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

• The Journal of the Acoustical Society of Korea
• /
• v.20 no.5
• /
• pp.14-20
• /
• 2001

The mass-spring system with four arms for the force-balance servo accelerometer was designed and fabricated. The response characteristics of a mass-spring system was calculated with the change of arms thickness and seismic mass by the finite element method (FEM). Furthermore, the response characteristics of accelerometer was measured using the change of interference pattern and response voltage value by Michelson interferometer. The response characteristics with changing length and thickness of arm was changed drastically, and changing seismic mass was minor effect for the response characteristics of mass-spring system. The measured resonant frequencies have good agreement with that of numerical analysis within 5％ range.

• Smart Structures and Systems
• /
• v.21 no.3
• /
• pp.349-358
• /
• 2018

This paper investigates the free vibration analysis of double-beam system coupled by a two-degree-of-freedom mass-spring system. In order to generalize the model, the main beams are assumed to be elastically restrained against translation and rotation at one end and free at the other. Furthermore, the mass-spring system is elastically connected to the beams at adjustable positions by means of four translational and rotational springs. The governing differential equations of the beams and the mass-spring system are derived and analytically solved by using the Fourier transform method. Moreover, as a second way, a finite element solution is derived. The frequency parameters and mode shapes of some diverse cases are obtained using both methods. Comparison of obtained results by two methods shows the accuracy of both solutions. The influence of system parameters on the free vibration response of the studied mechanical system is examined.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1995.10a
• /
• pp.197-200
• /
• 1995

Corrugation of railway track can be caused by the various dynamic behavior of travelling wheels and track. In this paper, the coupled vibrations of travelling wheel and railway track are analyzed as the cause of corrugations. To analyze the coupled vibrations, the track supported by the sleepers and the traveling wheel are identified to the elastically supported infinite beam and the spring-mass system which runs at constant speed. The Hertzian contact spring is considered betwen the infinite beam and spring-mass system. The dynamic responses of elastically supported infinite beam and spring-mass system are calculated. The cause and development of rail corrugation are discussed in the view point of contact force fluctuation affected by the elastic supports and the corrugated surface profile of the track. By the obtained results, the possibilities of resonance are checked between the excitation by the corrugated surface profile and the natural frequency of contact spring-moving mass system. It may be thought to a development of railway corrugation.

• Structural Engineering and Mechanics
• /
• v.16 no.3
• /
• pp.341-360
• /
• 2003

The goal of this paper is to determine the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems using an analytical-and-numerical-combined method (ANCM). To this end, a technique was presented to replace each "spring-damper-mass" system by a massless equivalent "spring-damper" system with the specified effective spring constant and effective damping coefficient. Then, the mode superposition approach was used to transform the partial differential equation of motion into the matrix equation, and the eigenvalues of the complete system were determined from the associated characteristic equation. To verify the reliability of the presented theory, all numerical results obtained from the ANCM were compared with those obtained from the conventional finite element method (FEM) and good agreement was achieved. Since the order of the property matrices for the equation of motion obtained from the ANCM is much lower than that obtained from the FEM, the CPU time required by the ANCM is much less than that by the FEM.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.768-773
• /
• 2004

Developed in this paper a mass-spring engine to represent and manipulate deformable objects. The deformable object model is a basic technology in the ‘Tangible Space Initiative’. The mass-spring model consists of structural, shear and bending springs. Various forces like external, friction, gravity, spring, and damping forces are considered and collision with planes and spheres are treated. When a sphere collide mass-spring model, mass-spring engine calculates external force to interface mass-spring model. A prototype system is implemented in C on an MS windows machine.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.24 no.4
• /
• pp.317-323
• /
• 2014

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton's principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.

• Journal of the Korean Society for Precision Engineering
• /
• v.13 no.2
• /
• pp.176-184
• /
• 1996

The paper describes the vibration characteristics of the mechanical system consisting of a uniform Timoshenko beam with a guided mass and an elastic spring support. The free end of the beam does not rotate and the spring attatched to the guided mass is elastically restrained against translation. The guided mass is assumed to be a rigid body having a finite size, but not a mass point as it has been assumed so far. The effect of magnitudes, rotary inertia and the size of the guided mass on the vibration characteristics is fully investigated by the numerical simulation using FEM and experiment. In order to verify the eigenvalue sensitivity for considered system, comparison exact solutions with FEM is conducted, and a good agreement between two solutions is also highlighted.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2012.04a
• /
• pp.819-824
• /
• 2012

This paper presents the wideband vibration system of an electromagnetic vibration energy harvester that obtained electric power for wireless sensor applications from the ever-change vibrations of bridge. It is a system with two degree of freedom vibrations that are composed of two mass and two spring respectively. One system is housing mass and spring, the other is the magnetic mass and spring that is the vibration system construction's element of electromagnetic vibration energy harvester. In other words, it is called dynamic vibration absorber. This paper show that the ratio of housing mass to magnetic mass decides the bandwidth and the size of amplitude of magnetic mass in electromagnetic vibration energy harvester. Therefore, it is necessary to improve the efficiency of energy in electromagnetic vibration energy harvester for wireless sensor applications.

• Journal of KSNVE
• /
• v.7 no.6
• /
• pp.953-958
• /
• 1997

Corrugation of railway track can be caused by the various dynamic behaviors of traveling wheels and track. In this paper, the coupled vibrations of traveling wheel and railway track are analyzed as the cause of corrugations. To analyze the coupled vibration, the track supported by the sleepers and the traveling wheels are identified to the elastically supported infinite beam and the spring-mass system which runs at constant speed. The Hertzian contact spring is considered between the infinite beam and spring-mass system are calculated. The cause and development of rail corrugation are discussed in the view point of contact force fluctuation affected by the elastic supports and the corrugated surface profile on the track. By the obtained results, the possibilities of resonance are checked between the excitation by the corrugated surface profile and the natural frequency of contact spring-mass system. It may be thought to a development of railway corrugation.