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• W3131645275 abstract "Abstract This review/research paper deals with the reduction of nonlinear partial differential equations governing the dynamic behavior of structural mechanical members with emphasis put on theoretical aspects of the applied methods and signal processing. Owing to the rapid development of technology, materials science and in particular micro/nano mechanical systems, there is a need not only to revise approaches to mathematical modeling of structural nonlinear vibrations, but also to choose/propose novel (extended) theoretically based methods and hence, motivating development of numerical algorithms, to get the authentic, reliable, validated and accurate solutions to complex mathematical models derived (nonlinear PDEs). The review introduces the reader to traditional approaches with a broad spectrum of the Fourier-type methods, Galerkin-type methods, Kantorovich–Vlasov methods, variational methods, variational iteration methods, as well as the methods of Vaindiner and Agranovskii–Baglai–Smirnov. While some of them are well known and applied by computational and engineering-oriented community, attention is paid to important (from our point of view) but not widely known and used classical approaches. In addition, the considerations are supported by the most popular and frequently employed algorithms and direct numerical schemes based on the finite element method (FEM) and finite difference method (FDM) to validate results obtained. In spite of a general aspect of the review paper, the traditional theoretical methods mentioned so far are quantified and compared with respect to applications to the novel branch of mechanics, i.e. vibrational behavior of nanostructures, which includes results of our own research presented throughout the paper. Namely, considerable effort has been devoted to investigate dynamic features of the Germain–Lagrange nanoplate (including physical nonlinearity and inhomogeneity of materials). Modified Germain–Lagrange equations are obtained using Kirchhoff’s hypothesis and relations based on the modified couple stress theory as well as Hamilton’s principle. A comparative analysis is carried out to identify the most effective methods for solving equations of mathematical physics taking as an example the modified Germain–Lagrange equation for a nanoplate. In numerical experiments with reducing the problem of PDEs to ODEs based on Fourier’s ideas (separation of variables), the Bubnov–Galerkin method of static problems and Faedo–Galerkin method of dynamic problems are employed and quantified. An exact solution governing the behavior of nanoplates served to quantify the efficiency of various reduction methods, including the Bubnov–Galerkin method, Kantorovich–Vlasov method, variational iterations and Vaindiner’s method (the last three methods include theorems regarding their numerical convergence). The numerical solutions have been compared with the solutions obtained by various combinations of the mentioned methods and with solutions obtained by FDM of the second order of accuracy and FEM for triangular and quadrangular finite elements. The studied methods of reduction to ordinary differential equations show high accuracy and feasibility to solve numerous problems of mathematical physics and mechanical systems with emphasis put on signal processing." @default.
• W3131645275 created "2021-03-01" @default.
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• W3131645275 date "2021-02-18" @default.
• W3131645275 modified "2023-09-25" @default.
• W3131645275 title "Review of the Methods of Transition from Partial to Ordinary Differential Equations: From Macro- to Nano-structural Dynamics" @default.
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• W3131645275 cites W1969202999 @default.
• W3131645275 cites W1971372368 @default.
• W3131645275 cites W1984853762 @default.
• W3131645275 cites W1992036149 @default.
• W3131645275 cites W1996199419 @default.
• W3131645275 cites W1998494366 @default.
• W3131645275 cites W2003803951 @default.
• W3131645275 cites W2005116317 @default.
• W3131645275 cites W2011285458 @default.
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• W3131645275 cites W2016032149 @default.
• W3131645275 cites W2016859302 @default.
• W3131645275 cites W2017277446 @default.
• W3131645275 cites W2017503182 @default.
• W3131645275 cites W2024491907 @default.
• W3131645275 cites W2030804071 @default.
• W3131645275 cites W2034087289 @default.
• W3131645275 cites W2037307097 @default.
• W3131645275 cites W2038137143 @default.
• W3131645275 cites W2047787595 @default.
• W3131645275 cites W2055556299 @default.
• W3131645275 cites W2056236973 @default.
• W3131645275 cites W2057159272 @default.
• W3131645275 cites W2058395306 @default.
• W3131645275 cites W2060749520 @default.
• W3131645275 cites W2065121429 @default.
• W3131645275 cites W2075894548 @default.
• W3131645275 cites W2081197300 @default.
• W3131645275 cites W2081211029 @default.
• W3131645275 cites W2084579178 @default.
• W3131645275 cites W2090313841 @default.
• W3131645275 cites W2111491256 @default.
• W3131645275 cites W2134385637 @default.
• W3131645275 cites W2139497848 @default.
• W3131645275 cites W2140280013 @default.
• W3131645275 cites W2144399742 @default.
• W3131645275 cites W2151231772 @default.
• W3131645275 cites W2168358956 @default.
• W3131645275 cites W2337150822 @default.
• W3131645275 cites W2343782912 @default.
• W3131645275 cites W2398034978 @default.
• W3131645275 cites W2411658012 @default.
• W3131645275 cites W2417895669 @default.
• W3131645275 cites W2496525735 @default.
• W3131645275 cites W2556346763 @default.
• W3131645275 cites W2558735048 @default.
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• W3131645275 doi "https://doi.org/10.1007/s11831-021-09550-5" @default.
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