• Computational Structural Engineering
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• v.8 no.4
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• pp.181-187
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• 1995

Recent researches in dynamics are focused on finding effective methods to analyze the dynamic behavior of structures by fewer mode shapes their number of dgrees of freedom. Ritz algorithm and mode acceleration method were developed to improved the mode superposition. Ritz algorithm can include distribution of external loads but be apt to lose the orthogonality condition, which is useful properties in the analysis. Also mode acceleration method should consider a large number of mode shapes to get a satisfactory results. Another method, combining previous two method, was developed but too much computational efforts and times were required. The purpose of this study is to develop and evaluate the Ritz algorithm modified with the lanczos algorithm to improve the efficiency and accuracy. As a result of !this study, dynamic analysis using modified Ritz algorithm was proved to be the rational analysis method.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.601-613
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• 1998

This paper reports the first-of-its-kind free vibration solutions for sectorial plates having re-entrant corners causing stress singularities when the circular edge is either clamped or simply supported. The Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. Accurate frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of sector angles.

• Transactions of the Korean Society of Automotive Engineers
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• v.17 no.4
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• pp.108-117
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• 2009

Leissa claimed in his article that the Rayleigh method is not the same as the Ritz method for determining natural frequencies and its corresponding mode shapes and contended that Rayleigh's name should not be attached to the method. The present article examines the methods in viewpoint of admissible functions and its minimization process, and of the historical developments. It concludes that Leissa's assertion is relevant, although Rayleigh did apply a conceptual theory systematized from the Lagrange method, and given 38 years earlier than Ritz's 'masterly exposition of theory'.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.8
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• pp.71-77
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• 2018

In order to estimate behavior of soil mass which is located straight up of reinforced concrete culvert, Ritz method and FEM were applied and arching effects between the soil mass and adjacent soil were considered for the analyses. Analysis results obtained from the Ritz method and finite element method were compared with analytical solution. In the case of estimating nodal forces considered in FEM, caution is needed that shear stress depending on depth from ground surface should be reflected regardless of local coordinate system. Comparing the displacements computed from Ritz method with those of the analytic solution, it is seen that as the power of assumed displacement function increases, differences between the computed displacements and those of analytic solution decreases. It seems that displacements of FEM becomes closer to those of analytical solution as the number of elements are increased. It is seen that stresses computed from the Ritz method don't get closer to those of the analytic solution as the power of assumed displacement function. Stresses from FEM become closer to those of analytic solution as the number of elements are increased. Comparing the analysis results from the Ritz method and FEM with those of analytic solution, it can be seen that FEM is more reliable than Ritz method.

• 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.

• Computational Structural Engineering
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• v.11 no.4
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• pp.275-286
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• 1998

본 논문은 고정, 단순, 또는 자유 연단 조건의 네 가지의 다른 조합을 갖는 마름모꼴형 평판의 자유진동 데이터를 처음으로 제시한 연구이다. 본 논문의 주된 관점은 마름모꼴 형 평판 둔각모서리의 휨응력의 특이도를 엄밀히 고려하여 해석하는 것이다. Ritz 방법을 이용하여 수직진동변위를 두 가지 적합 함수식으로 가정하였다. 힌지와 고정, 자유와 고정, 또한 힌지와 자유인 모서리 응력 특이도의 중대한 영향력이 이해될 수 있도록 충분히 큰 1650 둔각모서리를 갖는 마름모꼴형 평판에 대하여 엄밀한 무차원 진동수와 수직변동변위의 전형적인 등고선을 제시하였다.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.4
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• pp.209-216
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• 1998

본 논문에서는 부채꼴형 Mindlin 평판의 엄밀한 휨진동해를 제시하였다. 진동변위의 두 가지 적합 함수식, 즉 대수삼각다항식과 Mindlin 모서리함수를 Ritz방법에 적용하였다. 모서리함수는 부채꼴형 평판의 둔각 정점부에 존재하는 모멘트와 전단력의 특이도를 동시에 고려하고 있다. 이러한 모서리함수는 진동수의 수렴속도를 가속화한다. 본 연구에서는 부채꼴형 각도의 범위와 두께 비에 따른 엄밀한 진동수 및 수직진동 변위의 전형적인 등고선을 제시하였다.

• Journal of the Earthquake Engineering Society of Korea
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• v.23 no.5
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• pp.279-288
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• 2019

Safety-related cabinets and their electrical parts, such as relays and switches in nuclear power plants, should maintain continuous functioning, as well as structural safety according to the nuclear regulatory guidelines. Generally, an electrical part is qualified if its functioning is maintained without abnormality during excitement by motion compatible with the test response spectrum, which is larger than its in-cabinet response spectrum (ICRS). ICRS can be determined by shake-table test or dynamic analysis. Since existing cabinets in use can hardly be stopped and moved, dynamic analysis is preferred over shake-table test in determining ICRS. The simple method, suggested by the Electric Power Research Institute (EPRI) to determine ICRS, yields conservative or non-conservative results from time to time. In order to determine that the ICRS is better than EPRI method in a simple way, Ritz method considering global and local plate behaviors was suggested by Gupta et al. In this paper, the Ritz method is modified in order to consider the rocking and frame behaviors simultaneously, and it is applied to a simple numerical example for verification. ICRS is determined by Ritz method and compared with the results by finite element method (FEM). Based on this numerical example, recommendations for using Ritz method are suggested.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.869-872
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• 2005

The purpose of this study is on the prediction of the acoustic performance of the lined rectangular plenum chamber which can be used in the HVAC systems. The lined plenum chamber is modeled as a piston driven rectangular tube without mean flow and the acoustic pressure in the lined chamber is obtained by superposing the three dimensional pressure due to each of uniformly and harmonically fluctuating pistons. The arbitrary locations of inlet/outlet ports as well as the acoustic higher order modes generated at the area discontinuities of the port chamber interfaces are taken into consideration. The four-pole parameters can be derived by imposing the proper boundary conditions on each inlet and outlet ports. The lining material on the internal wall is assumed to be a bulk-reacting model. A single weak variation statement which satisfies the fluctuating rigid piston condition and the pressure and displacement continuity condition at the interface between the lining material and the airway was developed. The set of cosine functions were used as the admissible function when applying the Rayleigh-Ritz method. Computed results are compared with those predicted by using the locally-reacting lining material and experimental results, respectively. There are a good agreement shown between the results by the Rayleigh-Ritz method and the experiment results. The derived transfer matrices can be easily combined with other four-pole parameters of different types of mufflers for the calculation of the whole system performance.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.8 s.101
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• pp.968-974
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• 2005

An analytical method for the hydroelastic vibration of a vessel composed of an upper annular plate and a lower circular plate is developed by the Rayleigh-Ritz method. The two plates are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies comparing with the finite element analysis result.