• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.21-46
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• 2011

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

• Journal of the Korean Chemical Society
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• v.21 no.5
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• pp.362-371
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• 1977

In this paper application of the projection operator technique to the study of NMR absorption line shape and free induction decay curve is explored. It is found that the projection operator technique can provide a convenient means for deriving a set of hierarchy equations which may serve as a good starting point for theoretical calculation of the absorption line and free induction decay function by successive approximation or by an appropriate decoupling approximation. A brief review of linear response theory of NMR line shape and the relation between the absorption line shape and free induction decay function are also described.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Journal of KSNVE
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• v.8 no.6
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• pp.1130-1136
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• 1998

A modelling method for the vibration analysis of rotating cantilever plates with a concentrated mass is presented. The equations of motion for the rotating plates with a concentrated mass located in an arbitrary position are derived and transformed into a dimensionless form. For the mathematical modelling of the concentrated mass. a mass density Dirac delta function is used. The effects of concentrated mass and its location. angular speed. plate aspect ratio. and hub radius of the rotating plate on the natural frequencies are studied. Particularly. mode shape variations due to some parameter variations are investigated.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.304-309
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• 2003

In this study, natural flaws in welding parts are classified using the signal pattern classification method. The storage digital oscilloscope including FFT function and enveloped waveform generator is used and the signal pattern recognition procedure is made up the digital signal processing, feature extraction, feature selection and classifier design. It is composed with and discussed using the distance classifier that is based on euclidean distance the empirical Bayesian classifier. Feature extraction is performed using the class-mean scatter criteria. The signal pattern classification method is applied to the signal pattern recognition of natural flaws.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.115-136
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• 2014

In this study, an extended Kantorovich method, employing multi-term displacement functions, is applied to analyze the vibration problem of symmetrically laminated plates with arbitrary boundary conditions. The vibration behaviors of laminated plates are determined based on the variational principle of total energy minimization and the iterative Kantorovich method. The out-of-plane displacement is represented in the form of a series of a sum of products of functions in x and y directions. With a known function in the x or y directions, the formulation for the variation of total potential energy is transformed to a set of governing equations and a set of boundary conditions. The equations and boundary conditions are then numerically solved for the natural frequency and vibration mode shape. The solutions are verified with available solutions from the literature and solutions from the Ritz and finite element analysis. In most cases, the natural frequencies compare very well with the reference solutions. The vibration mode shapes are also very well modeled using the multi-term assumed displacement function in the terms of a power series. With the method used in this study, it is possible to solve the angle-ply plate problem, where the Kantorovich method with single-term displacement function is ineffective.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.5
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• pp.188-202
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• 2004

This research was designed to investigate biomechanical aspects of the evolution based on the hypothesis of dynamic cooperative interactions between the locomotion pattern and the body shape in the evolution of human bipedal walking The musculoskeletal model used in the computer simulation consisted of 12 rigid segments and 26 muscles. The nervous system was represented by 18 rhythmic pattern generators. The genetic algorithm was employed based on the natural selection theory to represent the evolutionary mechanism. Evolutionary strategy was assumed to minimize the cost function that is weighted sum of the energy consumption, the muscular fatigue and the load on the skeletal system. The simulation results showed that repeated manipulations of the genetic algorithm resulted in the change of body shape and locomotion pattern from those of chimpanzee to those of human. It was suggested that improving locomotive efficiency and the load on the musculoskeletal system are feasible factors driving the evolution of the human body shape and the bipedal locomotion pattern. The hypothetical evolution method employed in this study can be a new powerful tool for investigation of the evolution process.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.5
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• pp.833-839
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• 2003

The effects of stiffeners on the modal characteristics of rectangular plates are investigated. A modeling method for the modal analysis of rectangular plates with stiffeners is presented. A mass density Dirac's delta function is used to idealize the stiffeners mathematically. The equations of motion for the plates are derived and transformed into a dimensionless form. To confirm the accuracy of the method presented in this study, numerical result are obtained and compared to those of a commercial program. The mode shape variations due to some parameter variations are also exhibited.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.1
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• pp.29-37
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• 2012

This paper is concerned with the natural vibration characteristics of a rectangular plate with a rectangular hole in contact with the water. The addressed problem was solved by using the Rayleigh-Ritz method combined with the Green function method. This study presents the numerical approach, numerical results and experimental results. In addition, the validity of the approximate formula which mainly depends on the so-called non-dimensionalized added virtual mass incremental factor and the natural mode shape change due to the presence of the water were investigated. Experiments were also carried out to validate theoretical results. The theoretical results are in good agreement with the experimental results. It was found that the effect of a square hole on the natural frequencies of the square plate in contact with water is different from the effect of a square hole on the natural frequencies of the square plate in air and the approximate formula can predict lower natural frequencies in water with a good accuracy.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1015-1018
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• 2006

In this paper, new topology optimization technique is proposed. It mainly uses the strain energy distributions induced by the mode shapes associated with natural frequencies of the structure and so we can implicitly consider the dynamic characteristics of the structure in the topology optimization process. The strain energy to be minimized is employed as the objective function and the initial volume of structures is adopted as the constraint function. The resizing algorithm devised from the optimality criteria method is used to update the hole size of the cell existing in each finite element. The cantilever beam problem is adopted to test the proposed techniques. From numerical test, it is found to be that the optimum topology of the cantilever produced by the proposed technique has a hugh increase of natural frequency value and the technique is very effective to maximize the fundamental frequency of the structure.