• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.2
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• pp.108-114
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentration load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastical is obtained from the final equilibrium stage. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of simple beam are derived , and solved numberically . Three kinds of tapered beam types are considered . The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.453-465
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• 2000

In this paper, a new method for finding the approximate solution of a second order nonlinear partial differential equation is introduced. In this method the problem is transformed to an equivalent optimization problem. them , by considering it as a distributed parameter control system the theory of measure is used for obtaining the approximate solution of the original problem.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.297-306
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• 1997

The bouncing of a cantilever with the free end pressed against a stop can create high-frequency vibration that the Bernoulli-Euler beam theory is inadequate to solve. An analytic procedure is presented using Timoshenko beam theory to obtain the non-linear response of a cantilever supported by an elastic stop with clearance at the free end. Through a numerical example, the bouncing behavior of the Timoshenko and Bernoulli-Euler beam models are compared and discussed.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• Journal of Advanced Marine Engineering and Technology
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• v.15 no.1
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• pp.85-95
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• 1991

All physical systems are nonlinear to some degree. The examples are relay, backlash, deadzone, saturation element and so on. In the linear control system design, it is useful method to restrict the nonlinearity to the linearity of system over the operation range. It is worth noting that nonlinearities may be intentionally introduced in to a system. A simple of an intentional non-linearity is the Bang-Bang controller which uses the On-Off relay. In this paper, an angular position servosystem made of a DC servomotor controlled by a microcomputer is discribed. Authors use two methods in the design of controller. The one is linear controller designed by the optimal feedback control theory only and the other is nonlinear controller designed by On-Off relay with optimal feedback control theory. To do the real time control, the controller is designed by using 16bit personal computer and A/D.D/A converter(12bit) is used in order to convert the signal. According to this way, the results from real time control are as follows. 2) Under the On-Off controller with hysterisis the influence of disturbance is considerably smaller than the linerar controller. 3) An increase in the sampling period has a destabilizing effect. 4)In the controller performance, the response time of the On-Off controller is longer than that of the linear controller. To close, we note that the On-Off controller with hysterisis is more attractive than the linear controller in the presence of the input limit.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.191-203
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• 2011

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.803-806
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• 1998

A novel bipolar circuit technique for realizing linear transconductor is described. The proposed circuit has superior linearity and temperature characteristics when compared with the conventional transconductor. The theory of operation is presented and computer simulation results are used to verify theoretical predections. The simulation results show close agreement between predicted behaviours and experimental performances.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Wind and Structures
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• v.16 no.3
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• pp.279-300
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• 2013

This paper presents a new analysis framework for predicting the internal buffeting forces in bridge components under skew wind. A linear regressive model between the internal buffeting force and deformation under normal wind is derived based on mathematical statistical theory. Applying this regression model under normal wind and the time history of buffeting displacement under skew wind with different yaw angles in wind tunnel tests, internal buffeting forces in bridge components can be obtained directly, without using the complex theory of buffeting analysis under skew wind. A self-anchored suspension bridge with a main span of 260 m and a steel arch bridge with a main span of 450 m are selected as case studies to illustrate the application of this linear regressive framework. The results show that the regressive model between internal buffeting force and displacement may be of high significance and can also be applied in the skew wind case with proper regressands, and the most unfavorable internal buffeting forces often occur under yaw wind.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.401-415
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• 2017

A new higher shear deformation theory (HSDT) is presented for the thermal buckling behavior of functionally graded (FG) sandwich plates. It uses only four unknowns, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The theory considers a hyperbolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a new displacement field which includes undetermined integral terms. Material characteristics and thermal expansion coefficient of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are supposed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is used to derive the governing equations as an eigenvalue problem. The validation of the present work is carried out with the available results in the literature. Numerical results are presented to demonstrate the influences of variations of volume fraction index, length-thickness ratio, loading type and functionally graded layers thickness on nondimensional thermal buckling loads.