• Journal of KSNVE
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• v.6 no.6
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• pp.771-779
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• 1996

In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

• Journal of the Korean Society for Railway
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• v.6 no.3
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• pp.163-168
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• 2003

This paper considers the sound radiation characteristics of a cracked rectangular vibrating plate, varying the orientation angle of a line crack. The vibration response of the cracked vibrating plate is obtained by using ANSYS, the acoustic theory based on the lumped parameter model is used to calculate radiated sound power. The radiated sound powers are computed with varying the orientation angle of the crack: i.e, 0$^{\circ}$, 45$^{\circ}$, and 90$^{\circ}$. It is found that characteristics of the radiated sound power are very closely related to the crack orientation, vibration mode and crack location.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1177-1182
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have be en many methods developed for the free vibration of the rectangular plate with a rectangular cutout., very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian co ordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.643-650
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have been many methods developed for the free vibration of the rectangular plate with a rectangular cutout, very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian coordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.1
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• pp.73-79
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• 2001

In this study, a submerged plate-type breakwater is considered, which is supported by elastic foundation. This breakwater makes use of wave phase interaction among the incident, diffracted and radiated waves. We apply a three-dimensional singularity distribution method within the linear potential theory in order to describe the wave field. The submerged plate is assumed to be rigid and the elastic support be a linear spring with constant stiffness. A typical rectangle plate is exemplified for numerical calculation. The thickness of the plate is carefully selected in order to guarantee the solution to be stable by checking the condition number of the system matrix. A parametric study is carried out for examining the effect of the stiffness of the elastic support on performance of the breakwater. We also examine the effect of the submerged depth.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.116-125
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• 1995

In ship and of offshore structures, there exist many local panels of various shapes having many kinds of attachments reducible to damped spring-mass systems. For the vibration analysis of panels, analytical methods such as Rayleight-Ritz method or the assumed mode method can be efficiently applied. There have been many studies on the vibration analysis of rectangular panels using the analytical methods but relatively few for arbitrary shape panels. An efficient formulation based on the assumed mode method is presented for the vibration analysis of an arbitrary quadrangular plate having concentrated masses, supporting springs such as pillars and spring-mass systems. In the formulation, the natural coordinate system is used for the efficient treatment of an arbitrary quadrangular shape. Through some numerical calculations, accuracy and efficiency of the presented method are shown.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.12 s.91
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• pp.1131-1140
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• 2004

In this paper, we proposed a flate-plate antenna employing semi-annular slots for satellite broadcast reception. The radiating element of the antenna is dual annular slots fed by a strip dipole, which have a wider bandwidth than the rectangular slot. A $16{\times}16$ array antenna is designed using stripline T-junction power dividers. Measurements of the fabricated antenna show a gain of 28.0$\~$29.5 dB in 11.7$\~$12.8 GHz frequency range.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.40 no.3
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• pp.196-205
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• 2004

