• 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.

• 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.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.

• 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.

• 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.21 no.5
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• pp.430-436
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• 2011

The purpose of this study is to analyze the vibration and sound generation characteristics of the sandwich panel. Two thick panels were assumed to be separated by a compliant viscoelastic core. The transverse vibration induced by an external impact was analyzed using the Rayleigh-Ritz method. For applying arbitrary boundary condition of the panels, the edges were assumed to be supported by the translational and rotational springs. The beam functions were used as the trial functions. The effect of the boundary condition and viscoelastic core on the resulting vibration characteristics was investigated. The radiated sound power was analyzed using the proposed numerical model and the Rayleigh integral. The dynamic properties of the core and the mass-stiffness-mass resonance frequency had significant influence on the impact sound.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.921-925
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• 2003

An analytical method for the free vibration of single circular plate submerged in a fluid-filled rigid cylindrical vessel was developed by the Rayleigh-Ritz method based on the Fourier-Bessel series expansion. It was assumed that the plate is clamped at an offcentered location of the cylinder, and the non-viscous incompressible fluid contained in the cylinder is bisected by the plate. It was found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis results. The offcentered distance effect on the natural frequencies was also observed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.299-308
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• 2001

This paper presents the three-dimensional (3-D) study of the natural vibration of cantilevered laminated composite plates. The Ritz method is used to obtain stationary values of the associated Lagrangian functional with displacements approximated by mathematically complete polynomials satisfying the boundary conditions at the clamped edge exactly. The accuracy of the 3-D model is established through a convergence study of non-dimensional frequencies followed by a comparison of the converged 3-D solutions with analytical and experimental findings in the existing literature. A wide scope of 3-D frequency results explain the influence of a number of geometrical and material parameters for cantilevered laminated plates, namely aspect ratio (a/b), width-to-thickness ratio (a/h), orthotropy of material, number of plies (NP), fiber orientation angle(θ), and stacking sequence.