• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.709-729
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• 2004

This paper presents numerical and experimental investigations on damage detection of mono-coupled multistory buildings using natural frequency as only diagnostic parameter. Frequency equation of a mono-coupled multistory building is first derived using the transfer matrix method. Closed-form sensitivity equation is established to relate the relative change in the stiffness of each story to the relative changes in the natural frequencies of the building. Damage detection is then performed using the sensitivity equation with its special features and minimizing the norm of an objective function with an inequality constraint. Numerical and experimental investigations are finally conducted on a mono-coupled 3-story building model as an application of the proposed algorithm, in which the influence of modeling error on the degree of accuracy of damage detection is discussed. A mono-coupled 10-story building is further used to examine the capability of the proposed algorithm against measurement noise and incomplete measured natural frequencies. The results obtained demonstrate that changes in story stiffness can be satisfactorily detected, located, and quantified if all sensitive natural frequencies to damaged stories are available. The proposed damage detection algorithm is not sensitive to measurement noise and modeling error.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.366-375
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• 1991

In this study, vibrational behavior of uniform pipe carrying a moving medium is studied by using a transfer matrix and the displacement function derived from the conventional beam theory. In various boundary conditions, flow velocity and mechanical property change of the variation of natural frequency are investigated. The Coriolis term in the original differential equation of motion has been ignored in the investigation. This method is used to study the variation of natural frequency with flow velocity for clamped-clamped, cantilevered, clamped-pinned, pinned-pinned, free-free straight pipe element. It is shown that clamped-clamped, free-free pipe have the highest natural frequency and critical velocity values while cantilevered pipe have the smallest natural frequency for the same mechanical properties. From the vibration effects of mechanical property variation, it is shown that bending stiffness and pipe length variation has large influence on natural frequency and critical velocity. Since the order of transfer matrix is not changed with boundary conditions of pipe element, this method proposed can be easily applied to personal-computer for vibration analysis of pipe element. Furthermore, this method can be extended to three-dimensional system by using a coordinate transformation for the analysis of piping systems.

• Structural Engineering and Mechanics
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• v.46 no.2
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• pp.269-294
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• 2013

This paper is concerned with the determination of exact buckling loads and vibration frequencies of variable thickness isotropic plates using well known finite difference technique. The plates are subjected to uni, biaxial compression and shear loadings and various combinations of boundary conditions are considered. The buckling load is found out as the in plane load that makes the determinant of the stiffness matrix equal to zero and the natural frequencies are found out by carrying out eigenvalue analysis of stiffness and mass matrices. New and exact results are given for many cases and the results are in close agreement with the published results. In this paper, like finite element method, finite difference method is applied in a very simple manner and the application of boundary conditions is also automatic.

• Proceedings of the KSR Conference
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• 2000.11a
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• pp.358-365
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• 2000

For the general case of loading conditions and boundary conditions, it is very difficult to obtain closed form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. In consequence, most of previous finite element formulations are introduce approximate displacement fields to use shape functions as Hermitian polynomials, and so on. The Purpose of this study is to presents a consistent derivation of exact dynamic stiffness matrices of thin-walled straight beams, to be used ill tile free vibration analysis, in which almost types of boundary conditions are exist An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element of nonsymmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequency is evaluated for the thin-walled straight beam structure, and the results are compared with analytic solutions in order to verify the accuracy of this study.

• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.1-9
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• 1976

