• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.3
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• pp.202-209
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• 2003

A simply supported beam subjected to a uniformly distributed tangential follower force and the two successively moving spring-mass systems upon it constitute this vibration system. The influences of the velocities of the moving spring-mass system, the distance between two successively moving spring-mass systems and the uniformly distributed tangential follower force have been studied on the dynamic behavior of a simply supported beam by numerical method. The uniformly distributed tangential follower force is considered within its critical value of a simply supported beam without two successively moving spring-mass systems, and three kinds of constant velocities and constant initial displacement of two successively moving spring-mass systems are also chosen. Their coupling effects on the transverse vibration of the simply supported beam are inspected too. In this study the simply supported beam is deflected with small vibration proportional to natural frequency of the moving spring-mass systems. According to the increasing of initial displacement of the moving spring-mass systems the amplitude of the small vibration of the simply supported beam is increased due to the spring force. The velocity of the moving spring-mass system more affect on the transverse deflection of simply supported beam than other factors of the system and the effect is dominant at high velocity of the moving spring-mass systems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1496-1502
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• 1994

The influences of spring position and spring stiffness on the critical force of a cantilevered beam subjected to a follower force are investigated. The spring attatched to the beam is assumed to be a translational one and can be located at arbitrary positions of the beam as it has not been assumed so far. The effects of transeverse shear deformation and rotary intertia of the beam are also included in this analysis. The charateristic equation for the system is derived and a finite element model of the beam using local coordinates is formulated through extended Hamilton's principle. It is found that when the spring is located at position less than that of 0.5L, the flutter type instability only exists. It is shown that the spring position approaches to the free end of the beam from its midpoint, instability type is changed from flutter to divergence through the jump phenomina according to the increase of spring stiffness.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.659-676
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• 2008

The reports regarding the free vibration analysis of uniform beams carrying single or multiple spring-mass systems are plenty, however, among which, those with inertia effect of the helical spring(s) considered are limited. In this paper, by taking the mass of the helical spring into consideration, the stiffness and mass matrices of a spring-mass system and an equivalent mass that may be used to replace the effect of a spring-mass system are derived. By means of the last element stiffness and mass matrices, the natural frequencies and mode shapes for a uniform cantilever beam carrying any number of springmass systems (or loaded beam) are determined using the conventional finite element method (FEM). Similarly, by means of the last equivalent mass, the natural frequencies and mode shapes of the same loaded beam are also determined using the presented equivalent mass method (EMM), where the cantilever beam elastically mounted by a number of lumped masses is replaced by the same beam rigidly attached by the same number of equivalent masses. Good agreement between the numerical results of FEM and those of EMM and/or those of the existing literature confirms the reliability of the presented approaches.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.82-88
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• 2002

A simple beam subjected to a uniformly distributed tangential follower force and the successive two moving spring-mass systems upon it constitute this vibration system. The influences of the velocities of the moving spring-mass system, the distance between the successive two moving spring-mass systems and the uniformly distributed tangential follower force have been studied on the dynamic behavior of a simple beam by numerical method. The uniformly distributed tangential follower force is considered within its critical value of a simple beam without the successive two moving spring-mass systems, and three kinds of constant velocities and constant distance of the successive two moving spring-mass systems are also chosen. Their coupling effects on the transverse vibration of the simple beam are inspected too.

• Structural Engineering and Mechanics
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• v.42 no.1
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• pp.13-24
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• 2012

There are a large number of papers in the literature dealing with the free vibration analysis of single/multi-span uniform beam with multiple spring-mass systems, but that of coupled multi-span beams carrying spring-mass attachments is rare. In this note, free vibration analysis of a weakly coupled beam system with spring-mass attachments is conducted. The mode localization and frequency loci veering phenomena of the coupled beam system are investigated. Studies show that for weakly coupled beam system with spring-mass attachments, the mode localization and frequency loci veering will occur once there is a disorder in the system.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.321-331
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• 2010

A new technique is proposed for bridge structural damage detection based on spatial wavelet analysis of the time history obtained from vehicle body moving over the bridge, which is different from traditional detection techniques based on the bridge response. A simply-supported Bernoulli-Euler beam subjected to a moving spring-mass unit is established, with the crack in the beam simulated by modeling the cracked section as a rotational spring connecting two undamaged beam segments, and the equations of motion for the system is derived. By using the transfer matrix method, the natural frequencies and mode shapes of the cracked beam are determined. The responses of the beam and the moving spring-mass unit are obtained by modal decomposition theory. The continuous wavelet transform is calculated on the displacement time histories of the sprung-mass. The case study result shows that the damage location can be accurately determined and the method is effective.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.389-400
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• 2018

An exact solution for the title problem was obtained in closed-form fashion considering general boundary conditions. The expressions of moment, shear and shear coefficient (or shear factor) of cross section under the effect of arbitrary temperature distribution were first derived. In view of these relationships, the differential equations of Timoshenko beam under the effect of temperature were obtained and solved. Second, the characteristic equations of Timoshenko beam carrying several spring-mass systems under the effect of temperature were derived based on the continuity and force equilibrium conditions at attaching points. Then, the correctness of proposed method was demonstrated by a Timoshenko laboratory beam and several finite element models. Finally, the influence law of different temperature distribution modes and parameters of spring-mass system on the modal characteristics of Timoshenko beam had been studied, respectively.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.399-416
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• 2010

The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-step beam carrying multiple rigid bars, with each of the rigid bars possessing its own mass and rotary inertia, fixed to the beam at one point and supported by a translational spring and/or a rotational spring at another point. Where the fixed point of each rigid bar with the beam does not coincide with the center of gravity the rigid bar or the supporting point of the springs. The effects of the distance between the "fixed point" of each rigid bar and its center of gravity (i.e., eccentricity), and the distance between the "fixed point" and each linear spring (i.e., offset) are studied. For a beam carrying multiple various concentrated elements, the magnitude of each lumped mass and stiffness of each linear spring are the well-known key parameters affecting the free vibration characteristics of the (loaded) beam in the existing literature, however, the numerical results of this paper reveal that the eccentricity of each rigid bar and the offset of each linear spring are also the predominant parameters.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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• pp.1382-1389
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• 2006

Dynamic responses of a simply supported beam with a translational spring carrying a moving mass are studied. Governing equations of motion including all the inertia effects of a moving mass are derived by employing the Galerkin's mode summation method, and solved by using the Runge-Kutta integral method. Numerical solutions for dynamic responses of a beam are obtained for various cases by changing parameters of the spring stiffness, the spring position, the mass ratio and the velocity ratio of a moving mass. Some experiments are conducted to verify the numerical results obtained. Experimental results for the dynamic responses of the test beam have a good agreement with numerical ones.