• Tribology and Lubricants
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• v.31 no.6
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• pp.302-307
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• 2015

The use of turbocharger in internal combustion engines has increased as it is a key components for improving system efficiency without increasing engine size. Because of increasing demand, many studies have evaluated rotordynamic performance so as to increase rotation speed. This paper presents a linear and nonlinear analysis model for a turbocharger rotor supported by a floating ring bearing. We constructed rotor model by using the finite element method and approximated bearings as being infinitely short. In the linear model, we considered fluid film force as stiffness and damping element. In nonlinear analysis, calculation of the fluid film force involved solving the time dependent Reynolds equation. We verified the developed model by comparing the results to those of previous research. The analysis results show that there are four unstable modes, which are rigid body modes combining ring and rotor motion. As the rotating speed increases, the logarithmic decrement shows that certain unstable modes goes into the stable area or the stable mode goes into the unstable area. These unstable modes appear as sub-synchronous vibrations in nonlinear analysis. In nonlinear analysis frequency jump phenomenon demonstrated in several experimental studies appears. The analysis results also showed that frequency jump phenomenon occurs when the vibration mode changes and the sequence of unstable mode matches the linear analysis result. However, the natural frequency predicted using linear analysis differs from those obtained using nonlinear analysis.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.637-654
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• 2011

The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh's statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, "new" modes are found to be a combination of the subsystem's modes (two rotations, traslation) and the bare plate's modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate's modes enable distinct motions of the 3-DOF system contributing differently to the "new' modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.

• Steel and Composite Structures
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• v.21 no.1
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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.

• Journal of the Korean Society for Nondestructive Testing
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• v.21 no.2
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• pp.182-188
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• 2001

This paper presents the vibration characteristics of a rectangular plate with $45^{\circ}$ oblique crack subjected to a uniaxial tension. The experiment is adopted by the time-average Electronic Speckle Pattern Interferometry(ESPI) method. The natural frequency and mode shape are considered accurately according to the increase of tensile load. When tensile load is zero, the vibration modes we agreed with the smooth and the $45^{\circ}$ obliquely cracked plate. But according to the increasement of load it is shown that vibration modes are extremely varied. The effects of the crack under the vibration are discussed in detail. It is indicated that the increase of load makes the variation of the frequencies and modes complicate in the range of even a small load. The results are agreed with the FEM analysis within 5%.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.1
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• pp.172-178
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• 2003

Two types of bolted lap joints, one with a viscoelastic layer and the other without the viscoelastic layer were chosen to analyze the dynamic characteristics of the joints with the mechanical properties of the bolts in the joints are considered as computational variables. The finite element method was used along with the modal testing to verify the PEM model. The results in the bolted lap joints reveal that the higher the Young's modulus for the bolts we use the higher the natural frequencies we obtain fur the joints. However, the natural frequency differences in the first and second mode are not substantial but become noticeable in the higher modes. Lower natural frequencies were obtained for the bolted lap joints with the viscoelastic layer when compared with those of the bolted lap joints without the viscoelastic layer. And the differences in the natural frequencies for the two types of joints are relatively small in the first and second mode whereas in the higher mode the differences become significant. The loss factors were observed to be significant especially in the second mode for the bolted lap joints with the viscoelastic layer.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.624-629
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• 2001

Two types of bolted lap joints, one with a viscoelastic layer and the other without the viscoelastic layer were chosen to analyze the dynamic characteristics of the joints with the mechanical properties of the bolts of the joints being taken as computational variables. The finite element method was used along with the impact hammer technique to verify the FEM model. The results in the bolted lap joints reveal that the higher the Young's Modulus for the bolts are the higher the natural frequencies results for the joints. However, the natural frequency differences in the first and second mode are not substantial but become noticeable in the higher modes. Lower natural frequencies were obtained for the bolted lap joints with the viscoelastic layer when compared with those of the bolted lap joints without the viscoelastic layer. And the differences in the natural frequencies for the two types of joints are relatively small in the first and second mode whereas in the higher mode the differences become significant. The loss factors were observed to be significant especially in the second mode for the bolted lap joints with the viscoelastic layer.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.326-332
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• 1997

Recently to develop an automobile with better prosperities, many researches and investments have been executed. In this paper we intend to improve the automobile properties by reducing the weights of the engine without changing the dynamic characteristics. At first we perform the vibration analysis by the Substructure Synthesis Method and execute the exciting test for the engine model, and observe the coincidences of two results to confirm the reliability of the analyzing tools used. The weight minimization is performed by the Sensitivities of the Natural frequencies of the engine block. To decrease the engine weight ideally, the parts of the sensitivity zero are to be cut mainly, and the changing quantity of natural frequency by the cut is to be recovered by the structural modification for the parts with the good sensitivity. But, as actually the mathematical solution for the homogeneous problem(i.e. 0 object function) do not exist, we hereby redesign the block with much thinner thickness and recover the natural frequencies and natural modes to original structure's by the sensitivity analysis. And the Frequency Response Functions(FRF) are to be observed for the interesting points. In this analysis, the original thickness of the engine model has 8 mm of thickness, and the thickness redesigned is 5 mm and 6 mm. And we are to try to recover the 1, 2, 4, and 5 lower natural frequencies interested.

• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.691-709
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• 2012

This paper provides a variety of viewpoints to illustrate the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges. Based on the smooth and convergent bridge shapes obtained by the initial shape analysis, the one-element cable system (OECS) and multi-element cable system (MECS) models of the Kao Ping Hsi Bridge in Taiwan are developed to verify the applicability of the analytical model and numerical formulation from the field observations in the authors' previous work. For this purpose, the modal analysis of the two finite element models are conducted to calculate the natural frequency and normalized mode shape of the individual modes of the bridge. The modal coupling assessment is also performed to obtain the generalized mass ratios among the structural components for each mode of the bridge. The findings indicate that the coupled modes are attributed to the frequency loci veering and mode localization when the "pure" deck-tower frequency and the "pure" stay cable frequency approach one another, implying that the mode shapes of such coupled modes are simply different from those of the deck-tower system or stay cables alone. The distribution of the generalized mass ratios between the deck-tower system and stay cables are useful indices for quantitatively assessing the degree of coupling for each mode. These results are demonstrated to fully understand the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1580-1588
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• 1997

A modeling method for the flapwise bending vibration of a rotating cantilever beam which has small slenderness ratio is presented in this paper. It is shown that as the slenderness ratio decreases the shear and rotary inertia effects increase. Such effects become critical for the accurate estimation of the natural frequencies and modeshapes, especially higher frequencies and modes, as the angular speed increases. It is also shown that the flapwise bending natural frequencies are higher than the chordwise bending natural frequencies. The discrepancy between first natural frequencies are especially significant when the hub radius ratio is small.

• Journal of the Korea institute for structural maintenance and inspection
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• v.17 no.3
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• pp.20-27
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• 2013

Simple Iteration Method for calculating the natural frequency is presented in this paper. This method is simple but exact method of calculating natural frequencies corresponding to the modes of vibration of beams and tower structures with irregular cross sections and arbitrary boundary conditions. This method consists of determining the deflected mode shape of the member due to the inertia force under resonance condition. Finite difference method is used for this purpose. The influence of the $D_{22}$ stiffness on the natural frequency is rigorously investigated. In this paper, the influence of the loading sizes, different cross section on the natural frequency of vibration of some structural elements is presented. This method extends to two dimensional problems including advanced composite material structures.