• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.11
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• pp.8064-8073
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• 2015

One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In-plane vibrations of curved beams with inextensibility and extensibility of the arch axis are analyzed by the differential quadrature method (DQM). Fundamental frequencies are calculated for the member with various end conditions and opening angles. The results are compared with exact experimental and numerical results by other methods for cases in which they are available. The DQM gives good accuracy even when only a limited number of grid points is used, and new results according to diverse variation are also suggested.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.831-836
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• 2000

In this study, the Rayleigh inextensional theory and extensional theory for thin shells was employed to predict the natural frequencies of the hemi-spherical shell with free and simply. supported boundary condition. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. Modal test and FEM analysis of the free, simply supported and clamped boundary condition was also carried out.

• Journal of Korean Society of Steel Construction
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• v.14 no.3
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• pp.423-432
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• 2002

This study presented analytical and numerical solutions for spatial free vibration of nonsymmetric thin-walled circular curved beams. The closed-form solutions were obtained for in-plane free vibration analylsis of monosymmetric curved beams. Likewise, two types of thin-walled curved beam elements were developed using the third and the fifth order Hermitian polynomials. In order to illustrate the accuracy and usefulness of the present method, this study presented analytical and numerical solution and compared these with the results using the ABAQUS's shell elements. In particular, effects of the thickness-curvature as well as the inextensional condition were investigated on the free vibration of curved beams with nonsymmetric sections.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.1
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• pp.9-17
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• 2021

Curved beams are increasingly used in buildings, vehicles, ships, and aircraft, which has resulted in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic circular arches has been the subject of a large number of investigations. One of the efficient procedures for the solution of ordinary differential equations or partial differential equations is the differential quadrature method DQM. This method has been applied to a large number of cases to overcome the difficulties of the complex computer algorithms, as well as excessive use of storage due to conditions of non-linear geometries, loadings, or material properties. This study uses DQM to analyze the in-plane vibration of the circular arches considering the effects of midsurface extension and rotatory inertia. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The solutions from DQM are compared with exact solutions or other numerical solutions for cases in which they are available and given to analyze the effects of midsurface extension and rotatory inertia on the frequency parameters of the circular arches.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.835-841
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• 2013

Modern solid-state gyroscopes (HRG) with hemispherical resonators from high-purity quartz glass and special surface superfinishing and ultrathin gold coating become the best instruments for precise-grade inertial reference units (IRU) targeting long-term space missions. Designing of these sensors could be a notable contribution into development of Korea as a space nation. In participial, 40mm diameter thin-shell resonator from high-purity fused quartz, fabricated as a single-piece with its supporting stem has been designed, machined, etched, tuned, tested, and delivered by STM Co. (ATS of Ukraine) several years ago; an extremely-high Q-factor (upto 10~20 millions) has been shown. Understanding of the best way how to match such a unique sensor with inner glass assembly of the gyro means how to use the high potential in a maximal extent; and this has become the urgent task. Inner quartz glass assembly has a very thin indium (In) layer soldered the resonator and its silica base (case), but effects of internal resonances between operational modal pair of the shell-cup and its side (parasitic) modes can notable degrade the potential of the sensor as a whole, instead of so low level of resonator's intrinsic losses. Unfortunately, there are special combinations of dimensions of the parts (so-called, "resonant sizes"), when intensive losses of energy occurs. The authors proposed to use the length of stem's fixture as an additional design parameter to avoid such cases. So-called, a cyclic scheme of finite element method (FEM) and ANSYS software were employed to estimate different combinations of gyro assembly parameters. This variant has no mismatches of numerical origin due to FEM's discrete mesh. The optimum length and dangerous "resonant lengths" have been found. The special attention has been paid to analyses of 3D effects in a cup-stem transient zone, including determination of a difference between the positions of geometrical Pole of the resonant hemisphere and of its "dynamical Pole", i.e., its real zone of oscillation node. Boundary effects between the shell (cup) and 3D short "beams" (inner and outer stems) have been ranged. The results of the numerical experiments have been compared with the classic model of a quasi-hemispherical shell band with inextensional midsurface, and the solution using Rayleigh's functions of the $1^{st}$ and $2^{nd}$ kinds. To guarantee the truth of the recommended sizes to a designer of the real device, the analytical and FEM results have been compared with experimental data for a party of real resonators. The consistency of the results obtained by different means has been shown with errors less than 5%. The results notably differ from the data published earlier by different researchers.