As far as an opening device of fishing gears is concerned, applications of a kite are under development around the world. The typical examples are found in the opening device of the stow net on anchor and the buoyancy material of the trawl. While the stow net on anchor has proved its capability for the past 20 years, the trawl has not been wildly used since it has been first introduced for the commercial use only without sufficient studies and thus has revealed many drawbacks. Therefore, the fundamental hydrodynamics of the kite itself need to ne studied further. Models of plate and canvas kite were deployed in the circulating water tank for the mechanical test. For this situation lift and drag tests were performed considering a change in the shape of objects, which resulted in a different aspect ratio of rectangle and trapezoid. The results obtained from the above approaches are summarized as follows, where aspect ratio, attack angle, lift coefficient and maximum lift coefficient are denoted as A, B, $C_L$ and $C_{Lmax}$ respectively : 1. Given the rectangular plate, $C_{Lmax}$ was produced as 1.46${\sim}$1.54 with A${\leq}$1 and 40$^{\circ}$${\leq}$B${\leq}$42$^{\circ}$. And when A${\geq}$1.5 and 20$^{\circ}$${\leq}$B${\leq}$22$^{\circ}$, $C_{Lmax}$ was 10.7${\sim}$1.11. Given the rectangular canvas, $C_{Lmax}$ was 1.75${\sim}$1.91 with A${\leq}$1 and 32$^{\circ}$${\leq}$B${\leq}$40$^{\circ}$. And when A${\geq}$1.5 and 18$^{\circ}$${\leq}$B${\leq}$22$^{\circ}$, $C_{Lmax}$ was 1.24${\sim}$1.40. Given the trapezoid kite, $C_{Lmax}$ was produced as 1.65${\sim}$1.89 with A${\leq}$1.5 and 34$^{\circ}$${\leq}$B${\leq}$44$^{\circ}$. And when A=2 and B=14${\sim}$48, $C_L$ was around 1. Given the inverted trapezoid kite, $C_{Lmax}$ was 1.57${\sim}$1.74 with A${\leq}$1.5 and 24$^{\circ}$${\leq}$B${\leq}$36$^{\circ}$. And when A=2, $C_{Lmax}$ was 1.21 with B=18$^{\circ}$. 2. For a model with A=1/2, an increase in B caused an increase in $C_L$ until $C_L$ has reached the maximum. Then there was a tendency of a gradual decrease in the value of $C_L$ and in particular, the rectangular kite showed a more rapid decrease. For a model with A=2/3, the tendency of $C_L$ was similar to the case of a model with A=1/2 but the tendency was a more rapid decrease than those of the previous models. For a model with A=1, and increase in B caused an increase in $C_L$ until $C_L$ has reached the maximum. Soon after the tendency of $C_L$ decreased dramatically. For a model with A=1.5, the tendency of $C_L$ as a function of B was various. For a model with A=2, the tendency of $C_L$ as a function of B was almost the same in the rectangular and trapezoid model. There was no considerable change in the models with 20$^{\circ}$${\leq}$B${\leq}$50$^{\circ}$. 3. The tendency of kite model's $C_L$ in accordance with increase of B was increased rapidly than plate models until $C_L$ has reached the maximum. Then $C_L$ in the kite model was decreased dramatically but in the plate model was decreased gradually. The value of $C_{Lmax}$ in the kite model was higher than that of the plate model, and the kite model's attack angel at $C_{Lmax}$ was smaller than the plate model's. 4. In the relationship between aspect ratio and lift force, the attack angle which had the maximum lift coefficient was large at the small aspect ratio models, At the large aspect ratio models, the attack angle was small. 5. There was camber vertex in the position in which the fluid pressure was generated, and the rectangular & trapezoid canvas had larger value of camber vertex when the aspect ratio was high, while the inverted trapezoid canvas was versa. 6. All canvas kite had larger camber ratio when the aspect ratio was high, and the rectangular & trapezoid canvas had larger one when the attack angle was high.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.4
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• pp.336-343
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• 2004

This paper reports the first known free vibration data for thin rectangular plates with V-notches. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets include (1) mathematically complete algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained, and (2) corner functions which account for the bending moment singularities at the sharp reentrant corner of the Y-notch. Extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of nondirectional frequencies for rectangular plates having the V-notch. In this paper, accurate frequencies and normalized contours of vibratory transverse displacement are presented for various notched plates, so that the effect of corner stress singularities may be understood.

• Transactions of the Korean Society of Mechanical Engineers
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• v.1 no.3
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• pp.141-145
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• 1977

In this paper, approximate solutions of the von Karman equations for the free flexural vibration of a transversely isotropic thin rectangular plate with two simply supported edges and two clamped edges are obtained. Applying one term Ritz-Galerkin procedure, the spatial dependent part of the equation is separated and time dependent function is found to be the Duffing's equation. Then the relation between nonlinear period and amplitude of the vibration is obtained by using averaging method which is a method of the perturbation procedure. It can be seen that averaging method is easy and agrees well with prior results.