• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.133-139
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• 2001

The nonlinear response statistics of an spring-pendulum system with internal resonance under narrow band random excitation is investigated analytically- The center frequency of the filtered excitation is selected to be close to natural frequency of directly excited spring mode. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The nonlinear phenomena, such as jump and multiple solutions, under narrow band random excitation were found by Gaussian closure method.

• Structural Engineering and Mechanics
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• v.85 no.4
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• pp.545-562
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• 2023

In this work, superharmonic and subharmonic resonance of rotating stiffened FGM truncated conical shells exposed to harmonic excitation in a thermal environment is investigated. Utilizing classical shell theory considering Coriolis acceleration and the centrifugal force, the governing equations are extracted. Non-linear model is formulated employing the von Kármán non-linear relations. In this study, to model the stiffener effects the smeared stiffened technique is utilized. The non-linear partial differential equations are discretized into non-linear ordinary differential equations by applying Galerkin's method. The method of multiple scales is utilized to examine the non-linear superharmonic and subharmonic resonances behavior of the conical shells. In this regard, the effects of the rotating speed of the shell on the frequency response plot are investigated. Also, the effects of different semi-vertex angles, force amplitude, volume-fraction index, and temperature variations on the frequency-response graph are examined for different rotating speeds of the stiffened FGM truncated conical shells.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1303-1308
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of ail relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.893-898
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• 2004

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the coordinates, velocities, and accelerations are tightly coupled by the position, velocity, and acceleration level constraints, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all coordinates, velocities, and accelerations, which are coupled by the constraints. The position, velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The perturbed constraint equations are then simultaneously solved for variations of all coordinates, velocities, and accelerations only in terms of the variations of the independent coordinates, velocities, and accelerations. Finally, the relationships between the variations of all coordinates, velocities, accelerations and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent coordinate, velocity, and acceleration variations.

• 전기의세계
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• v.13 no.4
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• pp.16-24
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• 1964

The dynamic equations of the void fraction and the water velocity in boiling region of the BWR reactor core are derived. And these equations are approximated to be able to set on an PACE analog computor. The transient analysis and the frequency response obtained by analog computer are compared with other by digital computor.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.103-119
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• 2018

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.

• Journal of Advanced Marine Engineering and Technology
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• v.17 no.4
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• pp.87-99
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• 1993

Nowadays, the cartridge valve can be controlled proportionally in remote place by adopting proportional solenoid and it becomes widely used as control component in hydraulic systems. Especially, multi stage proportional valve is attractive because it consumes less input power though its characteristics might slightly be defected. But, the system parameter should be carefully chosen to obtain optimistic characteristics. This study concerning three stage proportional throttle control valve is purposed to examine the influences of paameters to the dynamic characteristics. The typical transient and frequency responses of proportional throttle control valve were inspected through the experiments and compared to those derived from the theoritical analyses. And it was confirmed that the analyses are appropriate. Then the influences of various system parameters to the dynamic characteristics were examined by means of simulations. For the analyses, the basic equations derived from lumped model were linearized and the linearized equations were transformed to the transfer functions between inputs and outputs. Then the transient responses and frequency responses were obtained from transfer functions. 1. It is appropriate to estimate the dynamic characteristics of valve which has relatively sophisticated structure by means of system analyses using linearized equations. 2. Though the valve has two pilot stages, fairly good characteristics can be obtained by carefully choosing system parameters. 3. Main valve very quickly follows the movement of second pilot valve when the parameters of main valve(the oil supply passage and discharge passage fpr second pilot valve) are appropriately chosen.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.3 s.108
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• pp.263-269
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• 2006

The objective of the present work is to develop a time-domain numerical method of broadband noise in a cascade of airfoils. This paper focuses on dipolar broadband noise sources, resulting from the interaction of turbulent inflows with the flat-plate airfoil cascade. The turbulence response of a two-dimensional cascade is studied by solving both of the linearised and the full nonlinear Euler equations employing accurate higher order spatial differencing, time stepping techniques and non-reflecting inflow/outflow boundary condition. The time-domain result using the linearised Euler equations shows good agreement with the analytical solution using the modified LINSUB code. Through the comparison of the nonlinear time-domain result using the full nonlinear Euler equations with the linear, it is found that the acoustic mode amplitude of the nonlinear response is less than that of the linear response due to the energy cascade from low frequency components to the high frequency ones. Considering the merits of the time-domain methods over the typical time-linearised frequency-domain analysis, the current method is expected to be promising tools for analyzing the effects of the airfoil shapes, non-uniform background flow, linear-nonliear regimes on the broadband noise due to turbulence-cascade interaction.

• Smart Structures and Systems
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• v.18 no.5
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• pp.1029-1062
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• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.812-817
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• 2005

The objective of the present work is to develop a time-domain numerical method of broadband noise in a cascade of airfoils. This paper focuses on dipole broadband noise sources, resulting from the interaction of turbulent inflows with the flat-plate airfoil cascade. The turbulence response of a two-dimensional cascade is studied by solving both of the linearised and full nonlinear Euler equations employing accurate higher order spatial differencing, time stepping techniques and non-reflecting inflow/outflow boundary condition. The time-domain result using the linearised Euler equations shows good agreement with the analytical solution using the modified LINSUB code. Through the comparison of the nonlinear time-domain result using the full nonlinear Euler equations with the linear, it is found that the acoustic mode amplitude of the nonlinear response is less than that of the linear response due to the energy cascade from low frequency components to the high frequency ones. Considering the merits of the time-domain methods over the typical time-linearised frequency-domain analysis, the current method is expected to be promising tools for analyzing the effects of the airfoil shapes, non-uniform background flow, linear-nonliear regimes on the broadband noise due to gust-cascade interaction.