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Symmetry and complexity are the focus of a selection of outstanding papers, ranging from pure Mathematics and Physics to Computer Science and Engineering applications. This collection is based around fundamental problems arising from different fields, but all of them have the same task, i.e. breaking the complexity by the symmetry. In particular, in this Issue, there is an interesting paper dealing with circular multilevel systems in the frequency domain, where the analysis in the frequency domain gives a simple view of the system. Searching for symmetry in fractional oscillators or the analysis of symmetrical nanotubes are also some important contributions to this Special Issue. More papers, dealing with intelligent prognostics of degradation trajectories for rotating machinery in engineering applications or the analysis of Laplacian spectra for categorical product networks, show how this subject is interdisciplinary, i.e. ranging from theory to applications. In particular, the papers by Lee, based on the dynamics of trapped solitary waves for special differential equations, demonstrate how theory can help us to handle a practical problem. In this collection of papers, although encompassing various different fields, particular attention has been paid to the common task wherein the complexity is being broken by the search for symmetry.

History of engineering & technology --- fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes

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Engineering practice requires the use of structures containing identical components or parts, useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analyses of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Machine building, automotive, aerospace, and civil engineering are the main areas in which such applications appear, but they are found in most engineering fields.

History of engineering & technology --- exact solutions --- the generalized Benjamin–Bona–Mahony equation --- generalized exponential rational function method --- solitary wave solutions --- symbolic computation --- Thomson effect --- initial stress --- magneto-thermoelastic --- voids --- normal mode method --- G-N theory --- eigenvalue problem --- axisymmetric and non-axisymmetric vibrations --- multiparametric special functions --- circular plate --- functionally graded porous material --- initially stressed bodies --- dipolar structure --- volume fraction --- domain of influence --- chaotic time series prediction --- neural network --- firefly algorithm --- CEEMDAN --- VMD --- symmetric geometry --- guitar’s plate --- modal analysis --- skew symmetric eigenmodes --- comparison --- Friedman test --- linear regression --- nonlinear regression --- sign test --- symmetric errors --- Wilcoxon test --- coefficient of variation --- ratio --- symmetric and asymmetric distributions --- test of hypothesis --- multi-body system --- finite element method (FEM) --- linear elastic elements --- Lagrange’s equations --- two-dimensional finite element --- plane motion --- backward in time problem --- dipolar thermoelastic body --- uniqueness of solution --- Cesaro means --- partition of energies --- α-fractional calculus --- vibration isolation --- fractional-order differential equation --- rubber-like elastomers --- Riemann–Liouville/Caputo/Grünwald-Letnikov fractional derivative --- advanced mechanics --- analytical dynamics --- acceleration energies --- robotics --- viscoelasticity --- type III thermal law --- finite elements --- error estimates --- numerical results --- symmetry --- topology --- mechanical structures --- robots --- vibration --- mechanical engineering --- applied mechanics --- bird-strike impact --- composite laminate --- damage equivalency --- fan blade --- symmetrical configurations --- exact solutions --- the generalized Benjamin–Bona–Mahony equation --- generalized exponential rational function method --- solitary wave solutions --- symbolic computation --- Thomson effect --- initial stress --- magneto-thermoelastic --- voids --- normal mode method --- G-N theory --- eigenvalue problem --- axisymmetric and non-axisymmetric vibrations --- multiparametric special functions --- circular plate --- functionally graded porous material --- initially stressed bodies --- dipolar structure --- volume fraction --- domain of influence --- chaotic time series prediction --- neural network --- firefly algorithm --- CEEMDAN --- VMD --- symmetric geometry --- guitar’s plate --- modal analysis --- skew symmetric eigenmodes --- comparison --- Friedman test --- linear regression --- nonlinear regression --- sign test --- symmetric errors --- Wilcoxon test --- coefficient of variation --- ratio --- symmetric and asymmetric distributions --- test of hypothesis --- multi-body system --- finite element method (FEM) --- linear elastic elements --- Lagrange’s equations --- two-dimensional finite element --- plane motion --- backward in time problem --- dipolar thermoelastic body --- uniqueness of solution --- Cesaro means --- partition of energies --- α-fractional calculus --- vibration isolation --- fractional-order differential equation --- rubber-like elastomers --- Riemann–Liouville/Caputo/Grünwald-Letnikov fractional derivative --- advanced mechanics --- analytical dynamics --- acceleration energies --- robotics --- viscoelasticity --- type III thermal law --- finite elements --- error estimates --- numerical results --- symmetry --- topology --- mechanical structures --- robots --- vibration --- mechanical engineering --- applied mechanics --- bird-strike impact --- composite laminate --- damage equivalency --- fan blade --- symmetrical configurations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Engineering practice requires the use of structures containing identical components or parts, useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analyses of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Machine building, automotive, aerospace, and civil engineering are the main areas in which such applications appear, but they are found in most engineering fields.

exact solutions --- the generalized Benjamin–Bona–Mahony equation --- generalized exponential rational function method --- solitary wave solutions --- symbolic computation --- Thomson effect --- initial stress --- magneto-thermoelastic --- voids --- normal mode method --- G-N theory --- eigenvalue problem --- axisymmetric and non-axisymmetric vibrations --- multiparametric special functions --- circular plate --- functionally graded porous material --- initially stressed bodies --- dipolar structure --- volume fraction --- domain of influence --- chaotic time series prediction --- neural network --- firefly algorithm --- CEEMDAN --- VMD --- symmetric geometry --- guitar’s plate --- modal analysis --- skew symmetric eigenmodes --- comparison --- Friedman test --- linear regression --- nonlinear regression --- sign test --- symmetric errors --- Wilcoxon test --- coefficient of variation --- ratio --- symmetric and asymmetric distributions --- test of hypothesis --- multi-body system --- finite element method (FEM) --- linear elastic elements --- Lagrange’s equations --- two-dimensional finite element --- plane motion --- backward in time problem --- dipolar thermoelastic body --- uniqueness of solution --- Cesaro means --- partition of energies --- α-fractional calculus --- vibration isolation --- fractional-order differential equation --- rubber-like elastomers --- Riemann–Liouville/Caputo/Grünwald-Letnikov fractional derivative --- advanced mechanics --- analytical dynamics --- acceleration energies --- robotics --- viscoelasticity --- type III thermal law --- finite elements --- error estimates --- numerical results --- symmetry --- topology --- mechanical structures --- robots --- vibration --- mechanical engineering --- applied mechanics --- bird-strike impact --- composite laminate --- damage equivalency --- fan blade --- symmetrical configurations