Buckling analysis of functionally graded sandwich cylindrical micro/nanoshells based on the couple stress theory

2017 ◽  
Vol 21 (3) ◽  
pp. 917-937 ◽  
Author(s):  
Hamid Zeighampour ◽  
Milad Shojaeian
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length

Buckling of functionally graded sandwich cylindrical microshell under axial load is investigated. For this purpose, Donnell shell theory as well as material length scale parameter as considered by the couple stress theory is used, and equations of motion of the functionally graded sandwich cylindrical microshell along with boundary conditions are developed using Hamilton’s principle. Finally, dimensionless critical buckling load is determined for three functionally graded sandwich cylindrical microshells using the Navier procedure. Results of the new model are compared with the classical theory. The results indicate that the rigidity of the functionally graded sandwich cylindrical microshell in the couple stress theory is higher than that in the classical theory, which leads to increased dimensionless critical buckling load. Besides, the effect of material length scale parameter on dimensionless critical buckling load of the functionally graded sandwich cylindrical microshell in different wavenumbers is considerable.

scholarly journals The vibration of nanobeam resting on elastic foundation using modified couple stress theory

2018 ◽  
Vol 12 (4) ◽  
pp. 221-225 ◽  
Author(s):  
Necla Togun ◽  
Süleyman M. Bağdatli
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length

In this paper, the vibration of nanobeams resting on the Winkler foundation is proposed using the modified couple stress theory. Hamilton’s principle is utilized to construct the governing equations. The size effect of the nanobeam cannot be captured by using classical Euler-Bernoulli beam theory, but the modified couple stress theory model can capture it because it includes material length scale parameter that a newly developed model has. Once the material length scale parameter is assumed to be zero, the classical Euler-Bernoulli beam theory equation is obtained. Multiple scale method is employed to obtain the result. Simply supported boundary condition is used to study natural frequencies. The influence of material length scale parameter and the Winkler elastic foundation parameter on the fundamental frequencies of the nanobeam is investigated and tabulated. Also, in the present study, Poisson’s ratio is taken as constant. Nanobeam resting on the Winkler foundation which is simply supported is analyzed to illustrate the size effects on the free vibration. Numerical results for the simply supported nanobeam indicate that the first fundamental frequency calculated by the presented model is higher than the classical one. Moreover, it is obtained that the size influence is more substantial for higher vibration modes. The results indicate that the significant importance of the size influences the analysis of nanobeams. The vibration of nanobeam exhibits a hardening spring behavior, and the newly developed models are the beams stiffer than according to the classical beam theory. Modified couple stress theory tends to be more helpful in describing the size-dependent mechanical properties of nanoelectromechanical systems (NEMS).

Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings

2017 ◽  
Vol 24 (15) ◽  
pp. 3471-3486 ◽  
Author(s):  
Mehdi Mohammadimehr ◽  
S Javad Atifeh ◽  
Borhan Rousta Navi
Keyword(s):  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Inner Radius ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length

In this article, stresses and free-vibration behaviors of annular circular piezoelectric nanocomposite plate reinforced by functionally graded single-walled boron nitride nanotubes (FG-SWBNNTs) embedded in an elastic foundation based on modified couple stress theory (MCST) are explored. The mechanical properties of FG-SWBNNT-reinforced nanocomposite plate are assumed to be graded in the direction of thickness and estimated through the micro-mechanical approach. The governing equations are obtained using the energy method. The natural frequencies and stresses of FG-SWBNNT-reinforced nanocomposite plate are computed using the differential quadrature method (DQM). An excellent agreement is observed between the obtained results and the results in the literature. Influences of the internal radius to the external radius, the thickness to the internal radius ratio, the material length scale parameter, the functionally graded parameter, temperature changes and elastic coefficients on the natural frequencies and stresses of the hollow circular nanocomposite plate are investigated. The results of this research show that the natural frequencies of the piezoelectric nanocomposite plate increase by increasing the material length scale parameter, the elastic foundation parameters, the ratio of the inner radius to the outer radius, the ratio of the thickness to the inner radius, and decreasing the power index and temperature change. The radial stress of the nanocomposite plate varies proportionally to its mode shape. The results can be employed to design smart structures in micro-electro-mechanical systems (MEMS).

Vibration and thermal buckling analyses of three-layered centrosymmetric piezoelectric microplates based on the modified consistent couple stress theory

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1253-1265
Author(s):  
Fatemeh Abbaspour ◽  
Hadi Arvin
Keyword(s):  
Forced Vibration ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Open Circuit ◽  
Thermal Buckling ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Proposed Modification ◽  
Material Length Scale ◽  
Material Length

In this study, free and forced vibration investigations and thermal buckling analysis of three-layered centrosymmetric piezoelectric microplates are examined. To model the size effects, the size-dependent consistent couple stress theory is used. To be compatible with the modified coupled stress theory, a modification is proposed to apply to the consistent couple stress theory. Resorting to the Navier’s approach, the governing equations are treated in the case of simply supported boundary conditions to extract the free and forced vibration outcomes and the thermal buckling numerical results. The verifications demonstrate the effectiveness of the proposed modification. The effects of the material length scale parameter and the flexoelectricity coefficient on the findings are investigated. Moreover, the closed- and open-circuit condition impacts on the free and forced vibration and the thermal buckling analyses are studied.

Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST

2017 ◽  
Vol 22 (1) ◽  
pp. 55-86 ◽  
Author(s):  
Mohammad Arefi ◽  
Masoud Kiani ◽  
Ashraf M Zenkour
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length ◽  
Exponentially Graded

The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.

scholarly journals A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

2019 ◽  
Vol 40 (12) ◽  
pp. 1695-1722 ◽  
Author(s):  
Lu Lu ◽  
Li Zhu ◽  
Xingming Guo ◽  
Jianzhong Zhao ◽  
Guanzhong Liu
Keyword(s):  
Strain Gradient ◽  
Scale Parameter ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Length Scale ◽  
Proposed Model ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length ◽  
Nonlocal Strain Gradient

AbstractIn this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

A NONLOCAL CURVED BEAM MODEL BASED ON A MODIFIED COUPLE STRESS THEORY

2011 ◽  
Vol 11 (03) ◽  
pp. 495-512 ◽  
Author(s):  
Y. P. LIU ◽  
J. N. REDDY
Keyword(s):  
Couple Stress Theory ◽  
Classical Model ◽  
Modified Couple Stress Theory ◽  
Curved Beam ◽  
Beam Model ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length

A nonlocal Timoshenko curved beam model is developed using a modified couple stress theory and Hamilton's principle. The model contains a material length scale parameter that can capture the size effect, unlike the classical Timoshenko beam theory. Both bending and axial deformations are considered, and the Poisson effect is incorporated in the model. The newly developed nonlocal model recovers the classical model when the material length scale parameter and Poisson's ratio are both taken to be zero and the straight beam model when the radius of curvature is set to infinity. In addition, the nonlocal Bernoulli–Euler curved beam model can be realized when the normal cross-section assumption is restated. To illustrate the new model, the static bending and free vibration problems of a simply supported curved beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko curved beam model. Also, the differences in both the deflection and rotation predicted by the current and classical Timoshenko model are very large when the beam thickness is small, but they diminish with the increase of the beam height. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the nonlocal model is higher than that by the classical model, and the difference between them is significantly large only for very thin beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally.

scholarly journals Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

2020 ◽  
Vol 64 (2) ◽  
pp. 97-108
Author(s):  
Mehdi Alimoradzadeh ◽  
Mehdi Salehi ◽  
Sattar Mohammadi Esfarjani
Keyword(s):  
Differential Equation ◽  
Forced Vibration ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Length Scale ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

Free Vibration of Edge Cracked Functionally Graded Microscale Beams Based on the Modified Couple Stress Theory

2017 ◽  
Vol 17 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Cracked Beam ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, the free vibration analysis of edge cracked cantilever microscale beams composed of functionally graded material (FGM) is investigated based on the modified couple stress theory (MCST). The material properties of the beam are assumed to change in the height direction according to the exponential distribution. The cracked beam is modeled as a modification of the classical cracked-beam theory consisting of two sub-beams connected by a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces to the classical one when the length scale parameter is zero. The problem considered is investigated using the Euler–Bernoulli beam theory by the finite element method. The system of equations of motion is derived by Lagrange’s equations. To verify the accuracy of the present formulation and results, the frequencies obtained are compared with the results available in the literature, for which good agreement is observed. Numerical results are presented to investigate the effect of crack position, beam length, length scale parameter, crack depth, and material distribution on the natural frequencies of the edge cracked FG microbeam. Also, the difference between the classical beam theory (CBT) and MCST is investigated for the vibration characteristics of the beam of concern. It is believed that the results obtained herein serve as a useful reference for research of similar nature.

scholarly journals Fluid-Induced Nonlinear Vibration of a Cantilevered Microtube with Symmetric Motion Constraints

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yong Guo
Keyword(s):  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Critical Flow Velocity ◽  
Stress Theory ◽  
Motion Constraints ◽  
Material Length Scale Parameter ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
The Galerkin Method ◽  
Material Length

This paper investigates the dynamic behavior of a cantilevered microtube conveying fluid, undergoing large motions and subjected to motion-limiting constraints. Based on the modified couple stress theory and the von Kármán relationship, the strain energy of the microtube can be deduced and then the governing equation of motion is derived by using the Hamilton principle. The Galerkin method is applied to produce a set of ordinary differential equations. The effect of the internal material length scale parameter on the critical flow velocity is investigated. By using the projection method, the Hopf bifurcation is demonstrated. The results show that size effect on the vibration properties is significant.

Sign in / Sign up

Export Citation Format

Share Document