• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.04a
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• pp.369-373
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• 1992

Force control of a planar two-link structurally flexible robotic manipulator is considered in this study. The dynamic model is obtained by using the extended Hamilton's principle and the Galerkin criterion. A method is pressented toobtain the linearized equations of motion in Cartesian space for use in designing the control system. The approachto solving the control problem is to use feedforward and feedback control torques. The feedforward torques maneuver the flexible manipulatro along a nominal trajectory and the feedback torques minimize any deviations from the nominal trajectory. The linear quadratic Gaussian/loop transfer recovery (LQG/LTR) design methodology is explotied to design a robust feedback control system that can handle modeling errors and sensor noise, and operates on Cartesian space trajectory errors. The Lqg/LTR compenstaor together with a feedforward ollp is used to control the flexible manipulator. Simulated results are presented for a numerical example.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.4 s.181
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• pp.67-74
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• 2006

The paper presents gravitational effect on eigenvalue branches and flutter modes of a vertical cantilevered pipe conveying fluid. The eigenvalue branches and modes associated with flutter of cantilevered pipes conveying fluid are fully investigated. Governing equations of motion are derived by extended Hamilton's principle, and the related numerical solutions are sought by Galerkin's method. Root locus diagrams are plotted for different values of mass ratios of the pipe, and the order of branch in root locus diagrams is defined. The flutter modes of the pipe at the critical flow velocities are drawn at every one of the twelfth period. The transference of flutter-type instability from one eigenvalue branches to another is investigated thoroughly.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.435-445
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• 2018

This paper is concerned with thermo-mechanical vibration behavior of flexoelectric/piezoelectric nanobeams under uniform and linear temperature distributions. Flexoelectric/piezoelectric nanobeams have higher natural frequencies compared to conventional piezoelectric ones, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric/piezoelectric nanobeams for the first time. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameter, surface elasticity, temperature rise, beam thickness and various boundary conditions on the vibration frequencies of thermally affected flexoelectric/piezoelectric nanobeam.

• Smart Structures and Systems
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• v.26 no.2
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• pp.185-193
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• 2020

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.945-952
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• 1994

In this paper, a mathematical model for a belt driven system is proposed to analyse the vibtation characteristics of the driving units with belts and the free and forced vibration analyses are carried out. The mathematical model for model for the belt-driven system includes belts,pulleys, spindle and bearings. Using the Hamilton principle, the 4 nonlinear governing equations and the 12 nonlinear boundary conditions are derived. To linearize and discretize the nonlinear govering equations and boundary conditions, the perturbation method and Galerkin method are used. Also, the free vibration analyses for the various parameters of the belt driven system, which are belt tension, belt length, material property of belt, belt speed and pulley mass are made. The forced vibration analyses of the system are made and the dynamic responses for the main parmeters are analysed with the belt driven system.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.2 s.107
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• pp.198-206
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• 2006

The dynamic responses of both the in-plane and out-of-plane vibrations are investigated for an axially moving membrane. The equations of motion are derived for the moving membrane with no-slip boundary conditions by using the extended Hamilton principle. Based on the Galerkin method, the discretized equations of motion are derived. The generalized-time integration method is applied to compute the dynamic responses for the in-plane and out-of-plane motions. From the computed results, the responses are compared between the in-plane and out-of-plane vibrations. Furthermore. the effects of velocity and acceleration on the dynamic behaviours for displacements and stresses are presented.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.3
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• pp.221-227
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• 2002

The longitudinal and lateral in-plane vibrations of an axially moving membrane are investigated when the membrane has translating acceleration. By extended Hamilton's principle, the governing equations are derived. The equations of motion for the in-plane vibrations are linear and coupled. These equations are discretized by using the Galerkin approximation method after they are transformed into the variational equations, j.e., the weak forms so that the admissible functions can be used for the bases of the in-plane deflections. With the discretized equations for the in-plane vibrations, the natural frequencies and the time histories of the deflections are obtained.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.569-574
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• 2009

The paper presents the influences of the external damping and the tip mass on dynamic stability of a vertical cantilevered pipe conveying fluid. In general, real pipe systems may have some valves and attached mechanical parts, which can be regarded as attached lumped masses and support-dampers. The support-dampers can be assumed as viscous dampers. The equations of motion are derived by energy expressions using extended Hamilton's principle, and some numerical results using Galerkin's method are presented. Critical flow velocities and stability maps of the pipe with external dampers and tip mass are obtained for various tip mass ratios, external damping coefficients and positions of the viscous dampers.

• Korean Journal of Hydrosciences
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• v.2
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• pp.13-24
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• 1991

The governing partial differential equation of flow in porous media is developed on the bases of the continuity equation of fluid for transient flow through a saturated-unsaturated zone, and substitution of Dercy's law. The numerical solution is obtained by the Galerkin finite element method based on the principle of weighted residuals. The analysis is carried out by using the unsteady storm data observed and the functional relationships between the hydraulic conductivities, capillary pressure heads, and volumetric water contents under saturated-unsaturated conditions. As the results the hydraulic conductivities, rates of change of storage and initial moisture conditions are significantly influened on the responses of subsurface flow on a hillslope.

• Steel and Composite Structures
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• v.11 no.1
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• pp.59-76
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• 2011

Dynamic analysis of an embedded single-walled carbon nanotube (SWCNT) traversed by a moving nanoparticle, which is modeled as a moving load, is investigated in this study based on the nonlocal Timoshenko beam theory, including transverse shear deformation and rotary inertia. The governing equations and boundary conditions are derived by using the principle of virtual displacement. The Galerkin method and the direct integration method of Newmark are employed to find the dynamic response of the SWCNT. A detailed parametric study is conducted to study the influences of the nonlocal parameter, aspect ratio of the SWCNT, elastic medium constant and the moving load velocity on the dynamic responses of SWCNT. For comparison purpose, free vibration frequencies of the SWCNT are obtained and compared with a previously published study. Good agreement is observed. The results show that the above mentioned effects play an important role on the dynamic behaviour of the SWCNT.