear deformation theory (HSDT). In order to take into account the viscoelastic influence, the Kelvin-Voight model is presented. In this paper, the constituent material of the core is made of an epoxy matrix which is reinforced by both macro- and nano-size reinforcements, namely carbon fiber (CF) and carbon nanotube (CNT). The effective material properties like Young's modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin–Tsai model. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived. The detailed parametric study is conducted, focusing on the combined effects of the viscoelastic foundation, CNT' weight fraction, core to total thickness ratio, small radius to total thickness ratio, and carbon fiber angle on the wave propagation behavior of sandwich structure. The results show that as well as increasing the phase velocity of the sandwich structure by increasing the wave number, this influence will be much more effective by increasing the damping factor. It is also observed that there is a critical value for the viscoelastic foundation that the relation between wave number and phase velocity will change from direct to indirect. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

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 the current report, characteristics of the propagated wave in a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets are investigated. The higher-order shear deformable theory (HSDT) is applied to formulate the stresses and strains. Rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the multi-hybrid nanocomposite face sheets of the sandwich panel. By employing Hamilton’s principle, the governing equations of the structure are derived. Via the compatibility rule, the bonding between the composite layers and a soft core is modeled. Afterward, a parametric study is carried out to investigate the effects of the CNTs' weight fraction, core to total thickness ratio, various FG face sheet patterns, small radius to total thickness ratio, and carbon fiber angel on the phase velocity of the FML panel. The results show that the sensitivity of the phase velocity of the FML panel to the $${W}_{\rm{CNT}}$$ and different FG face sheet patterns can decrease when we consider the core of the panel more much thicker. It is also observed that the effects of fiber angel and core to total thickness ratio on the phase velocity of the FML panel are hardly dependent on the wavenumber. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring.

In this article, thermal buckling and resonance frequency of a composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) under bi-directional thermal loading are presented. The temperature-dependent material properties of piece-wise GNP-reinforced composites (GNPRC) are assumed to be graded in the thickness direction of a cylindrical nanoshell. Also, Halphin-Tsai nanomechanical model is used to surmise the effective material properties of each layer. The size-dependent GNPRC nanoshell is analyzed using modified couple stress parameter (FMCS). For the first time, in the presented study show that bi-directional thermal buckling occurs if the percent of relative frequency change tends to 30%. The novelty of the current study is in considering the effects of bi-directional thermal loading in addition of FMCS on relative frequency, resonance frequencies, thermal buckling, and dynamic deflection of the GNPRC nanoshell. The governing equations and boundary conditions are developed using Hamilton’s principle and solved with the aid of analytical method. The results show that, various bi-directionasl thermal loading and other geometrical and mechanical properties have important role on resonance frequency, relative frequency change, thermal buckling, and dynamic deflection of the GNPRC cylindrical nanoshell. The results of the current study are useful suggestions for design of materials science, micro-mechanical and nano-mechanical systems such as microactuators and microsensors.

In this article, frequency analysis of multi-sized hybrid nano-composites (MHC) disk (MHCD) resting on elastic media and located in an environment with gradually changed temperature feature is pres...

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.

Due to wide-ranging applications of piezoelectric nanostructures as the next generation of smart devices, this article analyzes size-dependent buckling and free vibration performance of fluid-conve...

As the most rigid cytoskeletal filaments, tubulin-labeled microtubules bear compressive forces in living cells, balancing the tensile forces within the cytoskeleton to maintain the cell shape. The current structure is often under several environmental conditions as well as various dynamic or static loads that can decrease the stability of the viscoelastic tubulin-labeled microtubules. For this issue, the dynamic stability analysis of size-dependent viscoelastic tubulin-labeled microtubules using modified strain gradient theory by considering the exact three-length scale parameter. Viscoelastic properties are modeled using Kelvin-Voight model to study the time-dependent tubulin-labeled microtubules structure. By applying energy methods (known as Hamilton's principle), the motion equations of the tubulin-labeled microtubules are developed. The dynamic equations are based on first-order shear deformation theory (FSDT), and generalized differential quadrature and fourth-order Runge-Kutta methods are employed to find the model for the natural frequencies. The novelty of the current study is to consider the effects of viscoelastic properties, and exact values of size-dependent parameters on dynamic behaviors of the tubulin-labeled microtubules. Considering three-length scale parameters (

