Table of Content

01 July 2016, Volume 37 Issue 7

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Articles

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

M. AREFI, R. KARROUBI, M. IRANI-RAHAGHI

2016, 37(7):  821-834.  doi:10.1007/s10483-016-2098-9

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An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton's principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.

Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads

D. V. DUNG, P. M. VUONG

2016, 37(7):  835-860.  doi:10.1007/s10483-016-2099-9

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The nonlinear analysis with an analytical approach on dynamic torsional buckling of stiffened functionally graded thin toroidal shell segments is investigated. The shell is reinforced by inside stiffeners and surrounded by elastic foundations in a thermal environment and under a time-dependent torsional load. The governing equations are derived based on the Donnell shell theory with the von Kármán geometrical nonlinearity, the Stein and McElman assumption, the smeared stiffeners technique, and the Galerkin method. A deflection function with three terms is chosen. The thermal parameters of the uniform temperature rise and nonlinear temperature conduction law are found in an explicit form. A closed-form expression for determining the static critical torsional load is obtained. A critical dynamic torsional load is found by the fourth-order Runge-Kutta method and the Budiansky-Roth criterion. The effects of stiffeners, foundations, material, and dimensional parameters on dynamic responses of shells are considered.

Free vibration analysis of functionally graded material beams based on Levinson beam theory

Xuan WANG, Shirong LI

2016, 37(7):  861-878.  doi:10.1007/s10483-016-2094-9

Abstract ( 834 )   HTML   PDF (276KB) ( 254 )  

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Free vibration response of functionally graded material (FGM) beams is studied based on the Levinson beam theory (LBT). Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.

Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

D. V. DUNG, L. K. HOA, B. T. THUYET, N. T. NGA

2016, 37(7):  879-902.  doi:10.1007/s10483-016-2097-9

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An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material (FGM) coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variablecoefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.

Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory

R. ANSARI, T. POURASHRAF, R. GHOLAMI, H. ROUHI

2016, 37(7):  903-918.  doi:10.1007/s10483-016-2100-9

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The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Kármán's hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuckling characteristics of nanoshells with small sizes.

Axisymmetric Powell-Eyring fluid flow with convective boundary condition:optimal analysis

T. HAYAT, S. MAKHDOOM, M. AWAIS, S. SALEEM, M. M. RASHIDI

2016, 37(7):  919-928.  doi:10.1007/s10483-016-2093-9

Abstract ( 676 )   HTML   PDF (214KB) ( 200 )  

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The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method (OHAM). The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.

Local receptivity in non-parallel boundary layer

Luyu SHEN, Changgen LU

2016, 37(7):  929-940.  doi:10.1007/s10483-016-2092-9

Abstract ( 631 )   HTML   PDF (384KB) ( 181 )  

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Mode transition and oscillation suppression in supersonic cavity flow

Chao ZHANG, Zhenhua WAN, Dejun SUN

2016, 37(7):  941-956.  doi:10.1007/s10483-016-2095-9

Abstract ( 632 )   HTML   PDF (774KB) ( 236 )  

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Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation (DNS). For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter Ⅲ mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition (DMD) approach are consistent with the local power spectral density (PSD) analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.

Control strategy of central pattern generator gait movement under condition of attention selection

Wei WANG, Rubin WANG

2016, 37(7):  957-966.  doi:10.1007/s10483-016-2096-9

Abstract ( 586 )   HTML   PDF (791KB) ( 229 )  

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As a typical rhythmic movement, human being's rhythmic gait movement can be generated by a central pattern generator (CPG) located in a spinal cord by selfoscillation. Some kinds of gait movements are caused by gait frequency and amplitude variances. As an important property of human being's motion vision, the attention selection mechanism plays a vital part in the regulation of gait movement. In this paper, the CPG model is amended under the condition of attention selection on the theoretical basis of Matsuoka neural oscillators. Regulation of attention selection signal for the CPG model parameters and structure is studied, which consequentially causes the frequency and amplitude changes of gait movement output. Further, the control strategy of the CPG model gait movement under the condition of attention selection is discussed, showing that the attention selection model can regulate the output model of CPG gait movement in three different ways. The realization of regulation on the gait movement frequency and amplitude shows a variety of regulation on the CPG gait movement made by attention selection and enriches the controllability of CPG gait movement, which demonstrates potential influence in engineering applications.