• 전산구조공학
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• 제10권3호
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• pp.125-131
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• 1997

대부분의 동적계는 기진력 및 계 인자들에 있어서 다양한 불확정 특성을 갖고 있다. 본 연구에서는 기진력의 불확정성과 계 인자들의 불확정성을 모두 갖는 선형 동적계에 대한 응답해석 과정을 제안하였다. 확률특성을 갖는 계 인자와 응답은 섭동법에 의해 모델링되었으며, 응답해석은 불규칙 진동 이론에 의하여 정식화 되었다. 또한 제안된 응답 모델에 의해 계산되기 어려운 응답의 평균에 대한 해석은 확률유한요소법을 사용하였다. 적용 예로서 정상 백색잡음 기진력을 받으며 불확정 질량과 스프링 상수를 갖는 1자유도계 문제에 대하여 과도응답을 계산하고, 그 결과를 수치 시뮬레이션 결과와 비교하여 그 타당성을 검토하였다.

• 대한기계학회논문집A
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• 제33권1호
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• pp.27-33
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• 2009

Human postural responses appeared to have stereotyped modality, such as ankle mode, knee mode and hip mode in response to various perturbations. We examined whether human postural control gain of full-state feedback could be decoupled along with the eigenvector. To verify the model, postural responses subjected to fast backward perturbation were used. Upright posture was modeled as 3-segment inverted pendulum incorporated with feedback control, and joint torques were calculated using inverse dynamics. Postural modalities such as ankle, knee and hip mode were obtained from eigenvectors of biomechanical model. As oppose to the full-state feedback control, independent eigenvector control assumes that modal control input is determined by the linear combination of corresponding modality. We used optimization method to obtain and compare the feedback gains for both independent eigenvector control and full-state feedback control. As a result, we found that simulation result of eigenvector feedback was not competitive in comparison with that of full-state feedback control. This implies that the CNS would make use of full-state body information to generate compensative joint torques.

• 한국정밀공학회지
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• 제23권2호
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• pp.43-50
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• 2006

Recently, with rapid development of semiconductor and flat panel display, the manufacturing equipments are required to have large travel range, high productivity, and high accuracy. In this paper, an ultra precision decoupled dual servo (DDS) system is proposed to meet these requirements. And a control scheme for the DDS is studied. The proposed DDS consists of a $XY{\Theta}$ fine stage for handling work-pieces precisely and a XY coarse stage for large travel range. The fine stage consists of four voice coil motors (VCM) and air bearing guides. The coarse stage consists of linear motors and air bearing guides. The DDS is mechanically decoupled between coarse stage and fine stage. Therefore, both stages must be controlled independently and the performance of the DDS is mainly determined by the fine stage. For high performance tracking, the controller of fine stage consists of time delay control (TDC) and perturbation observer while the controller of coarse stage is TDC alone. With these individual controllers, two kinds of dual-servo control strategies are suggested: master-slave type and parallel type. By simulations and experiments, the performances of two dual-servo control strategies are compared.

• 대한전기학회논문지
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• 제35권1호
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• pp.26-35
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• 1986

In this paper, non-linear state equations for a 3-phase, 220V, 0.4 KW, squirrel cage induction motor have been derived using the d-q transformation and then these equations have been linearized around an operating point by a small perturbation method. Root loci on the s-plane with repect to the changes of slip S and supply frequency f have been studied. Based on the above results, the derived linear state equations have been augmented to the 6th order, including the output velocity feedback and a discrete PI speed controller. Using the new state equations, stability regions on the Kp-Kl plane have been investigated for slip S and sampling time T. In designing a discrete PI controller, the coefficients Kp and Kl around the normal operating point (220V,1,692rpm,60Hz)have been chosen under the assumptions that each response to a perturbation input of reference speed and load torque be underdamped and dominated by a pair of complex poles. Step responses in the experimental system using an Intel SDK-86 and an optimized PWM inverter show satisfactory results that the maximum overshoots and damped frequency are well coincided with ones from the computer simulation.

• Smart Structures and Systems
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• 제25권6호
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• pp.693-705
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• 2020

In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature dependent. The governing equations of the tube are obtained using a higher order shear deformation tube theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large displacements and small strains. Uniform temperature elevation of the tube is also included into the formulation. For the case of tubes which are simply supported in flexure and axially immovable, the governing equations are solved using the two-step perturbation technique. Closed form expressions are provided to obtain the small and large amplitude fundamental natural frequencies of the FGM shallow curved tubes in thermal environment. Numerical results are given to explore the effects of thermal environment, radius ratio, and length to thickness ratio of the tube on the fundamental linear and non-linear frequencies.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.525-534
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• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• Steel and Composite Structures
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• 제44권3호
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• Structural Engineering and Mechanics
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• 제62권5호
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• pp.607-618
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• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• Structural Engineering and Mechanics
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• 제35권4호
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• pp.387-407
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• 2010

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.