Relevant bibliographies by topics / Rayleigh- Ritz Method (RRM)

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Rayleigh- Ritz Method (RRM)'

Author: Grafiati
Published: 5 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Rayleigh- Ritz Method (RRM)"

1

Monterrubio, L. E. "Free vibration of shallow shells using the Rayleigh—Ritz method and penalty parameters." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 10 (2009): 2263–72. http://dx.doi.org/10.1243/09544062jmes1442.

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In the present work, the Rayleigh—Ritz method (RRM) and the penalty function method (PFM) are used to solve vibration problems of shallow shells of rectangular planform with spherical, cylindrical, and hyperbolic paraboloidal geometries with classical boundary conditions. Problems with more complicated constraints can also be solved using the method presented in this work, which consists in developing the stiffness and mass matrices of a completely free shallow shell using the RRM and then all constraints of the shell are defined by the PFM through the use of either artificial stiffness or art
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K., C. Nwachukwu, Ezeh J.C., Ibearugbulem O.M., Anya U.C., Atulomah F.K, and Mathew C.C. "Flexural Stability Analysis of Doubly Symmetric Single Cell Thin -Walled Box Column Based On Rayleigh- Ritz Method [RRM]." International Journal of Recent Research in Thesis and Dissertation (IJRRTD) 5, no. 1 (2024): 79–90. https://doi.org/10.5281/zenodo.10893911.

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<strong>Abstract:</strong> This research work is aimed at determining the Flexural [F] critical buckling load, &nbsp;for Doubly Symmetrical Single (DSS) cell Thin-Walled Columns [TWC] cross section&nbsp; at different boundary conditions using&nbsp; Rayleigh-Ritz Method (RRM) with Polynomial Shape Functions . It is the follow up of the works by Nwachukwu and others (2017) and Nwachukwu and others (2021a) where the governing equation for the Total Potential Energy Functional (TPEF) for a Thin- Walled Box Column (TWBC) applicable to RRM and peculiar TPEF for DSS cross &ndash; section were derived
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Han, Jie, Xianglin Gong, Chencheng Lian, et al. "An Analysis of Nonlinear Axisymmetric Structural Vibrations of Circular Plates with the Extended Rayleigh–Ritz Method." Mathematics 13, no. 8 (2025): 1356. https://doi.org/10.3390/math13081356.

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The nonlinear deformation and vibrations of elastic plates represent a fundamental problem in structural vibration analysis, frequently encountered in engineering applications and classical mathematical studies. In the field of studying the nonlinear phenomena of elastic plates, numerous methods and techniques have emerged to obtain approximate and exact solutions for nonlinear differential equations. A particularly powerful and flexible method, known as the extended Rayleigh–Ritz method (ERRM), has been proposed. In this approach, the temporal variable is introduced as an additional dimension
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Mohsen-Nia, Mohsen, Fateme Abadian, Naeime Abadian, Keivan Mosaiebi Dehkordi, Maryam Keivani, and Mohamadreza Abadyan. "Analysis of cantilever NEMS in centrifugal-fluidic systems." International Journal of Modern Physics B 30, no. 22 (2016): 1650148. http://dx.doi.org/10.1142/s0217979216501484.

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Electromechanical nanocantilevers are promising for using as sensors/detectors in centrifugal-fluidic systems. For this application, the presence of angular speed and electrolyte environment should be considered in the theoretical analysis. Herein, the pull-in instability of the nanocantilever incorporating the effects of angular velocity and liquid media is investigated using a size-dependent continuum theory. Using d’Alembert principle, the angular speed is transformed into an equivalent centrifugal force. The electrochemical and dispersion forces are incorporated considering the corrections
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Morachkovska, Iryna, Lidiya Kurpa, Anna Linnik, Galina Timchenko, and Tetyana Shmatko. "Dynamic analysis of functional gradient porous sigmoidal sandwich plates." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 1 (December 21, 2023): 39–44. http://dx.doi.org/10.20998/2078-9130.2023.1.281191.

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Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core i
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Žitňan, Peter. "The Rayleigh-Ritz method still competitive." Journal of Computational and Applied Mathematics 54, no. 3 (1994): 297–306. http://dx.doi.org/10.1016/0377-0427(94)90252-6.

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O Osuntoki, Joseph. "Advanced Solutions to Boundary Value Problems: A Comparative Study of Rayleigh-Ritz and the Finite Element Method." Innovative Journal of Applied Science 01, no. 01 (2024): 01–07. http://dx.doi.org/10.70844/ijas.2024.1.5.

