• 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.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.137-149
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• 2014

In this study, modal parameters such as natural frequencies, mode shapes and damping ratios of RC frames with low strength are determined for different construction stages using ambient vibration test. For this purpose full scaled, one bay and one story RC frames are produced and tested for plane, brick in-filled and brick in-filled with plaster conditions. Measurement time, frequency span and effective mode number are determined by considering similar studies and literature. To obtain experimental dynamic characteristics, Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification techniques are used together. It is shown that the ambient vibration measurements are enough to identify the most significant modes of RC frames. The results indicate that modal parameters change significantly depending on the construction stages. In addition, Infill walls increase stiffness and change the mode shapes of the RC frame. There is a good agreement between mode shapes obtained from brick in-filled and in-filled with plaster conditions. However, some differences are seen in plane frame, like expected. Dynamic characteristics should be verified using finite element analysis. Finally, inconsistency between experimental and analytical dynamic characteristics should be minimize by finite element model updating using some uncertain parameters such as material properties, boundary condition and section properties to reflect the current behavior of the RC frames.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.840-840
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• 2003

Operational Modal Analysis (OMA) is a technique for identification of modal parameters by measurement of only the system's response. On many lightweight structures, such as load-speaker cones and disk drive read/write heads, is impossible or impractical to measure the input forces. Another characteristic of lightweight structure is their sensitivity to mass loading from sensors. The Scanning Laser Doppler Vibrometry(SLDV) allows response measurements to be taken without mass loading. One disadvantage of OMA testing compared to tradition input output modal testing is the OMA mode shapes are un-scaled. This means that the mode shape obtained from an OMA test can not used for analytical structural modification studies. However, the un-scaled mode shapes from an OMA test can be used to update a Finite Element Model (FEM). The updated FEM can then be used to analytically predict the effect of structural modifications. This paper will present the results of an OMA test performed on a simple plate and motor in operating conditions. The un-scaled mode shapes from this test will be used to update a FEM model of the system. The updated FEM model will be then be used to predict the effect of attaching a mass to the plate. The shapes predicted by the FEM for the modified system will be compared to a second OMA test on the modified system

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.4
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• pp.148-156
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• 2001

Brake judder, one of low Sequency vibrations in brake system is determined by the excitation of Brake Torque Variation (BTV). The largest contributor to BTV is disc thickness variation. In this study, the static loads of brake torque at Suspension Mounting Points (SW) are obtained by the quasi-static analysis using DADS. The dynamic loads with frequency of BTV at SW are derived from correlation between forced vibration analysis with static loads and brake test results. And the accelerations at steering wheel were analyzed by forced vibration analysis with dynamic loads using commercial finite element program MSC/NASTRAN so that vibration characteristics of vehicle due to brake judder were investigated. Reliability of analysis results was verified through comparing the brake test results. Also, a parametric study with natural frequencies of frame, such as the 1st torsional mode and 1st bending mode, was conducted to reduce vibration amplitudes. As a result we could detect frame natural frequency conditions to improve vibration characteristics and obtained the frame model to reduce vibration amplitude.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.3
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• pp.117-125
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• 1991

Two methods are presented to calculate the natural frequency of an elastic thin circular cylindrical shell vibrating in fluid. Both of them give the natural frequency in analytical expression One is in a simple form and suitable for higher deformation mode of the shell. Another seems to be exact and be used to a case of the shell partially immersed in fluid. When the shell is fully immersed in fluid results show： fur the lower deformation mode of the shell, the surrounding fluid has remarkable effect upon the natural frequency； for the higher mode, the fluid effect becomes small. When the shell is partially immersed in fluid. it does not occur always that the greatest effect take place at the lowest deformation mode.

• Structural Engineering and Mechanics
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• v.21 no.3
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• pp.351-367
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• 2005

Multi-span beams carrying multiple point masses are widely used in engineering applications, but the literature for free vibration analysis of such structural systems is much less than that of single-span beams. The complexity of analytical expressions should be one of the main reasons for the last phenomenon. 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-span uniform beam carrying multiple point masses. First, the coefficient matrices for an intermediate pinned support, an intermediate point mass, left-end support and right-end support of a uniform beam are derived. Next, the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the related eigenfunctions respectively. The effects of in-span pinned supports and point masses on the free vibration characteristics of the beam are also studied.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.357-372
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• 2001

In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations, exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz method is also applied to determine the natural frequencies and mode shapes in the vertical direction for cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this paper are simple and convenient for engineering applications. Numerical example shows that the fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the proposed methods are in good agreement with the corresponding measured data. It is also shown that the selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall buildings.

• Journal of Power Electronics
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• v.10 no.2
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• pp.115-124
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• 2010

In this paper, a simple yet efficient auto mode-hop ripple control structure for buck converters with light load operation enhancement is proposed. The converter, which operates under a wide range of input and output voltages, makes use of a state-dependent hysteretic comparator. Depending on the output current, the converter automatically changes the operating mode. This improves the efficiency and reduces the output voltage ripple for a wide range of output currents for given input and output voltages. The sensitivity of the output voltage to the circuit elements is less than 14%, which is seven times lower than that for conventional converters. To assess the efficiency of the proposed converter, it is designed and implemented with commercially available components. The converter provides an output voltage in the range of 0.9V to 31V for load currents of up to 3A when the input voltage is in the range of 5V to 32V. Analytical design expressions which model the operation of the converter are also presented. This circuit can be implemented easily in a single chip with an external inductor and capacitor for both fixed and variable output voltage applications.

• Journal of Ocean Engineering and Technology
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• v.27 no.5
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• pp.43-50
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• 2013

In the present investigation, the hydrodynamic characteristics of a vertically floating hollow cylinder in regular waves have been studied. The potential theory for solving the diffraction and radiation problem was employed by assuming that the heave response motion was linear. By using the matched eigenfunction expansion method, the characteristics of the exciting forces, hydrodynamic coefficients, and heave motion responses were investigated with various system parameters such as the radius and draft of a hollow cylinder. In the present analytical model, two resonances are identified: the system resonance of a hollow cylinder and the piston-mode resonance in the confined inner fluid region. The piston resonance mode is especially important in the motion response of a hollow circular cylinder. In many cases, the heave response at the piston resonance mode is large, and its resonant frequency can be predicted using the empirical formula of Fukuda (1977). The present design tool can be applied to analyze the motion response of a spar offshore structure with a moon pool.

• Wind and Structures
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• v.17 no.3
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• pp.275-298
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• 2013

This paper presents a number of approximated analytical formulations for the flutter analysis of long-span bridges using the so-called uncoupled flutter derivatives. The formulae have been developed from the simplified framework of a bimodal coupled flutter problem. As a result, the proposed method represents an extension of Selberg's empirical formula to generic bridge sections, which may be prone to one of the aeroelastic instability such as coupled-mode or single-mode (either dominated by torsion or heaving mode) flutter. Two approximated expressions for the flutter derivatives are required so that only the experimental flutter derivatives of ($H_1^*$, $A_2^*$) are measured to calculate the onset flutter. Based on asymptotic expansions of the flutter derivatives, a further simplified formula was derived to predict the critical wind speed of the cross section, which is prone to the coupled-mode flutter at large reduced wind speeds. The numerical results produced by the proposed formulas have been compared with results obtained by complex eigenvalue analysis and available approximated methods show that they seem to give satisfactory results for a wide range of study cases. Thus, these formulas can be used in the assessment of bridge flutter performance at the preliminary design stage.