• Structural Engineering and Mechanics
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• 제51권3호
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• pp.519-530
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• 2014

This paper attempts to investigate the nonlinear dynamic analysis of strong nonlinear problems by proposing a new analytical method called Hamiltonian Approach (HA). Two different cases are studied to show the accuracy and efficiency of the method. This approach prepares us to obtain the nonlinear frequency of the nonlinear systems with the first order of the solution with a high accuracy. Finally, to verify the results we present some comparisons between the results of Hamiltonian approach and numerical solutions using Runge-Kutta's [RK] algorithm. This approach has a powerful concept and the high accuracy, so it can be apply to any conservative nonlinear problems without any limitations.

• Smart Structures and Systems
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• 제26권5호
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• pp.631-640
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• 2020

In this paper, nonlinear vibration behaviors of multi-phase Magneto-Electro-Elastic (MEE) doubly-curved nanoshells have been studied employing Jacobi elliptic function method. The doubly-curved nanoshell has been modeled by using nonlocal elasticity and classic shell theory. An exact estimation of nonlinear vibrational behavior of smart doubly-curved nanoshell has been obtained via Jacobi elliptic function method. This method can incorporate the influences of higher order harmonics leading to an exact estimation of nonlinear vibration frequency. It will be indicated that nonlinear vibrational frequency of doubly-curved nanoshell relies on nonlocal effect, material composition, curvature radius, center deflection and electro-magnetic field.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.27-36
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• 2018

The objective of this work is to analyze geometrically nonlinear static analysis a simply supported laminated composite beam subjected to a non-follower transversal point load at the midpoint of the beam. In the nonlinear model of the laminated beam, total Lagrangian finite element model of is used in conjunction with the Timoshenko beam theory. The considered non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. In the numerical results, the effects of the fiber orientation angles and the stacking sequence of laminates on the nonlinear deflections and stresses of the composite laminated beam are examined and discussed. Convergence study is performed. Also, the difference between the geometrically linear and nonlinear analysis of laminated beam is investigated in detail.

• Smart Structures and Systems
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• 제24권6호
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• pp.683-692
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• 2019

Traditional damage detection methods for nonlinear structures are often based on simplified models, such as the mass-spring-damper and shear-building models, which are insufficient for predicting the vibration responses of a real structure. Conventional global nonlinear finite element model updating methods are computationally intensive and time consuming. Thus, they cannot be applied to practical structures. A decentralized approach for identifying the nonlinear material parameters is proposed in this study. With this technique, a structure is divided into several small zones on the basis of its structural configuration. The unknown material parameters and measured vibration responses are then divided into several subsets accordingly. The structural parameters of each subset are then updated using the vibration responses of the subset with the Newton-successive-over-relaxation (SOR) method. A reinforced concrete and steel frame structure subjected to earthquake loading is used to verify the effectiveness and accuracy of the proposed method. The parameters in the material constitutive model, such as compressive strength, initial tangent stiffness and yielding stress, are identified accurately and efficiently compared with the global nonlinear model updating approach.

• Structural Engineering and Mechanics
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• 제89권1호
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.451-454
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• 1998

This paper proposes a new method of Model Predictive Control (MPC) of nonlinear process by us-ing the measured Volterra kernels as the nonlinear model. A nonlinear dynamical process is usually de-scribed as Volterra kernel representation, In the authors' method, a pseudo-random M-sequence is ar plied to the nonlinear process, and its output is measured. Taking the crosscorrelation between the input and output, we obtain the Volterra kernels up to 3rd order which represent the nonlinear characteristics of the process. By using the measured Volterra kernels, we can construct the nonlinear model for MPC. In applying Model Predictive Control to a nonlinear process, the most important thing is, in general, what kind of nonlinear model should be used. The authors used the measured Volterra kernels of up to 3rd order as the process model. The authors have carried out computer simulations and compared the simulation results for the linear model, the nonlinear model up to 2nd Volterra kernel, and the nonlinear model up to 3rd order Vol-terra kernel. The results of computer simulation show that the use of Valterra kernels of up to 3rd order is most effective for Model Predictive Control of nonlinear dynamical processes.

• Advances in aircraft and spacecraft science
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• 제5권1호
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• pp.21-49
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• 2018

In this paper, geometric nonlinear bending characteristics of single wall carbon nanotube reinforced composite (SWCNTRC) doubly curved shell panels subjected to uniform transversely loadings are investigated. The nonlinear mathematical model is developed for doubly curved SWCNTRC shell panel on the basis of higher-order shear deformation theory and Green- Lagrange nonlinearity. All nonlinear higher order terms are included in the mathematical model. The effective material properties of SWCNTRC are estimated by using Eshelby-Mori-Tanaka micromechanical approach. The governing equation of the shell panel is obtained using the total potential energy principle and a Newton-Raphson iterative method is employed to compute the nonlinear displacement and stresses. The present results are compared with published literature. The effect of SWCNT volume fraction, width-to-thickness ratio, radius-to-width ratio (R/a), boundary condition, linear and nonlinear deflection, stresses and different types of shell geometry on nonlinear bending response is investigated.

• 대한기계학회논문집A
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• 제21권11호
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• pp.1809-1818
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• 1997

Mathematical models of industrial robots or manipulators are highly nonlinear equations with nonlinear coupling between the variables of motion. As the working speed has been fast, the effects of nonlinear terms have become serious. So the control algorithm based on approximately linearized equation looses the efficiency. In order to design the control law for the nonlinear models, Hunt-Su's nonlinear transformation method and Marino's feedback equivalence condition are used with linear quadratic regulator(LQR) theory in this study. Nonlinear terms of the system are eliminated and coupled terms are decoupled by this feedback law. This method is applied to a 3-D.O.F. vertical articulated manipulator by both experiments and simulations and compared with PID control which is widely used in the industry.

• Korean Journal of Mathematics
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• 제21권2호
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• pp.117-124
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• 2013

We investigate the existence of weak solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We get a theorem which shows the existence of nontrivial solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We obtain this result by reducing the biharmonic problem with nonlinear term to the biharmonic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced biharmonic problem with bounded nonlinear term.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.1000-1003
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• 1996

Nonlinear unified predictive control(UPC) algorithm was applied to the temperature control of a batch polymerization reactor for polymethylmethacrylate(PMMA). Before the polymerization reaction is initiated, the parameters of the process model are determined by the recursive least squares(RLS) method. During the reaction, nonlinearities due to generation of heat of reaction and variation of heat transfer coefficients are predicted through the nonlinear model developed. These nonlinearities are added to the process output from the linear process model. And then, the predicted process output is used to calculate the control output sequence. The performance of nonlinear control algorithm was verified by simulation and compared with that of the linear unified predictive control algorithm. In the experiment of a batch PMMA polymerization, nonlinear unified predictive control was implemented to regulate the temperature of the reactor, and the validity of the nonlinear model was verified through the experimental results. The performance of the nonlinear controller turned out to be superior to that of the linear controller for tracking abrupt changes in setpoint.