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This study investigates the solution of a boundary value problem using two numerical methods: The Rayleigh-Ritz method and the Finite Element Method (FEM). The aim is to compare the performance of these methods and assess the reliability of FEM as a generalization of the Rayleigh-Ritz approach for more complex problems. The Rayleigh-Ritz method and the linear element formulation of the finite element method were employed to solve the boundary value problem. A detailed comparison of the results obtained from both methods was performed. Graphical illustrations were used to present the solutions,
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Stubbins, Calvin. "Recurrence Relations in the Rayleigh-Ritz Method." Progress of Theoretical Physics Supplement 138 (2000): 750–52. http://dx.doi.org/10.1143/ptps.138.750.

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Kumar, Yajuvindra. "The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review." Journal of Vibration and Control 24, no. 7 (2017): 1205–27. http://dx.doi.org/10.1177/1077546317694724.

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The Rayleigh–Ritz method is a classical method that has been widely used to investigate dynamic, static and buckling behavior, i.e., the natural frequencies, mode shapes, moments, stresses, critical buckling loads of vibrating structures and to solve boundary value problems. Different developments in the method have taken place from time to time. This paper presents a comprehensive literature review on the application of the Rayleigh–Ritz method to analyze vibration, static and buckling characteristics of beams, shells and plates using different theories.
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Liu, Xiao Wan, and Bin Liang. "Effect of Ring Support Position and Geometrical Dimension on the Free Vibration of Ring-Stiffened Cylindrical Shells." Applied Mechanics and Materials 580-583 (July 2014): 2879–82. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2879.

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Effect of ring support position and geometrical dimension on the free vibration of ring-stiffened cylindrical shells is studied in this paper. The study is carried out by using Sanders shell theory. Based on the Rayleigh-Ritz method, the shell eigenvalue governing equation is derived. The present analysis is validated by comparing results with those in the literature. The vibration characteristics are obtained investigating two different boundary conditions with simply supported-simply supported and clamped-free as the examples. Key Words: Ring-stiffened cylindrical shell; Free vibration; Rayl
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Dissertations / Theses on the topic "Rayleigh- Ritz Method (RRM)"

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Kaul, Sandeep P. "Numerical simulation of two-phase flow in discrete fractures using Rayleigh-Ritz finite element method." Thesis, Texas A&M University, 2003. http://hdl.handle.net/1969.1/373.

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Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element
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Sherar, P. A. "Variational based analysis and modelling using B-splines." Thesis, Cranfield University, 2004. http://hdl.handle.net/1826/125.

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The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations tha
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Жигилій, Дмитро Олексійович, Дмитрий Алексеевич Жигилий, Dmytro Oleksiiovych Zhyhylii та М. Л. Заїкіна. "Дослідження стійкості стрижня методом Релея-Рітца". Thesis, Сумський державний університет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/31849.

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Зазвичай задачі на стійкість при повздовжньому стисканні стержнів вирішуються інтегруванням диференційних рівнянь, а також за допомогою засобів, на основі аналогій диференційних рівнянь. Якщо точне інтегрування диференційних рівнянь ускладнене, можна інтегрувати їх з наближенням. Визначимо функцію (інтеграл рівняння), яка буде задовольняти граничним умовам і мінімізувати потенційну енергію, скориставшись методом Релея-Рітца. При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/31849
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Arvan, Prakash Ankitha. "Rigorous Implementation of the Galerkin method for Stepped Structures." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.

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In this study we investigate the application of the Galerkin’s method to evaluate the deflection of stepped beams. The naïve implementation, as usually executed in the literature, is contrasted with the rigorous version of the Galerkin method. Naïve implementation involves the integration extended over the steps of the beam where the cross-sectional area and flexural rigidity remains constant. Rigorous implementation treats flexural rigidity as the generalized function, with attendant additional terms associated with the derivatives of the generalized function. The above additional
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Aimmanee, Sontipee. "Deformation and Force Characteristics of Laminated Piezoelectric Actuators." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11219.

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This research discusses the mechanical characteristics of laminated piezoelectric actuators that are manufactured at an elevated temperature, to cure the adhesive bonding the layers together, or to cure the layers made of polymeric composite material, and then cooled to a service temperature. Mainly discussed are actuators that are composed of layers of passive materials and a layer of piezoelectric material. THUNDER (THin layer UNimorph ferroelectric DrivER and sensor) and LIPCA (LIghtweight Piezo-composite Curved Actuator) actuators, which consist of layers of metal, adhesive and piezoelectr
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Goh, Julian Kok Seng. "Analysis of Pressurized Arch-Shells." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/35576.

