• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.95-112
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• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.04a
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• pp.144-149
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• 2012

The transfer matrix method is used to determine the dynamic characteristics(natural frequencies and mode shapes) by rotational speed of wind turbine blade. The problems treated on this study is coupled flapwise bending and chordwise bending of pre-twisted nonuniform wind turbine blade. The orthogonality relations that exist between the vibrational modes is derived and the algorithm for determination of the natural vibrational characteristics is suggested.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.745-749
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• 2001

The rigid body properties of a structure may be estimated easily if the mass-line of the structure could be taken exactly. However, the exact mass-line cannot be obtained experimentally. In the past years, the modal analysis for which the structure is mounted on the flexible supporter is frequently used to acquire the mass-line. Unfortunately, it is difficult not only to mount the structure but also to decouple the coupled 6 dof mode. If the structure is pended by very long and flexible rope to act free, the rigid-body modes influenced by the rope will be eliminated and the improved mass-line will be obtained. In this paper, the method using the mass-line of F.R.F. for rigid body in free-condition is suggested. The robustness of the suggested method was tested and verified numerically. The experimental results also showed a good agreement with the true value.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.12
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• pp.107-112
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• 2010

A gas turbine consists of an upstream compressor and a downstream turbine with a combustion chamber, and also the compressor and the turbine are generally coupled using a single shaft. Large scale gas turbine compressor is designed as multi-stage axial flow and the blade is fan-type which is thick and wide. Recently radial cracking happens occasionally at the compressor blade tip of large scale gas turbine. So, FEM was performed on the compressor blade and vibration modes and dynamic stresses were analyzed. According to the analysis, 9th natural frequency mode of the blade, which is 2 strip mode, is near the vane passing frequency by the vane located at the upstream of the blade.

• Journal of Power System Engineering
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• v.9 no.3
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• pp.58-65
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• 2005

This paper deals with the free vibrations of truncated conical shell with uniform thickness by the transfer influence coefficient method. The classical thin shell theory based upon the $Fl\ddot{u}gge$ theory is assumed and the governing equations of a conical shell are written as a coupled set of first order differential equations using the transfer matrix. The Runge-Kutta-Gill integration and bisection method are used to solve the governing differential equations and to compute the eigenvalues respectively. The natural frequencies and corresponding mode shapes are calculated numerically for the truncated conical shell with any combination of boundary conditions at the edges. And all boundary conditions and the intermediate supports between conical shell and foundation could be treated only by adequately varying the values of the spring constants. Numerical results are compared with existing exact and numerical solutions of other methods.

• Ocean Systems Engineering
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• v.10 no.3
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• pp.317-332
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• 2020

This study examines the behaviors and properties of discharged liquid CO₂ from a long elastic pipe moving with a vessel for the oceanic CO₂ sequestration by considering pipe dynamics and vessel motions. The coupled vessel-pipe dynamic analysis for a typical configuration is done in the frequency and time domain using the ORCAFLEX program. The system's characteristics, such as vessel RAOs and pipe-axial-velocity transfer function, are identified by applying a broadband white noise wave spectrum to the vessel-pipe dynamic system. The frequency shift of the vessel's RAO due to the encounter-frequency effect is also investigated through the system identification method. Additionally, the time histories of the tip-of-pipe velocities, along with the corresponding discharged droplet size and Weber numbers, are generated for two different sea states. The comparison between the stiff non-oscillating pipe with the flexible oscillating pipe shows the effect of the vessel and pipe dynamics to the discharged CO₂ droplet size and Weber number. The pipe's axial-mode resonance is the leading cause of the fluctuation of the discharged CO₂ properties. The significant variation of the discharged CO₂ properties observed in this study shows the importance of considering the vessel-pipe motions when designing oceanic CO₂ sequestration strategy, including suitable sequestration locations, discharge rate, towing speed, and sea states.

• The Journal of the Acoustical Society of Korea
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• v.34 no.3
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• pp.219-226
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• 2015

In this paper, derivation of the STL (Sound Transmission Loss) of a square plate installed in an impedance tube is discussed using an analytic method. Coupled motion of the plate vibration and acoustic field is considered. Vibration of the plate and pressure field inside the tube are expressed in terms of the infinite series of modal functions. Under the plane wave assumption, it is shown that consideration of the first few modes yields sufficiently accurate results. When the boundary of the plate is clamped, vibration mode is assumed as a multiplication of the beam modes corresponding to the crosswise directions. The natural frequencies of the clamped plate are calculated using the Rayleigh-Ritz method. It is found that the STL shows a dip at the lowest natural frequency of the plate, and increases as the frequency decreases below the natural frequency. Comparison of the result in this paper with the STL obtained by measurements and FE computations in the reference shows an excellent agreement.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.2
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.9
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• pp.935-942
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• 2009

In this paper, the purpose is to investigate the natural frequency of a cracked Timoshenko cantilever beams by FEM(finite element method) and experiment. In addition, a method for detection of crack in a cantilever beams is presented based on natural frequency measurements. The governing differential equations of a Timoshenko beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The detection method of a crack location in a beam based on the frequency measurements is extended here to Timoshenko beams, taking the effects of both the shear deformation and the rotational inertia into account. The differences between the actual and predicted crack positions and sizes are less than 6 % and 23 % respectively.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.3 s.258
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• pp.331-337
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• 2007

Rotating cantilever beams can be found in several practical engineering applications such as turbine blades and helicopter rotor blades. For reliable and economic design, it is necessary to estimate the dynamic characteristics of those structures accurately and efficiently since significant variation of dynamic characteristics resulted from rotational motion of the structures. Recently, Differential Transformation Method(DTM) was proposed by Zhou. This method has been applied to fluid dynamics and vibration problems, and has shown accuracy, efficiency and convenience in solving differential equations. The purpose of this study, the free vibration analysis of a rotating cantilever beam, is to seek for the reliable property of DTM and confidence in the results obtained by this method by comparing the results with that of finite element method applied to linear partial differential equations. In particular, this study is worked by supposing optional T-function values because the equations governing chordwise motion are based on two differential equations coupled with each other. This study also shows mode shapes of rotating cantilever beams for various rotating speeds.