• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• Earthquakes and Structures
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• v.26 no.4
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• pp.251-259
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• 2024

In this paper, the thermal post-buckling behavior of graphene platelets reinforced metal foams (GPLRMFs) plate with initial geometric imperfections on nonlinear elastic foundations are studied. First, the governing equation is derived based on the first-order shear deformation theory (FSDT) of plate. To obtain a single equation that only contains deflection, the Galerkin principle is employed to solve the governing equation. Subsequently, a comparative analysis was conducted with existing literature, thereby verifying the correctness and reliability of this paper. Finally, considering three GPLs distribution types (GPL-A, GPL-B, and GPL-C) of plates, the effects of initial geometric imperfections, foam distribution types, foam coefficients, GPLs weight fraction, temperature changes, and elastic foundation stiffness on the thermal post-buckling characteristics of the plates were investigated. The results show that the GPL-A distribution pattern exhibits the best buckling resistance. And with the foam coefficient (GPLs weight fraction, elastic foundation stiffness) increases, the deflection change of the plate under thermal load becomes smaller. On the contrary, when the initial geometric imperfection (temperature change) increases, the thermal buckling deflection increases. According to the current research situation, the results of this article can play an important role in the thermal stability analysis of GPLRMFs plates.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.309-318
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• 2004

We consider a nonlinear AR-ARCH type process subject to Markov-switching and give sufficient conditions for geometric ergodicity of the process. Existence of moments is also obtained.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.317-323
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• 2018

We study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact manifolds with zero boundary condition. In particular, we obtain some geometric estimates for the first eigenvalue.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.10
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• pp.116-126
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• 2001

This paper suggests a numerical method to find optimal geometric path and minimum-time motion for a spatial 6-link manipulator arm (PUMA 560 type). To find a minimum-time motion, the optimal geometric paths minimizing 2 different dynamic performance indices are searched first, and the minimum-time motions are searched on these optimal paths. In the algorithm to find optimal geometric paths, the objective functions (performance indices) are selected to minimize joint velocities, actuator forces or the combinations of them as well as to avoid one static obstacle. In the minimum-time algorithm the traveling time is expressed by the power series including 21 terms. The coefficients of the series are obtained using nonlinear programming to minimize the total traveling time subject to the constraints of velocity-dependent actuator forces.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.327-330
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• 1989

Two recent nonlinear control methods of nonlinear geometric method and nonlinear optimal control method are applied to a pH control system with severe nonlinear characteristics. Simulations and experiments show that their performances are very good and robust for various realistic situations such as model parameter mismatches.

• Wind and Structures
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• v.20 no.2
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• pp.249-274
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• 2015

Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

• Structural Engineering and Mechanics
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• v.26 no.6
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• pp.725-739
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• 2007

In recent years there are many plate bending elements that emerged for solving both thin and thick plates. The main features of these elements are that they are based on mix formulation interpolation with discrete collocation constraints. These elements passed the patch test for mix formulation and performed well for linear analysis of thin and thick plates. In this paper a member of this family of elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both thin and thick plates with geometric nonlinearity. The Von K$\acute{a}$rm$\acute{a}$n's large displacement plate theory based on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterative-incremental procedure is implemented to solve the nonlinear equations. The element is then tested for plates with simply supported and clamped edges under uniformly distributed transverse loads. The results obtained using the geometrically NDRM element is then compared with the results of available analytical solutions. It has been observed that the NDRM results agreed well with the analytical solutions results. Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and thick plates with geometric non-linearity.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.1
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• pp.11-16
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• 1990

The effects on the dynamic behaviour of the geometric nonlinearity and large dynamic tensile forces occurring in hostile sea environments must be investigated for assessing extreme tensions and fatigue life expectancy of cable. In this paper, the combined effects on the cable dynamic responses are shown through comparisons between numerical solutions to the cable dynamic equations with geometric nonlinearity and large tensile force terms as well as nonlinear drag term and those to the cable equations with only nonlinear drag term. It is found that, in steady state, the cambined effects increase the maximum dynamic tension and reduce the magnitude of the minimum of the dynamic tension at the middle of the cable. This decrease together with the increase of the maximum dynamic tension, cause the average tension to become higher and, therefore, it may deteriorate the cable fatigue life.

• Structural Engineering and Mechanics
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• v.29 no.3
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• pp.259-278
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• 2008

This paper presents a nonlinear finite element procedure accounting for the effects of geometric as well as material nonlinearities for reinforced concrete bridge piers supported by laminated rubber bearings. Reinforced concrete bridge piers supported by laminated rubber bearings and carrying a cyclic load were analyzed by using a special purpose, nonlinear finite element program, RCAHEST. For reinforced concrete, the proposed robust nonlinear material model captures the salient response characteristics of the bridge piers under cyclic loading conditions and addresses with the influence of geometric nonlinearity on post-peak response of the bridge piers by transformations between local and global systems. Seismic isolator element to predict the behaviors of laminated rubber bearings is also developed. The seismic performance of reinforced concrete bridge piers supported by laminated rubber bearings is assessed analytically. The results show good correlation between the experimental findings and numerical predictions, and demonstrate the reliability and robustness of the proposed analytical model. Additionally, the studies and discussions presented in this investigation provide an insight into the key behavioral aspects of reinforced concrete bridge piers supported by laminated rubber bearings.