This is the first research on the frequency analysis of a graphene nanoplatelet composite circular microplate in the framework of a numerical-based generalized differential quadrature method. Stresses and strains are obtained using the higher order shear deformation theory. The microstructure is surrounded by a viscoelastic foundation. Rule of the mixture is used to obtain varying mass density and Poisson’s ratio, whereas the module of elasticity is computed by a modified Halpin–Tsai model. Governing equations and boundary conditions of the graphene nanoplatelet composite circular microplate are obtained by implementing Hamilton’s principle. The results show that outer to inner radius ratio [Formula: see text], ratios of length scale and nonlocal to thickness ( l/ h and [Formula: see text]), and graphene nanoplatelet weight fraction [Formula: see text] have significant influence on the frequency characteristics of the graphene nanoplatelet composite circular microplate. Another necessary consequence is that by increasing the value of [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 graphene nanoplatelet composite circular microplate at a low value of [Formula: see text], [Formula: see text] and [Formula: see text] should be given more attention, simultaneously. An interesting result which has come down from the article is that the effect of [Formula: see text] on the dimensionless frequency of the structure is really dependent on the value of C d.

The stability analysis of cantilevered curved microtubules in axons regarding various size elements and using the generalized differential quadrature method for solving equations is reported. The impacts of covering MAP Tau proteins along with cytoplasm are taken into account as the elastic medium. Curved cylindrical nanoshell considering thick wall is used to model the microtubules. The factor of length scale (l/R = 0.2) used in modified couple stress theory would result in more accuracy when it comes to comparison with experiments, while alternative theories presented in this paper provide less precise outcomes. Due to the reported precise results, at the lower value of the time-dependent viscoelastic factor ( $${\tau }_{s})$$ by rising the size-dependent factor, the frequency response of the cantilever microtubule increases and this relation between the size-dependent parameter and the structure’s natural frequency is changed from direct to indirect for the higher amount of the time-based viscoelastic factor that scientists should attend to this matter when it comes to the microtubule. Furthermore, physical neighboring situations in a cell will be prominent in microtubules’ dynamic stability responses, such as membrane and cell-matrix. Since microtubules are likely to be applied as biosensors, this feature could be employed to disclose virulent tumors.

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...

Over the last few years, some novel researches in the field of medical science made a tendency to have a therapy without any complications or side-effects of the disease with the aid of prognosis about the behaviors of the substructure living biological cell. Regarding this issue, nonlinear frequency characteristics of substructure living biological cell in axons with attention to different size effect parameters based on generalized differential quadrature method is presented. Supporting the effects of surrounding cytoplasm and MAP Tau proteins are considered as nonlinear elastic foundation. The Substructure living biological cell are modeled as a moderately thick curved cylindrical nanoshell. The displacement- strain of nonlinearity via Von Karman nonlinear shell theory is obtained. Extended Hamilton's principle is used for obtaining nonlinear equations of the living biological cells and finally, GDQM and PA are presented to obtain large amplitude and nonlinear frequency information of the substructure living biological cell. Based on presented numerical results, increasing the nonlinear MAP tau protein parameter causes to improve the hardening behavior and increase the maximum amplitudes of resonant vibration of the microtubule. The crucial consequence is when the fixed boundary conditions in the microstructure switch to cantilevered, the living part of the cells could manage to have irrational feedback at the broad field of the excitation frequency. The current study has been made into the influences of the NSG parameters, geometrical and physical parameters on the instability of the curved microtubule employing continuum mechanics model.Communicated by Ramaswamy H. Sarma.