• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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• pp.69-78
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• 1995

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine(SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the onlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increament. The method is applied to a nonlinear generic model of the high pressure oxygen turthods, the convolution approach proved to be more accurate and highly more efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance(IHB) method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic(subsynchronous) responses of the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-totor models to their coordinates at the bearing clearances.

• Journal of Power Electronics
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• v.16 no.5
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• pp.1928-1938
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• 2016

The three-phase four-wire shunt active power filter (APF) is an effective method to solve the harmonic problem in three-phase four-wire power systems. In addition, it has two possible topologies, a four-leg inverter and a three-leg inverter with a split-capacitor. There are some studies investigating DC-link voltage control in three-phase four-wire APFs. However, when compared to the four-leg inverter topology, maintaining the balance between the DC-link upper and lower capacitor voltages becomes a unique problem in the three-leg inverter with a split-capacitor topology, and previous studies seldom pay attention to this fact. In this paper, the influence of the balance between the two DC-link voltages on the compensation performance, and the influence of the voltage balance controller on the compensation performance, are analyzed. To achieve the balance between the two DC-link capacitor voltages, and to avoid the adverse effect the voltage balance controller has on the APF compensation performance, a new DC-link voltage balance control strategy for the three-phase four-wire split-capacitor APF is proposed. Representative simulation and experimental results are presented to verify the analysis and the proposed DC-link voltage balance control strategy.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.67-76
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• 2008

Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.751-764
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• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• Advances in nano research
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• v.3 no.1
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• pp.29-37
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• 2015

In the current study, the nonlinear vibration properties of an embedded zigzag single-walled carbon nanotube (SWCNT) are investigated. Winkler-type model is used to simulate the interaction of the zigzag SWCNTs with a surrounding elastic medium. The relation between deflection amplitudes and resonant frequencies of the SWCNT is derived through harmonic balance method. The equivalent Young's modulus and shear modulus for zigzag SWCNT are derived using an energy-equivalent model. The amplitude - frequency curves for large-amplitude vibrations are graphically illustrated. The simulation results show that the chirality of zigzag carbon nanolube as well as surrounding elastic medium play more important roles in the nonlinear vibration of the single-walled carbon nanotubes.

• Fibers and Polymers
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• v.7 no.2
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• pp.191-194
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• 2006

This paper adopts nonlinear vibration method to analyze the fluctuation process of fiber movement. Based on Hamilton Principle, this paper establishes differential equation of fiber axial direction movement. Using variable-separating method, this paper separates time variable from space variable. By using the disperse movement equation of Galerkin method, this paper also discusses stable region of transition curve and points out those influencing factor and variation trend of fiber vibration.

• Nuclear Engineering and Technology
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• v.56 no.5
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• pp.1627-1637
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• 2024

This research paper proposes a novel methodology for predicting the optimal location of friction supports to effectively mitigate vibrational energy in piping systems. The incorporation of friction forces in the dynamic characteristics of the system introduces inherent nonlinearity, making its analysis challenging. Typically, numerical solutions in the time domain are employed to circumvent the complexities associated with finding analytic solutions for nonlinear systems. However, time domain analysis (TDA) can be computationally intensive and demand significant computational resources due to the intricate calculations stemming from nonlinearity. To address this computational burden, this study presents an efficient approach based on linear analysis to predict the ideal position for installing friction supports as a replacement for fixed supports. Furthermore, we investigate the relationship between the installation positions of friction supports and their effectiveness in absorbing vibrations using the harmonic balanced method (HBM). Both methodologies are validated by comparing the obtained results with those obtained through time domain analysis (TDA) using the finite element method (FEM).

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.11-14
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• 1990

The Complex Harmonic Balance Finite Element Method CHBFEM ) is dicussed for the time - periodic magnetic field with saturation characteristics. And Jw - method which is used for analyzing liner system with sinusoidal voltage input can be generalized in nonlinear time-periodic magnetio field system. The CHBFEM enables us to calculate the each harmonic magnetic flux ditribution and the distortion of currents resulting from material at an AC voltage source and to save calculating time, the number of calculation and computer memory.

• Proceedings of the KIEE Conference
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• 2000.07e
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• pp.136-141
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• 2000

This paper proposes the novel control of a static synchronous compensator (STATCOM). This STATCOM system consists of cascade multilevel inverter which employs H-bridge inverter(HBI) The STATCOM system is modeled in the d-q transform matrix. This model is used to design a controller. The selective harmonic elimination method(SHEM) allows to keep the total harmonic distortion (THD) low in the output voltage. The switching method produces the staircase type waveform in cascade multilevel inverter. To balance the DC voltages in HBIs capacitor, the rotated switching scheme is newly proposed in this paper. The proposed control scheme is verified in the simulated results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.1
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• pp.42-48
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• 2003

To get a periodic trim solution from Level II helicopter flight dynamic equations, DAE based PPT A (partial Periodic Trimming Algorithm) has been proposed. Iterative update of state variables from PPT A can cause a numerical instability in DAE solver which needs compatible initial conditions. By simply adjusting the order of DAE solver a periodic trim can be obtained with good accuracy. Application for CBM (Common Baseline Model) helicopter showed the same trim result as harmonic balance method and the effective elimination of unrealistic initial responses at the start of flight simulation.