• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.767-780
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• 2015

Delaminations and cracks are common failures in structures. They may significantly reduce the stiffness of the structure and affect their vibration characteristics. In the present study, an analytical solution is developed to study the effect of an edge crack on the vibration characteristics of delaminated beams. The rotational spring model, the 'free mode' and 'constrained mode' assumptions in delamination vibration are adopted. This is the first study on how an edge crack affects the vibration characteristic of delaminated beams and new nondimensional parameters are developed accordingly. The crack may occur inside or outside the delaminated area and both cases are studied. Results show that the effect of delamination length and thickness-wise location on reducing the natural frequencies is aggravated by an increasing crack depth. The location of the crack also influences the effect of delamination, but such influence is different between crack occurring inside and outside the delaminated area. The difference of natural frequencies between 'free mode' and 'constrained mode' increases then decreases as the crack moves from one side of the delaminated region to the other side, peaking at the middle. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.

• 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.57 no.3
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• pp.543-567
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• 2016

This study attempts to address the buckling and free vibration characteristics of an isotropic cylindrical panel subjected to non-uniform temperature rise using numerical approach. Finite element analysis has been used in the present study. The approach involves three parts, in the first part non-uniform temperature field is obtained using heat transfer analysis, in the second part, the stress field is computed under the thermal load using static condition and, the last part, the buckling and pre-stressed modal analysis are carried out to compute critical buckling temperature as well as natural frequencies and associated mode shapes. In the present study, the effect of non-uniform temperature field, heat sink temperatures and in-plane boundary constraints are considered. The relation between buckling temperature under uniform and non-uniform temperature fields has been established. Results revealed that decrease (Case (ii)) type temperature variation field influences the fundamental buckling mode shape significantly. Further, it is observed that natural frequencies under free vibration state, decreases as temperature increases. However, the reduction is significantly higher for the lowest natural frequency. It is also found that, with an increase in temperature, nodal and anti-nodal positions of free vibration mode shapes is shifting towards the location where the intensity of the heat source is high and structural stiffness is low.

• Journal of Power System Engineering
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• v.9 no.4
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• pp.71-76
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• 2005

Marine structures are often in contact with inner or outer fluid as stern, ballast and oil tanks. The effect of interaction between fluid and structure has to be taken into consideration when we estimate the dynamic response of the structure appropriately. Fatigue damages can also be sometimes observed in these tanks which seem to be caused by resonance. Thin walled tank structures in ships which are in contact with water and located near engine or propeller where vibration characteristics are strongly affected by the added mass of containing water. Therefore it is essentially important to estimate the added mass effect to predict vibration characteristics of tank structures. But it is difficult to estimate exactly the magnitude of the added mass because this is a fluid-structure interaction problem and is affected by the free surface, vibration modes of structural panels and the depth of water. I have developed a numerical tool of vibration analysis of 3-dimensional tank structure using finite elements for plates and boundary elements for fluid region. In the present study, the effect of added mass of containing water, the effect of structural constraint between panels on the vibration characteristics are investigated numerically and discussed. Especially a natural frequencies by the fluid interaction between 2 panels and a breath mode of the water tank are focused on.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.04a
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• pp.336-342
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• 1997

In this paper, in order to analyze dynamic characteristics of automobile steering system consisting of many components, natural frequencies and transfer functions of each component and total system are found on FFT by experiments. Then, the data are transmitted to commercial package program, CADA-PC. By analyzing the data, the mode shape of each natural frequency and damping values are obtained. Also, the function of rubber coupling in column and telescoping effects on system are considered. C.A.E commercial program are used to compare with the results of experiments. For finite element modeling, I-DEAS is used. Data processing and post processing are operated on NASTRAN and XL, respectively. The ball-bearing and the linkage of shaft with column are modeled by spring elements. Stiffness is modified from the results of experiments. The results of those show close agreement. In the mode shape of total system, wheel mode is dominant at lower frequency while the column mode is main mode at higher . The role of rubber coupling in vibration isolation is clear on mode shape. Telescoping function makes natural frequency of column changed.

• Journal of KSNVE
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• v.11 no.2
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• pp.323-328
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• 2001

The paper describes a theoretical study on the flexural vibration of an elastic rectangular plate with periodically nonuniform material properties. The approximate solution of the natural frequency and mode shape has been obtained using the perturbation technique for sinusoidal modulation of the flexural rigidity and mass density. It has been shown that distributed modes exist in the plate which Is a two-dimensional model of the flat panel speaker.

• International Journal of Naval Architecture and Ocean Engineering
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• v.5 no.3
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• pp.478-491
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• 2013

Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved.

• Structural Engineering and Mechanics
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• v.9 no.3
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• pp.269-288
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• 2000

The governing differential equations for free vibration of multi-step orthotropic shear plates with variably distributed mass, stiffness and viscous damping are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jk-th natural frequency of a shear plate is equal to the square root of the square sum of the j-th natural frequency of a shear bar and the k-th natural frequency of another shear bar. The jk-th mode shape of the shear plate is the product of the j-th mode shape of a shear bar and the k-th mode shape of another shear bar. The general solutions of the governing equations of the orthotropic shear plates with various boundary conditions are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. A numerical example demonstrates that the present methods are easy to implement and efficient. It is also shown through the numerical example that the selected expressions are suitable for describing the distributions of stiffness and mass of typical multi-storey buildings.

• Journal of Aerospace System Engineering
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• v.16 no.4
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• pp.88-94
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• 2022

The vibration mode measurement test measures the natural vibration characteristics of the target specimen. The measured natural mode characteristics are compared with the numerical analysis result to verify the reliability of the numerical analysis. If necessary, it is used to supplement the numerical analysis model of the specimen used for the dynamic characteristic analysis. In this paper, the natural frequency and natural mode of the external fuel tank are respectively obtained through the vibration mode measurement test and the numerical analysis, using the finite element model. The results are compared to verify the reliability of the numerical analysis model of the external fuel tank to apply to the entire aircraft model. To measure the vibration mode of the test specimen, a bungee cord was used, to simulate the free boundary condition for the test specimen. And, 3-axis accelerometers were installed on the test specimen. The response characteristics of the test specimen were measured, by excitation with an impact hammer. As a result of the test, after performing the frequency response analysis on the response acceleration, the natural frequency of the test specimen and its vibration mode were confirmed. The reliability of the numerical analysis model was verified by comparing the frequency and vibration mode, obtained through the test and the numerical analysis.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1899-1909
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• 1994

This work presents the experimental and FEM results for the free vibration of cantilevered, symmetrically and antisymmetrically laminated composite rectangular plates. The natural frequencies, mode shapes and contour plots of a number of CFRP, GFRP, DFRP-Aluminum, GFRP-Aluminum and DFRP-GFRP hybrid composite plates are experimentally obtained. Determination of Young's modulus and test procedures are described. The natural frequencies are determined for a wide range of parameters : e.g. , composite material constants, fiber angles and stacking sequences. Natural frequency and nondimensional frequency parameter results are compared with the finite element analysis and existing literatures. Agreement between experimental and calculated frequencies is excellent. The effects of varing the parameters upon the free vibration frequencies and mode shapes are discussed.