• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2812-2818
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• 1996

A cantilever beam with a mass and a spring at the end can be use to model a miniature flexible arm. It is necessary to know the natural frequencies and mode shapes to discuss its free vibration, especially when modal analysis is employed. A beam is clamped-free. In this paper we look at the lateral vibration of beams that have step changes in the properties of their cross sections. The frequency equation is derived by Bernoulli-Euler formulation and is sloved by the separation of variable. The parameters of the beam, 'mass and spring stiffness' are defined as nondimensionalized parameters for wide application of the results. According to the change of eigenvalues and mode shape are presented for this beam. The results presented are the eigenvalues and the natural frequencies for the first three modes of vibration. Results show that the parameters have a significant effect on the natural frequency.

• Steel and Composite Structures
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• v.19 no.3
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• pp.635-659
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• 2015

In this study, natural frequency analysis of a large deflected cantilever laminated composite beam fixed at both ends, which forms the case of a pre-stressed curved beam, is investigated. The laminated beam is considered to have symmetric and asymmetric lay-ups and the effective flexural modulus of the beam is used in the analysis. In order to obtain the pre-stressed composite curved beam case, an external vertical concentrated load is applied at the free end of a cantilever laminated composite beam and then the loading point of the deflected beam is fixed. The non-linear deflection curve of the flexible beam undergoing large deflection is obtained by the Reversion Method. The curved laminated composite beam is modeled by using the Finite Element Method with a straight-beam element approach. The effects of orientation angle and vertical load on the natural frequency parameter for the first four modes are examined and the results obtained are given in graphics. It has been found that the effect of the load parameter, which forms the curved laminated beam, on the natural frequency parameter, almost disappears after a certain value of the load parameter. This certain value differs for each laminated curved beam and each vibration mode.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.6
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• pp.49-56
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• 2000

Due to the rapid increase of long-distance transportation, particular attentions have been paid to truck tires, especially to their dynamic characteristics. In this research, experimental modal analysis on two kinds of light-duty truck tires, i.e., radial tire and bias tire, are performed by using GRFP(global rational fraction polynomial) method to investigate differences of the dynamic behavior of the two tires. The test results have shown that the modal frequencies of bias tire are much higher than the corresponding values of radial tire with a similar mode shape, which is in accordance with the fact that the radial rigidity of bias tire is higher than that of radial tire. And most of the modal decay rates of bias tire are larger than those of radial tire within the scope of this experiment. In the frequency domain range of test, the bias tire has extra modes, which do not occur in the radial tire. This difference is based on the fact that the circumferential rigidity of the bias tire is quire low whereas that of radial tire is so high that the frequencies of the corresponding modes are out of the frequency range of test.

• Journal of the Korean Institute of Gas
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• v.20 no.6
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• pp.58-64
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• 2016

Vibrational characteristics of curved pipe structures are investigated with respect to the change of inside flow velocities. Based upon the Hamilton's principle, the equations of motions are derived, and the finite element equation is constructed to solve the frequency equation for curved pipe structures. When the initial tension is neglected in cured pipes, the natural frequencies are reduced as flow velocity increases, and the rapid decreases of the natural frequencies take place. However, when the initial tension is taken into account, the natural frequencies are not changed with the change of the flow velocity. In free vibrational simulation of pipe systems, it is necessary to calculate the initial force due to the velocity and the pressure of the fluid flow from the equilibrium. The force should be included in the equation of motion of the systems to get more accurate natural frequencies. The mechanical properties like stiffness or the location of pipe support need to be changed to avoid resonance. The natural frequencies are to be isolated from the frequency range of dominant vibration modes. The angles of elbows do not affect the change of the fundamental natural frequency, but affect the change of the third or higher natural frequencies.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.6
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• pp.36-42
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• 2010

