• 대한기계학회논문집A
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• 제20권3호
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• pp.968-977
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• 1996

The linear/nonlinear vibration response of the rotating hybrid cylindrical shell with simply supported boundary condition is studied. The Ritz-Galerkin method is applied to obtain the nonlinear frequency equation, which excludes in-plane and rotatory inertia but includes bending stretching coupling terms. The bifurcation phenomena for the linear frequency and the frequency ratio(nonlinear/linear frequency ratio) are presented. The hybrid cylindrical shells are composed of composite(GFRP, CFRP) metal(aluminium, steel) with symmetric and antisymmetric stacking sequence. The effects of the Coriolis and centrifugal force are considered The results also present the effects of length-to- radies ratio, radius-to-thickness ratio, the circumferential wave number, the stacking sequence, the material property, the initial excitation amplitude and the rotating speed. The present linear frequency results are compared with those of the available literature.

• Wind and Structures
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• 제26권6호
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• pp.355-367
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• 2018

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

• Nuclear Engineering and Technology
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• 제55권11호
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• pp.4295-4306
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• 2023

The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.451-463
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• 2020

In this paper, a new semi-analytical solution for estimating the pull-in parameters of electrically actuated functionally graded (FG) nanobeams is proposed. All the bulk and surface material properties of the FG nanoactuator vary continuously in thickness direction according to power law distribution. Here, the modified couple stress theory (MCST) and Gurtin-Murdoch surface elasticity theory (SET) are jointly employed to capture the size effects of the nanoscale beam in the context of Euler-Bernoulli beam theory. According to the MCST and SET and accounting for the mid-plane stretching, axial residual stress, electrostatic actuation, fringing field, and dispersion (Casimir or/and van der Waals) forces, the nonlinear nonclassical equation of motion and boundary conditions are obtained derived using Hamilton principle. The proposed semi-analytical solution is derived by employing Galerkin method in conjunction with the Particle Swarm Optimization (PSO) method. The proposed solution approach is validated with the available literature. The freestanding behavior of nanoactuators is also investigated. A parametric study is conducted to illustrate the effects of different material and geometrical parameters on the pull-in response of cantilever and doubly-clamped FG nanoactuators. This model and proposed solution are helpful especially in mechanical design of micro/nanoactuators made of FGMs.

• Steel and Composite Structures
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• 제50권2호
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• pp.201-216
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• 2024

This paper is motivated by the lack of studies relating to vibration and nonlinear resonance of fluid-conveying cantilever porous GPLR pipes with fractional viscoelastic model resting on nonlinear foundations. A dynamical model of cantilever porous Graphene Platelet Reinforced (GPLR) pipes conveying fluid and resting on nonlinear foundation is proposed, and the vibration, natural frequencies and primary resonant of such system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with fractional viscoelastic model is used to govern the construction relation of the nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied on pipe and excitation frequency is close to the first natural frequency. The governing equation for transverse motion of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.17-30
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• 1997

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

• Structural Engineering and Mechanics
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• 제88권2호
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• pp.159-168
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• 2023

Cost-effective high precision hybrid elements are presented in a hierarchical form for dynamic analysis of plates. The costs associated with controlling the vibrations of ferromagnetic plates can be minimized by adequate determination of the amount of electric current and magnetic field. In the present study, the effect of magnetic field and electric current on nonlinear vibrations of ferromagnetic plates is investigated. The general form of Lorentz forces and Maxwell's equations have been considered for the first time to present new relationships for electromagnetic interaction forces with ferromagnetic plates. In order to derive the governing nonlinear differential equations, the theory of third-order shear deformations of three-dimensional plates has been applied along with the von Kármán large deformation strain-displacement relations. Afterward, the nonlinear equations are discretized using the Galerkin method, and the effect of various parameters is investigated. According to the results, electric current and magnetic field have different effects on the equivalent stiffness of ferromagnetic plates. As the electric current increases and the magnetic field decreases, the equivalent stiffness of the plate decreases. This is a phenomenon reported here for the first time. Furthermore, the magnetic field has a more significant effect on the steady-state deflection of the plate compared to the electric current. Increasing the magnetic field and electric current by 10-times results in a reduction of about 350% and an increase of 3.8% in the maximum steady-state deflection, respectively. Furthermore, the nonlinear frequency decreases as time passes, and these changes become more intense as the magnetic field increases.

• Structural Engineering and Mechanics
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• 제42권4호
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• pp.589-608
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• 2012

In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

• 한국농공학회지
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• 제39권2호
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• pp.19-25
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• 1997

Abstract [] The prediction of changes in the tidal regime due to the sea dike closure in the Saemankum area was performed using the nonlinear finite element model, TIDE. Based upon an overall comparison of calibrated model results with available field data, the TIDE model behaves well and is good representation of the hydrodynamic of the Saemankum tidal project area. It is shown that the TIDE model does an excellent job of computing the changes of tidal characteristics resulting in sea dike closure in an estuary area.

• Smart Structures and Systems
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• 제4권4호
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• pp.407-428
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• 2008

The nonlinear mechanics of cable vibration is caught either by analytical or numerical models. Nevertheless, the choice of the most appropriate method, in consideration of the problem under study, is not straightforward. A feedback control policy might even enhance the complexity of the system. Thus, in order to design a suitable controller, different approaches are here adopted. Devices mounted transversely to the cable in the two directions, close to one of its ends, supply the feedback control action based on the observation of the response in a few points. The low order terms of the control law are, at first, analyzed in the framework of linear models. Explicit analytic solutions are derived for this purpose. The effectiveness of high order terms in the control law is then explored by means of a finite element model(FEM), which accounts for high order harmonics. A suitably dimensional analytical Galerkin model is finally derived, to investigate the effectiveness of the proposed control strategy, when applied to a physical model.