• Journal of Korean Society of Steel Construction
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• v.12 no.4 s.47
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• pp.363-374
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• 2000

An accurate method is presented for vibrations of rhombic plates having three different combinations of clamped, simply supported, and free edge conditions. A specific feature here is that the analysis explicitly considers the moment singularities that occur in the two opposite corners having obtuse angles of the rhombic plates. Stationary conditions of single-field Lagrangian functional are derived using the Ritz method. Convergence studies of frequencies show that the corner functions accelerate the convergence rate of solutions. In this paper, accurate frequencies and normalized contours of the vibratory transverse displacement are presented for highly skewed rhombic plates, so that a significant effect of corner stress singularities nay be understood.

• Advances in concrete construction
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• v.8 no.1
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• pp.9-19
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• 2019

This paper describes an experimental investigation on hybrid fiber reinforced concrete (HYFRC) beams. And the main aim of this present paper is to examine the dynamic characteristics and damage evaluation of undamaged and damaged HYFRC beams under free-free constraints. In this experimental work, totally four RC beams were cast and analyzed in order to evaluate the dynamic behavior as well as static load behavior of HYFRCs. Hybrid fiber reinforced concrete beams have been cast by incorporating two different fibers such as steel and polypropylene (PP). Damage of HYFRC beams was obtained by cracking of concrete for one of the beams in each set under four-point bending tests with different percentage variation of damage levels as 50%, 70% and 90% of maximum ultimate load. And the main dynamic characteristics such as damping, fundamental natural frequencies, mode shapes and frequency response function at each and every damage level has been assessed by means of non-destructive technique (NDT) with hammer excitation. The fundamental natural frequency and damping values obtained through dynamic tests for HYFRC beams were compared with control (reference) RC beam at each level of damage which has been acquired through static tests. The static experimental test results emphasize that the HYFRC beam has attained higher ultimate load as compared with control reinforced concrete beam.

• Journal of the Society of Naval Architects of Korea
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• v.55 no.1
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• pp.37-44
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• 2018

To understand the dynamic characteristics of the vessel with hydroelastic response, it is very important to estimate the dynamic modal parameters such as mode shapes, natural frequency, and damping ratio. These dynamic modal parameters of full scale ship are a priori unknowns, hence to be estimated directly based upon the full scale measurement data. In this paper, dynamic modal parameters were extracted by signal processing of acceleration and strain data measured from a large container ship whose loading capacity is 9400TEU. The mode shapes of the vibrating hull were identified using the proper orthogonal decomposition and the vibration response of hull was decomposed into its modal magnitudes. Natural frequencies of specific modes were derived via Fourier transform of these modal magnitude. Also, the free decay signal of the vibrating hull was obtained through the random decrement technique and the damping ratio was estimated with accuracy.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.4
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• pp.329-335
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• 2014

This study aimed to understand the internal flow characteristics of a liquid droplet subject to periodic forced vibration. In order to predict the resonance frequency of a droplet, a high-speed camera and macro lens were used to capture internal flow characteristics of a droplet placed on a vibrating hydrophobic surface. Results showed that the droplet assumed a variety of shapes depending on the resonance mode of free droplet, particularly in modes 2, 4, 6, and 8. In addition, the induced internal vortex flow inside the droplet was also observed in each mode. Typically, the induced flow moved upwards along the axis of symmetry and downwards along the surface of the droplet, that is, from the apex to the contact line in modes 2 and 4, after which it broke into a smaller vortex. On the other hand, the large-scale vortex always remained steady in modes 6 and 8. The speed of the flow in mode 4 was always greater than that in mode 2, but those in modes 6 and 8 were similar.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.113-128
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• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• Bulletin of the Society of Naval Architects of Korea
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• v.14 no.1
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• pp.1-10
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• 1977