In this study, the deformation and stress are analyzed through modal and harmonic response analysis at resonance on leaf spring. The displacement range of 7 to 14 mm is shown at natural frequencies as 6 kinds of resonance modes. The maximum deformation is shown as 8.8781mm at Mode 2. The maximum displacement and stress at leaf spring are shown as 0.0458 mm and 72.533 MPa respectively on 1200 Hz. The comfortability of passenger becomes better on leaf spring at suspension system by use of this design model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2174-2181
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• 1996

Equations of chordwise and flapwise bending motions of pretwisted rotatin cantilever beams are derived. The two motions are coupled to each other due to the pretwist angle of the beam cross section. As the angular speed, hub radius ratio, and pretwist angle vary, the vibration characteristics of the beam change. It is found that engenvalue loci veering phenomena and associated mode shape variations occur between two vibration modes due to the pretwist angle. The effect of the pretwist angle on the critical angular speed is also investigated.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.220-223
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• 2000

A method of calculating the natural frequency corresponding to the modes of vibration of beams and tower structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the three span continuous reinforced concrete bridge with elastic intermediate supports is presented. Such bridge represents either concrete or sandwich type three span bridge on polymeric supports for passive control or on actuators for active control The concrete slab is considered as a special orthotropic plate. The influence of the modulus of the foundation and $D_{22}$, $D_{12}$, $D_{66}$ stiffnesses on the natural frequency is thoroughly studied.

• Steel and Composite Structures
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• v.8 no.4
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• pp.265-280
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• 2008

An investigation on the combined effect of foundation type, foundation flexibility, axial load and PR (semi-rigid) connections on the natural frequencies of steel frames is presented. These effects were investigated using a suitable modified FE program for cases where the foundation flexibility, foundation connectivity, and semi-rigid connections could be treated as equivalent linear springs. The effect of axial load on the natural frequency of a structure was found to be significant for slender structures subjected to high axial loads. In general, if columns of medium slenderness are designed without consideration of axial load effects, the frequency of the structure will be overestimated. Studies on the 3-story Los Angeles PR SAC frame indicate that the assumption of rigid connections at beam-column and column-base interfaces, as well as the assumption of a rigid foundation, can lead to significant errors if simplified design procedures are used. These errors in an equivalent static analysis are expected to lead to even more serious problems when considering the effect of higher modes under a non-linear dynamic analysis.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.34-39
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• 2015

Experimental studies were conducted on the liquid sloshing characteristics in a spherical tank covered with a flexible membrane. A spherical acrylic tank with 145.2 mm in radius was used as a test tank, and it was half-filled with water. Silicon membranes with 0.2 mm thickness were used as a test membrane with plane or hemispherical types. The test tank was harmonically excited in a vertical direction by an electro-dynamic exciter. In this case, a parametric instability vibration comes up when the excitation frequency is twice the natural frequency. Parametric instability regions of natural modes were measured for three cases, i.e. liquid surface is free, covered with plane membrane and hemi-spherical membrane.

• Tribology and Lubricants
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• v.32 no.4
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• pp.107-112
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• 2016

This paper presents a rotordynamic analysis of the reduction gear system applied to the 250 kW super critical CO₂ cycle. The reduction gear system consists of an input shaft, intermediate shaft, and output shaft. Because of the high rotating speed of the input shaft, we install tilting pad bearings, rolloer bearings support the intermediate and output shafts. To predict the tilting pad bearing performance, we calculate the applied loads to the tilting pad bearings by considering the reaction forces from the gear. In the rotordynamic analysis, gear mesh stiffness results in a coupling effect between the lateral and torsional vibrations. The predicted Campbell diagram shows that there is not a critical speed lower than the rated speed of 30,000 rpm of the input shaft. The predicted modes on the critical speeds are the combined bending modes of the intermediate and output shaft, and the lateral vibrations dominate when compared to the torsional vibrations. The damped natural frequency does not strongly depend on the rotating speeds, owing to the relatively low rotating speed of the intermediate and output shaft and constant stiffness of the roller bearing. In addition, the logarithmic decrements of all the modes are positive; therefore all modes are stable.