• 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.

• 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.

• Computers and Concrete
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• v.30 no.6
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• pp.433-443
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• 2022

In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FG-GPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.295-301
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• 2001

An investigation into asymmetric vibrations of a clamped circular plate under a hannonic excitation is made. We examine a primary resonance, in which the frequency of excitation is near the natural frequency of an asymmetric mode of the plate. We found not only a response having the form of standing wave but also one having the form of traveling wave, which was not observed by Sridhar, Mook and Nayfeh(1978; Journal of Sound and Vibration 59(2), pp. 159-170).

• Steel and Composite Structures
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• v.17 no.1
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• pp.133-143
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• 2014

In this paper, we try to prepare an accurate analytical solution for solving nonlinear vibration of thin circular sector cylinder. A new approximate solution called variational approach is presented and correctly applied to the governing equation of thin circular sector cylinder. The effect of important parameters on the response of the problem is considered. Some comparisons have been presented between the numerical solution and the present approach. The results show an excellent agreement between these methods. It has been illustrated that the variational approach can be a useful method to solve nonlinear problems by considering the effects of important parameters.

• Geomechanics and Engineering
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• v.16 no.4
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• pp.355-361
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• 2018

In this paper, nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation is studied. It has been tried to prepare a semi-analytical solution for whole domain of vibration. Only one iteration lead us to high accurate solution. The effects of linear elastic foundation on the response of the beam vibration are considered and studied. The effects of important parameters on the ratio of nonlinear to linear frequency of the system are studied. The results are compared with numerical solution using Runge-Kutta $4^{th}$ technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.203-213
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• 2018

This paper presents a study of geometric nonlinear forced vibration of carbon nano-tubes (CNTs) reinforcement composite plates on nonlinear elastic foundations. The plate is bonded with piezoelectric layers. The von Karman geometric nonlinearity assumptions with classical plate theory are employed to obtain the governing equations. The Galerkin and homotopy perturbation method (HPM) are utilized to investigate the effect of carbon nano-tubes volume fractions, large amplitude vibrations, elastic foundation parameters, piezoelectric applied voltage on frequency ratio and primary resonance. The results indicate that the carbon nano-tube volume fraction, applied voltage and elastic foundation parameters have significant effect on the hardening response of carbon nanotubes reinforced composite (CNTRC) plates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.7
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• pp.1106-1115
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• 1997

A method of obtaining a control input to reduce residual vibration was developed for nonlinear time-varying systems moving along pre-determined two dimensional paths. First, the nonlinear system equation was solved with nominal input then linearized by nominal response which is defined at equilibrium point. Next an additional input can be obtained by solving the linearized equation that should satisfied the required boundary conditions. Residual vibration reduction was experimentally verified by applying the control input, which is sum of nominal and additional input, to a moving pendulum whose length is varying time.

• 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.

• Journal of Korean Port Research
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• v.13 no.2
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• pp.389-398
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• 1999

In the biological immunity, the immune system of organisms regulates the antibody and T-cells to protect the attack from the foreign materials which are virus, germ cell, and other antigens, and supports their stable state. It has similar characteristics that has the adaptation and robustness to overcome disturbances and to control the plant of engineering application. In this paper, we build a model of the T-cell regulated immune response mechanism. We have also designed an immune response controller(IRC) focusing on the T-cell regulated immune response of the biological immune system that include both a help part to control the response and a suppress part to adjust system stabilization effect. We show some computer simulation to control the vibration of building structure system with strong wind forces excitation also demonstrate the efficiency of the proposed controller for applying a practical system even with existing nonlinear terms.