Using the computer programs for calculation of natural vibrations of ship's hull developed by the authors et al., an investigation into influences of various parameters on the accuracy of calculation was done through example calculations of a 30,000 DWT petroleum products carrier M/S Sweet Brier built by Korea Shipbuilding and Engineering Corporation. The methodical principles employed for the computer program development are as follows; (a) the ship system is reduced to an equivalent discrete elements system conforming to Myklestad-Prohl model, (b) the problem formulation is of transfer matrix method, and (c) to obtain solutions an extended $G\ddot{u}mbel's$ initial value method is introduced. The scope of the investigation is influences of number of discrete elements, choice of significant system parameters such as rotary inertia, bending stiffness and shear stiffness, and simplification of distributions of added mass and stiffness as trapezoidal ones referred to those of midship section on the calculation accuracy. From the investigation the followings are found out; (1) To obtain good results for the modes up to the seven-noded thirty or more divisions of the hull is desirable. For fundamental mode fifteen divisions may give fairly good results. (2) The influence of rotary inertia is negligibly small at least for the modes up to the 5- or 6- noded. (3) In the case of assuming either bending modes or shear modes the calculation results in considerably higher frequencies as compared with those based on Timoshenko beam theory. However, the calculation base on the slender beam theory surprisingly gives frequencies within 10% error for fundamental modes. (4) It is proved that to simplify distributions of added mass and stiffness as trapezoidal ones referred to those of midship section is a promising approach for the prediction of natural frequencies at preliminary design stage; provided good accumulation of data from similar type ships, we may expect to obtain natural frequencies within 5% error.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.11
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• pp.2033-2048
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• 1992

This paper presents the theoretical development and qualitative evaluation of a new concept in the mathematical modeling of dynamic structures. We use both test data and analytical approximations to identify the parameters of an incomplete model. The model has the capability of predicting the response of the points of interest on the structure over the frequency range of interest and can be used to predict the changes in natural frequencies and normal modes due to structural changes. The theory was tested by running simulated tests on a relatively simple structure, identifying the parameters of the incomplete model, and using this model to predict the effects on frequency and mode shapes of several mass and stiffness changes. The conditions of the tests were varied by selecting different numbers of points of measurement, varying the frequency range, and by including assumed measurement error. It is recommended that the theoretical development be continued and that applications to more complex structures be carried out in order to develop a better understanding of the limitations and capabilities of the method. A successful, more definitive sevaluation could lead to immediate practical applications.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.11 s.170
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• pp.1912-1921
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• 1999

The equipments mounted on guided-missile undertake heavy vibrational disturbance. Sometimes the equipments mounted on guided-missile go wrong so that the guided-missile flies over unintended place. For the vibration isolation of the equipments mounted on guided-missile, active vibration control was performed. In the case of active vibration technique, the stiffness matrix and the mass matrix are derived based on FEM (ANSYS5.0). Model reduction was carried out and, as a result, we got 7 DOF mass and stiffness matrix. For the sake of FEM model identification, modal experiment was carried out. With the help of Sensitivity Analysis, the natural frequencies of FEM were tuned to those of Experiment. In this work, the Sky Hook and the LQG control theory were adopted for v iteration control using stacked piezoactuator. Experiments were performed with changing excitation frequency from 10 Hz upto 200 Hz and we got frequency response function of guided-missile equipments. The magnitude of 3rd mode of guided-missile equipments is 8.6 % that of Uncontrolled in Skyhook controller and is 3.4 % that of uncontrolled in LQG controller.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1053-1060
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• 2006

This paper consider an initially deformed state caused by the pressurized fluid flowing through the pipe at a constant velocity. When the initial forte is neglected in curved pipes, the natural frequencies are reduced as flow velocity increases. However, when the initial tension took into account, the natural frequencies are not changed with the change of the flow velocity. As the internal pipe pressure is increased the natural frequencies are also slightly increased. In free vibrational simulation of piping systems in petrochemical plants, it is necessary to calculate the initial state force due to the velocity and the pressure of the fluid flow from the equilibrium first, then the force should be included in the equation of motion of the systems to get more accurate natural frequencies. In this study, calculate the mass matrix and stiffness matrix of piping system by MATLAB

• Journal of the Korean Society for Railway
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• v.7 no.3
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• pp.239-244
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• 2004

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics may provide very accurate solutions, together with drastically reducing the number of degrees of freedom to improve the computation efficiency and cost problems. Thus, this paper develops a spectral element model for the coupled thermoelastic beam which axially moves with constant speed under a uniform tension. The accuracy of the spectral element model is then evaluated by comparing the natural frequencies obtained by the present element model with those obtained by the conventional finite element model.

• Structural Engineering and Mechanics
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• v.47 no.3
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• pp.345-359
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• 2013

For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius' scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.