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A pressurized arch-shell structural component made of flexible material is considered. The component is inflated with high internal pressure. The behavior of similar types of structures, such as a pair of leaning pressurized arches and pressurized arch-supported membrane shelters, has been investigated in the past. More recently, several types of pressurized structures have been incorporated as part of the framework for a variety of structural systems. Particularly, the U.S. Army has been investigating the use of large lightweight and transportable pressurized arch-shell structures to be
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Jilani, Adel Benhaj. "Deformations of Piezoceramic-Composite Actuators." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/29540.

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In the past few years a new class of layered piezoceramic and piezoceramic-composite actuators, known as RAINBOW and GRAPHBOW, respectively, that are capable of achieving 100 times greater out-of-plane displacements than previously available has been developed. Prior to the development of RAINBOW and GRAPHBOW, large stacks of piezoelectric actuators, requiring complicated electronic drive circuits, were necessary to achieve the displacement now possible through the use of a single RAINBOW actuator. The major issues with both RAINBOW and GRAPHBOW are the prediction of their room-temperature sha
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Djato, Anani. "Identification rapide des propriétés diffuso-mécaniques de matériaux polymères et composites pour applications aéronautiques." Thesis, Chasseneuil-du-Poitou, Ecole nationale supérieure de mécanique et d'aérotechnique, 2018. http://www.theses.fr/2018ESMA0010/document.

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L’emploi de matériaux composites à matrice organique (CMO) pour la réalisation de structures aéronautiques « tièdes », peut exposer ces matériaux à l’action d’environnements agressifs, qui peuvent entrainer des phénomènes de vieillissement et de dégradation sévères associés à la diffusion d’espèces au sein du réseau macromoléculaire des matrices polymères. La complexité de la microstructure des CMO utilisés pour ces applications peut complexifier la compréhension de phénomènes de dégradation. Le vieillissement humide des CMO préoccupe particulièrement les industriels du secteur aéronautique ;
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Жигилій, Дмитро Олексійович, Дмитрий Алексеевич Жигилий, Dmytro Oleksiiovych Zhyhylii та М. Ю. Ветер. "Сравнение метода конечных разностей с методом Релея-Ритца в задаче прямого изгиба консольной балки". Thesis, Сумский государственный университет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/31851.

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В работе проводится сравнение метода конечных разностей с методом Релея-Ритца в задаче прямого изгиба консольной балки. При цитировании документа, используйте ссылку http://essuir.sumdu.edu.ua/handle/123456789/31851
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Güttel, Stefan. "Rational Krylov Methods for Operator Functions." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola&quot, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-27645.

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We present a unified and self-contained treatment of rational Krylov methods for approximating the product of a function of a linear operator with a vector. With the help of general rational Krylov decompositions we reveal the connections between seemingly different approximation methods, such as the Rayleigh–Ritz or shift-and-invert method, and derive new methods, for example a restarted rational Krylov method and a related method based on rational interpolation in prescribed nodes. Various theorems known for polynomial Krylov spaces are generalized to the rational Krylov case. Computational
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Books on the topic "Rayleigh- Ritz Method (RRM)"

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Laura, Patricio A. A. Optimized Rayleigh-Ritz method. Dept. of Engineering, Universidad Nacional del Sur, 1995.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.

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W, Hyer M., Nemeth Michael P, and United States. National Aeronautics and Space Administration., eds. The buckling response of symmetrically laminated composite plates having a trapezoidal planform area. National Aeronautics and Space Administration, 1994.

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Rosen, I. Gary. Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1985.

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Mochida, Yusuke, Luis Monterrubio, and Sinniah Ilanko. Rayleigh-Ritz Method for Structural Analysis. Wiley & Sons, Incorporated, John, 2014.

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Mochida, Yusuke, Luis Monterrubio, and Sinniah Ilanko. Rayleigh-Ritz Method for Structural Analysis. Wiley & Sons, Incorporated, John, 2014.

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Mochida, Yusuke, Luis Monterrubio, and Sinniah Ilanko. Rayleigh-Ritz Method for Structural Analysis. Wiley & Sons, Incorporated, John, 2014.

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Mochida, Yusuke, Luis Monterrubio, and Sinniah Ilanko. Rayleigh-Ritz Method for Structural Analysis. Wiley & Sons, Incorporated, John, 2014.

