• Journal of the Korean Society for Precision Engineering
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• v.11 no.6
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• pp.75-85
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• 1994

주기함수의 외력을 갖는 버선형 시스템의 다양한 응답 특성을 구하기 위해 새로운 조화함수법(HBM)을 적용하였다. 새로운 조화함수법의 해는 비선형항을 선형항으로부터 따로 분리시킨 다음 같은 주파수 성분을 갖는 비선형 방정식들을 Newton-Raphosn법으로 풀어서 구하였다. 다양한 천이(Bifurcation) 특성을 해석적으로 판별하기 위하여 HBM의 해를 이용하여 구한 섭동 방정식의 Floquet 지수의 고유해를 사용하였다. 새로이 개발한 HBM과 천이 판별법을 1차원 비선형항을 갖는 구조물인 ALP(Articulated Loading Platform) 모델과 다차원인 비선 형 회전체 모델에 적용시켜 HBM의 해의 정확성과 이들 시스템의 천이 특성의 하나인 Chaos 존재를 확인 하였다.

• Smart Structures and Systems
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• v.14 no.5
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• pp.743-763
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• 2014

The paper presents an investigation of the nonlinear dynamical system of an electrostatically actuated micro-cantilever by the incremental harmonic balance (IHB) method. An efficient approach is proposed to tackle the difficulty in expanding the nonlinear terms into truncated Fourier series. With the help of this approach, periodic and multi-periodic solutions are obtained by the IHB method. Numerical examples show that the IHB solutions, provided as many as harmonics are taken into account, are in excellent agreement with numerical results. In addition, an iterative algorithm is suggested to accurately determine period doubling bifurcation points. The route to chaos via period doublings starting from the period-1 or period-3 solution are analyzed according to the Floquet and the Feigenbaum theories.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.67.5-67
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• 2001

A closed loop system with a linear plant and nonlinearity in the feedback connection is analyzed for its quasi-static orbital stability by a state-space approach. First a periodic orbit is assumed to exist in the loop which is determined by describing function method for the given nonlinearity. This is possible by selecting a proper nonlinearity and a rigorous justification of the describing function method.[1-3, 18, 20]. Then by introducing residual operator, a linear perturbed model can be formulated. Using various transformations like a modified eigenstructure decomposition, periodic-averaging, charge of variables and coordinate transformation, the stability of the periodic orbit, as a solution of harmonic balance, can be shown by investigating a simple scalar function and result of linear algebra. This is ...

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.449-454
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• 2000

A three-parameter model of viscoelastic damper, which has a non-linear spring as an element is incorporated into an oscillator. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by three-dimensional non-linear dynamical system of equations. The harmonic balance method is applied to get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurences of such non-linear phenomena. A direct time integration of the original equation of motion validifies the use of the harmonic balance method to this sort of problem.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.185-188
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• 2001

In this paper, we design and implement high-power amplifier with 18 watt for W-CDMA repeater. We simulate microwave circuits using RF simulator, ADS1.3 and optimize the circuit to obtain the linear and high power using Harmonic balance method. Harmonic balance is an excellent method in the analysis of nonlinear system. The HPA is fabricated on tefron substrate($\varepsilon_{{\gamma}}$=3.48, h=0.5mm, T=0.035mm). From the measured result, the HPA has gain of 52dB, 1 dB compression power of 52.8dBm and good ACPR (Adjacent Channel Power Radio) performance.l Power Radio) performance.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.3
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• pp.526-533
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• 1990

The dynamic stability of a single cam drive mechanism is investigated by an analytical approach. The nonlinear differential equation describing the motion of a single cam drive mechanism is linearized with respect to the imput power angle, and results a linear parametric differential equation. The instability region is examined by applying the harmonic balance method to linearized parametric equation having periodicity. Through the dynamic stability analysis of a single cam drive mechanism, it is observed that the parametric resonances exist and the instability regions tend to become wide as increasing the drive speed and follower mass.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.4
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• pp.7-15
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• 1989

A technique is suggested which enables the large signal current and voltage waveforms to be determined for a GaAs Schottky-Barrier diode mixer by extracting the algorithm for the nonlinear circuit analysis from the Gauss-Jacobi relaxation and the application of the Harmonic Balance Technique. Both the nonlinear and linear steps of the analysis are included. This analysis permitts accurate determination of the conversion loss for microwave mixer and the computer simulation provides an method applicable to MMIC design. The validity of the nonlinear and linear analysis is confirmed by comparing the simulation results with experimental data of the conversion loss.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.1-14
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• 2016

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

• Steel and Composite Structures
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• v.44 no.1
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• pp.91-104
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• 2022

The purpose of the present work is to study the parametric nonlinear vibration behavior of three layered symmetric laminated plate. In the analytical formulation; both normal and shear deformations are considered in the core layer by means of the refined higher-order zig-zag theory. Harmonic balance method in conjunction with Galerkin procedure is adopted for simply supported laminate plate, to obtain its natural and damping properties. For these aims, a set of complex amplitude equations governed by complex parameters are written accounting for the geometric nonlinearity and viscoelastic damping factor. The frequency response curves are presented and discussed by varying the material and geometric properties of the core layer.

• Steel and Composite Structures
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• v.46 no.5
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• pp.659-667
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• 2023

Nonlinear forced vibration behaviors of sandwich plates having graphene platelets (GPL) based face sheets have been researched in this article. Possessing low weight together with low stiffness, square honeycomb cores are mostly constructed by aluminum. Herein, the square shaped core has been fortified by two skins of GPL-based type in such a way that the skins have uniform and linearly graded GPL dispersions. The square shaped core has the effective material specification according to the relative density concept. The whole formulation has been represented based upon classical plate theory (CPT) while harmonic balance approach is applied for solving the problem and plotting the amplitude-frequency curves. The forced vibration behaviors of such plates are influenced by square-shaped core and the relative density, skin's height and GPL fortification.