The major objects of this report are to supplement data of natural frequencies of thin elastic rectangular plates to the available data, and to give an experimental verification for natural frequencies obtained by Rayleigh-Ritz method, the generation set of which are eigenfunctions of Euler beams. For the first object the following five models, for which data only for the fundamental mode or data only for square plates are available, are adopted; (1) two opposed edges are clamped and the other two opposed edges simply supported (C-C, S-S), (2) one edge is simply supported and the other three edges clamped (C-C, C-S), (3) one edge is free and the other three edges clamped (C-C, C-F), (4) two adjacent edges are clamped and the other two adjacent edges free (C-F, C-F). For the (C-C, S-S) model the frequency equation obtained with the mode shapes assumed as of a single trigonometric series is solved. And for the other four models Rayleigh-Ritz method taking eigenfunctions of Euler beams as the generating set is applied. The numerical examples are obtained up to the fourth, the fifth or the sixth order depending on the range of the aspect ratio (0.1-10.0). The number of terms in the generating set for Rayleigh-Ritz method is fifteen for all models. For the experiment three models made of 3.2mm thickness mild steel plate for general structure use were prepared in following size; $300mm{\times}600mm,\;600mm{\times}600mm\;and\;900mm{\times}600mm$. Their boundary conditions are made to fit (C-C, C-F) condition. From the experiment mechanical impedance curves based on the frequency response method were obtained together with phase relation diagrams. The experimental data are resulted in good conformity to calculated values.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.399-407
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• 2002

A three-dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components$U_\Phi, U_z, U_\theta$ in the meridional, normal and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in$\theta$, and algebraic polynomials in the$\Phi$and z directions. Potential(strain) and kinetic energies of the entire body are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degrees of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations. Convergence to four digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.140-148
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• 1992

The free vibration problem of symmetrically laminated composite rectangular plates is formulated based on anisotropic thick plate theory including the effects of shear deformation and rotary inertia. Considering the difficulty of obtaining closed-form solutions, Rayleigh-Ritz analysis using polynomials having the property of Timoshenko beam functions as trial functions is adopted. The boundary conditions elastically restrained against rotation are accomodated as well as classical boundary conditions. From the results of numerical studies, the validity of the present method is verified. And it is also found that the adoption of thick plate theory for the vibration analysis of laminated composite plates is essential because of the relatively large shear deformation effect, and that the convergence of the Rayleigh quotient to the stationary value is less rapid in anisotropic composite plates than that in the orthotropic ones due to more complicated mode shapes of the former.

• Structural Monitoring and Maintenance
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• v.2 no.1
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• pp.1-18
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• 2015

Traditionally, it is not easy to carry out tests to identify modal parameters from existing railway bridges because of the testing conditions and complicated nature of civil structures. A six year (2007-2012) research program was conducted to monitor a group of 25 railway bridges. One of the tasks was to devise guidelines for identifying their modal parameters. This paper presents the experience acquired from such identification. The modal analysis of four representative bridges of this group is reported, which include B5, B15, B20 and B58A, crossing the Caraj$\acute{a}$s railway in northern Brazil using three different excitations sources: drop weight, free vibration after train passage, and ambient conditions. To extract the dynamic parameters from the recorded data, Stochastic Subspace Identification and Frequency Domain Decomposition methods were used. Finite-element models were constructed to facilitate the dynamic measurements. The results show good agreement between the measured and computed natural frequencies and mode shapes. The findings provide some guidelines on methods of excitation, record length of time, methods of modal analysis including the use of projected channel and harmonic detection, helping researchers and maintenance teams obtain good dynamic characteristics from measurement data.

• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.5
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• pp.9-13
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• 2009

Modal parameters including resonant frequencies and mode shapes are heavily utililized in most damage identification throries for structural health monitoring. However, extracting modal parameters from dynamic responses needs postprocessing which inevitably involves errors in curve-fitting resonants as well as transforming the domain of responses. In this paper, the applicability of a damage identification method based on free vibration responses to the in-sevice responses is experimentally verified. The experiment is performed via applying periodic and nonperiodic moving loads to a simply supported beam and displacement responses are measured. The moving load is simulated using steel balls and a downhill device. The damage identification results show that the in-service response may be applicable to identifying damage in the beam.