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Mochida, Yusuke, Luis Monterrubio, and Sinniah Ilanko. Rayleigh-Ritz Method for Structural Analysis. Wiley & Sons, Incorporated, John, 2014.

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Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1985.

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Book chapters on the topic "Rayleigh- Ritz Method (RRM)"

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "The RRM in Finite Elements Method." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch14.

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Preumont, André. "Rayleigh-Ritz Method." In Twelve Lectures on Structural Dynamics. Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6383-8_5.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "Lagrangian Multiplier Method." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch4.

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Jin, Guoyong, Tiangui Ye, and Zhu Su. "Modified Fourier Series and Rayleigh-Ritz Method." In Structural Vibration. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46364-2_2.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "The Rayleigh-Ritz Method and Simple Applications." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch3.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "Principle of Conservation of Energy and Rayleigh's Principle." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch1.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "Natural Frequencies and Modes of Plates of Rectangular Planform." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch10.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "Natural Frequencies and Modes of Shallow Shells of Rectangular Planform." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch11.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "Natural Frequencies and Modes of Three-Dimensional Bodies." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch12.

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Ilanko, Sinniah, Luis E. Monterrubio, and Yusuke Mochida. "Vibration of Axially Loaded Beams and Geometric Stiffness." In The Rayleigh-Ritz Method for Structural Analysis. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118984444.ch13.

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Conference papers on the topic "Rayleigh- Ritz Method (RRM)"

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Kaul, Sandeep P., Putra Erwinsyah, and David S. Schechter. "Spontaneous Imbibition Simulation with Rayleigh-Ritz Finite Element Method." In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 2004. http://dx.doi.org/10.2118/90053-ms.

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Ding, Shu-dong, Jing-hui Wu, Long-tao Xie, Yang-yang Zhang, Rong-xing Wu, and Ji Wang. "In-Plane Free Vibrations of Curved Beams by Rayleigh-Ritz Method." In 2019 13th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA). IEEE, 2019. http://dx.doi.org/10.1109/spawda.2019.8681787.

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KAO, PI-JEN. "Coupled Rayleigh-Ritz/finite element structural analysis using penalty function method." In 33rd Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-2238.

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Wu, Jinghui, Ji Wang, and Erasmo Carrera. "Analysis of Rayleigh Waves in Piezoelectric Solids with Metal Coatings by the Rayleigh-Ritz Method." In 2023 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS). IEEE, 2023. http://dx.doi.org/10.1109/eftf/ifcs57587.2023.10272225.

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Wang, Ji, Peng Hu, Bin Huang, et al. "Free vibrations of finite quartz crystal cylinders with the Rayleigh-Ritz method." In 2016 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA). IEEE, 2016. http://dx.doi.org/10.1109/spawda.2016.7830018.

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Lin Zhu and De-Shuang Huang. "A scalable rayleigh-ritz style method for large scale Canonical Correlation Analysis." In 2012 International Joint Conference on Neural Networks (IJCNN 2012 - Brisbane). IEEE, 2012. http://dx.doi.org/10.1109/ijcnn.2012.6252373.

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Tian, Lin-jie, Ming Yang, and Zhe Li. "Analysis of Lateral Torsional Buckling of Steel I-Beams within Preflexed Beams in Pre-Bending Stage." In IABSE Congress, Nanjing 2022: Bridges and Structures: Connection, Integration and Harmonisation. International Association for Bridge and Structural Engineering (IABSE), 2022. http://dx.doi.org/10.2749/nanjing.2022.1887.

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&lt;p&gt;In order to study the lateral torsional buckling (LTB) law of steel I-beams within preflexed beams in pre-bending stage, the traditional Rayleigh Ritz method was applied, and the modified Rayleigh Ritz method was proposed by considering the restraint effects caused by lateral braces. A large number of finite element models were established by ABAQUS. The theoretical and simulation results show that the modified Rayleigh Ritz method proposed in this paper can reduce the maximum relative error of traditional Rayleigh Ritz method by about 13%. The effects of different parameters on the L
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Irvine, Tom. "Practical Application of the Rayleigh-Ritz Method to Verify Launch Vehicle Bending Modes." In 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-1608.

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MEIROVITCH, L., and M. KWAK. "On the modeling of flexible multi-body systems by the Rayleigh-Ritz method." In Orbital Debris Conference: Technical Issues andFuture Directions. American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1245.

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Lee, L. T., and W. F. Pon. "Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method." In ASME 1992 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/cie1992-0083.

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Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial funct
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