• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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• pp.143-147
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• 1998

In this study, nonlinear stiffness characteristics of a discharge valve in a small hermetic compressor was considered. It was approximated, with piecewise-linearity, and cubic or quintic nonlinearity by the static load-displacement experimental results. Based on the fluid-structure interaction effects and mass flow rate, the derived 1-DOF equation of motion for the valve model was analyzed. Finally, the dynamic response of the discharge valve was studied with parameters such as the ratio of the running frequency of the compressor to the linear natural frequency of the valve.

• Advances in aircraft and spacecraft science
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• 제2권2호
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• pp.199-215
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• 2015

This study focuses on the limit cycle oscillations (LCOs) of cantilever swept-back wings containing a cubic nonlinearity in an incompressible flow. The governing aeroelastic equations of two degrees-of-freedom swept wings are derived through applying the strip theory and unsteady aerodynamics. In order to apply strip theory, mode shapes of the cantilever beam are used. The harmonic balance method is used to calculate the frequencies of LCOs. Linear flutter analysis is conducted for several values of sweep angles to obtain the flutter boundaries.

• Structural Engineering and Mechanics
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• 제50권4호
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• pp.487-500
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• 2014

An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

• Advances in aircraft and spacecraft science
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• 제4권5호
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• pp.585-611
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• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• 한국해안해양공학회지
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• 제7권1호
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• pp.116-125
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• 1995

파하중과 해류하중을 받는 단일 자유도계를 동적 해석하여 비선형 거동을 나타냄을 보이고 고차의 비선형 전이함수를 포함한 모델을 적용하여 그 비선형 차수를 알아낸다. 먼저 구조물에 단일 정현파, 두 파의 합성파 그리고 불규칙파 하중을 차례로 가하면서 각 하중조건마다 세가지 비선형 요인의 효과를 조사한다. 이로부터 단일 자유도계의 공진주파수에서 파의 에너지는 존재하지 않지만 비선형 요인에 의해 응답 성분이 나타남을 보인다. 다음으로 Volterra 급수에 근거한 고차 전이함수(higher order transfer function)모델을 적용하여 유연한 단일 자유도계의 비선형 거동이 성공적으로 모델화됨을 보이며 또한 비선형성이 2차나 3차로 명백히 나타남을 보인다.

• 한국해안해양공학회지
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• 제3권1호
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• pp.45-53
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• 1991

본 논문에서는 변조된 입사파의 쐐기에 의한 비선형 산란을 해석하였다. 쐐기의 목이 작다고 가정하여 포물형 근사를 도입하여 문제를 단순화시켰다. 이 문제에는 척도가 서로 다른 시간 및 공간 변수가 포함되어 있으므로 다척도 전개기법을 이용하였다. 비선형 산란파의 전개식은 일종의 3차 Schrodinger 방정식으로 기술할 수 있음을 밝혔는 데, 이 식에는 군속도로 진행하는 선형시간전개항, 선형측면분산항 그리고 3차 비선형항이 포함되어 있다. 유한차분법을 사용하여 수행 한 수치 계산의 결과에 의하면 산란파는 비선형항이 클 수록 그리고 변조비가 작을 수록 불안정해지며, 초기에 형성되는 스템파는 곧 여러 개의 파성분으로 분리되어 시간에 따라 변동한다. 전반적으로 보아 산란파의 전개에는 비선형항이 지배적인 인자라는 결론을 내릴 수 있다.

• Steel and Composite Structures
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• 제17권1호
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• pp.123-131
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• 2014

In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

• Smart Structures and Systems
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• 제19권4호
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• pp.403-413
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• 2017

The present article encompasses a nonlinear finite element (FE) and genetic algorithm (GA) based optimal vibration energy harvesting from nonprismatic piezo-laminated cantilever beams. Three cases of cross section profiles (such as linear, parabolic and cubic) are modelled to analyse the geometric nonlinear effects on the output responses such as displacement, voltage, and power. The simultaneous effects of taper ratios (such as breadth and height taper) on the output power are also studied. The FE based nonlinear dynamic equation of motion has been solved by an implicit integration method (i.e., Newmark method in conjunction with the Newton-Raphson method). Besides this, a real coded GA based constrained optimization scheme has also been proposed to determine the best set of design variables for optimal harvesting of power within the safe limits of beam stress and PZT breakdown voltage.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.281-286
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• 2003

A Suspension system of a car is composed of dampers and springs. The dampers and springs usually have nonlinear characteristics. However, the nonlinear characteristics of the springs and dampers through analytical model cannot agree with the experimental results. Therefore, the nonlinearity of the suing and damper should be known from the experimental results. In this study, the methods of system identification for nonlinear dynamic system in time domain are discussed and the nonlinear parameter estimation lot experimental data of an EF-SONATA car was done. The results show that a cubic and a coupled term should be considered to model the suspension system.

• Smart Structures and Systems
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• 제26권3호
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• pp.361-371
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• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.