• Steel and Composite Structures
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• 제42권3호
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• pp.397-405
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• 2022

The existing researches on the dynamics of the fluid-conveying pipes only focus on stability and vibration problems, and there is no literature report on the wave propagation of the fluid-conveying pipes. Therefore, the purpose of this paper is to explore the propagation characteristics of longitudinal and flexural waves in the fluid-conveying pipes. First, it is assumed that the material properties of the fluid-conveying pipes vary based on a power function of the thickness. In addition, it is assumed that the material properties of both the fluid and the pipes are closely depended on temperature. Using the Euler-Bernoulli beam equation and based on the linear theory, the motion equations considering the thermal-mechanical-fluid coupling is derived. Then, the exact expressions of phase velocity and group velocity of longitudinal waves and bending waves in the fluid-conveying pipes are obtained by using the eigenvalue method. In addition, we also studied the free vibration frequency characteristics of the fluid-conveying pipes. In the numerical analysis, we successively studied the influence of temperature, functional gradient index and liquid velocity on the wave propagation and vibration problems. It is found that the temperature and functional gradient exponent decrease the phase and group velocities, on the contrary, the liquid flow velocity increases the phase and group velocities. However, for vibration problems, temperature, functional gradient exponent parameter, and fluid velocity all reduce the natural frequency.

• 한국기계가공학회지
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• 제10권4호
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• pp.8-15
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• 2011

In this paper, the influence of a crack on the natural frequency of cracked cantilever L-shaped beam with coupled bending and torsional vibrations by analytically and experimentally is analyzed. The L-shaped beam with a crack is modeled by Hamilton's principle with consideration of bending and torsional energy. The two coupled governing differential equations are reduced to one sixth-order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first, second and third mode of fracture and to be always opened during the vibrations. The theoretical results are validated by a comparison with experimental measurements. The maximal difference between the theoretical results and experimental measurements of the natural frequency is less than 7.5% in the second vibration mode.

• 한국소음진동공학회논문집
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• 제15권6호
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• pp.749-756
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• 2005

This paper presents vibration analyses of hard disk drive (HDD) spindle systems based on the finite element method. The systems under investigation have a cantilevered shaft rotating on hydrodynamic bearings. In particular, the influence of stator's flexibility on major modes has been taken into account in dual ways lumped and distributed-parameter model approfches. Even the latter employs relatively macroscopic elements instead of extremely fine ones Popular in commercial codes. In order to prove the effectiveness of such formulated models, two types of HDD prototypes featuring different hub and stator structures are selected as examples. Compared to the first, the second type has a reinforced stator that would raise the natural frequency of the hub's translational (or sideway) mode. Both free and forced vibration characteristics are computed, and subsequently compared with the experimental data. It is our conclusion that Particularly the Proposed distributed model method is an efficient design tool for state-of-the-art HDD spindle systems.

• Steel and Composite Structures
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• 제21권1호
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• pp.195-216
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• 2016

The dynamic characteristics of continuous steel-concrete composite beams considering the effect of interlayer slip were investigated based on Euler Bernoulli's beam theory. A simplified calculation model was presented, in which the Mode Stiffness Matrix (MSM) was developed. The natural frequencies and modes of partial-interaction composite continuous beams can be calculated accurately and easily by the use of MSM. Proceeding from the present method, the natural frequencies of two-span steel-concrete composite continuous beams with different span-ratios (0.53, 0.73, 0.85, 1) and different shear connection stiffnesses on the interface are calculated. The influence pattern of interfacial stiffness on bending vibration frequency was found. With the decrease of shear connection stiffness on the interface, the flexural vibration frequencies decrease obviously. And the influence on low order modes is more obvious while the reduction degree of high order is more sizeable. The real natural frequencies of partial-interaction continuous beams commonly used could have a 20% to 40% reduction compared with the fully-interaction ones. Furthermore, the reduction-ratios of natural frequencies for different span-ratios two-span composite beams with uniform shear connection stiffnesses are totally the same. The span-ratio mainly impacts on the mode shape. Four kinds of shear connection stiffnesses of steel-concrete composite continuous beams are calculated and compared with the experimental data and the FEM results. The calculated results using the proposed method agree well with the experimental and FEM ones on the low order modes which mainly determine the vibration properties.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 춘계학술대회 논문집
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• pp.795-798
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• 2002

In this investigation, experimental attempts were made to observe and determine the variations in elastic of the PVC depending on the amounts of MBS added to the mixture, PVC/MBS, and also on the thicknesses of the specimens. An acoustic resonance technique was used for the tests in this investigation. It serves as a method to characterize properties of materials set in vibrational motions, which is initiated by low level stresses generated by externally supplied acoustic energy. Substantial variations were observed in the test results with the addition of the MBS to the PVC. It was found that the magnitudes of elastic constants decrease when MBS rubber was added in the range up to 9 phr and the shape factor effect in torsional vibration is more significant than the shape factor effect in flexural vibration.

• Structural Engineering and Mechanics
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• 제2권1호
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• pp.95-112
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• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

• 소음진동
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• 제9권5호
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• pp.1029-1035
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• 1999

This paper relates to the flexural vibration analysis of slender spindle systems with multiple thin disks, supported by the ball bearings by means of the finite element method. Each system component is analytically modeled taking into account its flexibility and also the centrifugal effect especially for the disk. In order to show the rapid convergence rate and accuracy of the proposed approach, an experimental set-up is built to be versatile. In two distinct cases, its natural modes are numerically computed using only a small number of total element meshes as the shaft rotational speed is varied, and verified through experimental frequency response function obtained by the impact test.

• 한국농공학회지
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• 제28권1호
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• pp.68-74
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• 1986

The governing differential equations and the boundary conditions for the free vibra- tion of the unsymmetric parabolic arch with fixed ends are derived on the basis of the equilibrium equations and the D'Alembert principle. The effect of the rotary inertia as well as the extensional and the flexural deformations is considered in the governing differential equations. A trial eigenvalue method is used for determining the natural frequencies. The Ru- uge-Kutta method is used in this method to perform the integration of the differential equations. The detailed studies are made of the lowest three vibration frequencies for the par- abolic chord length equal to 10m. The effect of the rotary inertia is analyzed and it's numerical data are presented in table. And as the numerical results the frequency versus the rise of arch and the radius of gyration are presented in figures.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1999년도 춘계학술대회 논문집
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• pp.99-104
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• 1999

In this paper, dynamic behavior of a two stage gear train system is analyzed. This system consists of three shafts supported by ball bearing at the ends of them and two pairs of spur gear sets. For exact analysis, the meshing tooth pair of gears is modeled as spring having time-dependent meshing stiffness and damping. The result of this analysis is compared to that of analysis using other model of spring having mean mesh stiffness. The effect of the excitation force by the imbalance of a rotor of a motor on the vibration of a gear train system is also analyzed. Finally, the change of a natural frequency of the whole system due to the change of an angle between three shafts is compared in each case, and from this analysis, the avoiding angle for design is advised.

• Structural Engineering and Mechanics
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• 제62권6호
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• pp.759-769
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• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.