• Structural Engineering and Mechanics
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• v.86 no.2
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• pp.221-235
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• 2023

To calculate the vibrations of a tout cable subjected to axial support excitations, a nonlinear relationship of cable force and the support displacement under static situations are employed to depict the quasi-static vibration of the cable. The dynamic components of quasi-static vibration are inputted as "direct loads" to cause the parametric vibrations on the cable. Both the governing equations of motion and deformation compatibility for parametric vibrations are then derived, which indicates the high coupling of cable parametric force and deformation. Numerical solutions, based on the finite difference method, are put forward for the parametric vibrations, which is validated by the finite element method under periodic axial support excitations. For the quasi-static response, the shorter cables are more sensitive to support excitations than longer ones at small cable force. The quasi-static cable force makes the greatest contribution to the total cable force, but the parametric cable force is responsible for the occurrence of cable loosening at large excitation amplitudes. Moreover, this study also revealed that the traditional approach, assuming a linear relationship between quasi-static cable force and axial support displacement, would result in some great error of the cable parametric responses.

• Steel and Composite Structures
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• v.21 no.2
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• pp.395-409
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• 2016

Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman's large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton's principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

• Wind and Structures
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• v.6 no.1
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• pp.41-52
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• 2003

Rain-wind induced vibrations of cables are a challenging problem in the design of cable-stayed bridges. The precise excitation mechanism of the complex interaction between structure, wind and rain is still unknown. A theoretical model that is able to accurately simulate the observed phenomena is not available. This paper presents a mathematical model describing rain-wind induced vibrations as movement-induced vibrations using the quasi-steady strip theory. Both, the vibrations of the cable and the movement of the water rivulet on the cable surface can be described by the model including all geometrical and physical nonlinearities. The analysis using the stability and bifurcation theory shows that the model is capable of simulating the basic phenomena of the vibrations, such as dependence of wind velocity and cable damping. The results agree well with field data and wind tunnel tests. An extensive experimental study is currently performed to calibrate the parameters of the model.

• Smart Structures and Systems
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• v.23 no.3
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• pp.307-318
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• 2019

The frequently excessive vibrations presented in civil structures during seismic events or service conditions may result in users' discomfort, or worst, in structures failure, producing economic and even human casualties. This work contributes in proposing the synthesis of a nonlinear optimal control strategy for semiactive structural control, with the main characteristic that the synthesis considers both the structure model and the semiactive actuator nonlinear dynamics, which produces a nonlinear system that requires a nonlinear controller design. The aim is to reduce the unwanted vibrations in the response of civil structures, by means of intelligent fluid semiactive actuator such as the Magnetorheological Damper (MRD), which is a device with a low level of power consumption. The civil structures for which the proposed control methodology can be applied are those admitting a state-dependent coefficient factorized representation model, such as buildings, bridges, among others. A scaled model of a three storey building is analyzed as a case study, whose dynamical response involves displacement, velocity and acceleration of each one of the storeys, subjected to the North-South component of the September 19th., 2017, Puebla-Morelos (7.1M), Mexico earthquake. The investigation rests on comparing the structural response over time for two different conditions: with no control device installed and with one MRD installed between the first floor and the ground, where a nonlinear optimal signal for the MRD input voltage is determined. Simulation results are presented to show the effectiveness of the proposed controller for reducing the building's dynamical response.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.87-93
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• 2002

In this study, basic concepts of magnet were introduced, and dynamic characteristics of magnet coupling were explored. Based on these characteristics, it was proposed how to analyze transverse and torsional vibrations of a spindle system with magnet coupling. Proposed theoretical approaches were applied to a precision power transmission system machined for this study, and the transverse and torsional vibrations were simulated. The force on magnet coupling was shown as a form of nonlinear function of the gap and the eccentricity. Also, the form of torque transmitted by magnet coupling was considered as a sinusoidal function. Main spindle connected to a coupling of a follower part was assumed to be a rigid body. Nonlinear partial differential equation was derived to be as a function of angular displacement. By using the equation, torsional vibration analysis of a spindle system with magnet coupling was performed. Free and forced vibration analyses of a spindle system with magnetic coupling were explored by using FEM.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1910-1919
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• 1994

The nonlinear behavior of continuous structural systems which possess external resonances as well as internal resonances are found be exhibit interesting reponses, arising because of the exhange of energy between the coupled modes. In this paper, the undamped forced vibrations was studied on the effect of primary resonance based on the concept of normal modes. By using the concept of normal mode the stability relation between free and forced vibrations was investigated in case of small exciting force. Numerical results show that the excitation of one unstable mode has a great influence on the response of the other mode but that of one stable mode does not.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1354-1359
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of floating flexible body. In dealing with the dynamics of free-floating body, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In the previous paper, we proposed the use of perturbation method to the coupled equations of motion and derived zero-order and first-order equations of motion. The derivation process was lengthy and tedious. Hence, in this paper, we propose a new approach to the same problem by applying the perturbation method to the Lagrange's equations, thus providing a systematic approach to the addressed problem. Theoretical derivations show the efficacy of the proposed method.

• Earthquakes and Structures
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• v.11 no.1
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• pp.129-140
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• 2016

This paper presents He's Energy Balance Method (EBM) for solving nonlinear oscillatory differential equations. Three strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with numerical solutions using Runge-Kutta's algorithm. The effects of different important parameters on the nonlinear response of the systems are studied. The results show the presented method is potentially to solve high nonlinear vibration equations.

• Structural Engineering and Mechanics
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• v.25 no.2
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• pp.219-237
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• 2007

The effect of cable loosening on the nonlinear parametric vibrations of inclined cables is discussed in this paper. In order to overcome the small-sag limitation in calculating loosening for inclined cables, it is necessary to first derive equations of motion for an inclined cable. Using these equations and the finite difference method, the effect of cable loosening on the nonlinear parametric response of inclined cables under periodic support excitation is evaluated. A new technique that takes into account flexural rigidity and damping is proposed as a solution to solve the problem of divergence. The regions of inclined cables that undergo compression are also indicated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.441-448
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• 2000

An investigation into the nonlinear free vibrations of a cantilever beam which can have not only planar motion but also nonplanar motion is made. Using Galerkin's method based on the first mode in each motion, we transform the boundary and initial value problem into an initial value problem of two-degree-of-freedom system. The system turns out to have two normal modes. By Synge's stability concept we examine the stability of each mode. In order to check validity of the stability we obtain the numerical Poincare map of the motions neighboring on each mode.