The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Filippo Gazzola - One of the best experts on this subject based on the ideXlab platform.
-
Structural Instability of nonlinear plates modelling suspension bridges mathematical answers to some long standing questions
Nonlinear Analysis-real World Applications, 2016Co-Authors: Elvise Erchio, Alberto Ferrero, Filippo GazzolaAbstract:Abstract We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic-like equation describing the dynamics of the bridge. In order to emphasize the Structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a Structural Instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of Instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.
-
mathematical models for suspension bridges nonlinear Structural Instability
2015Co-Authors: Filippo GazzolaAbstract:This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear Structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of Instability
-
Structural Instability of nonlinear plates modelling suspension bridges mathematical answers to some long standing questions
arXiv: Analysis of PDEs, 2015Co-Authors: Elvise Erchio, Alberto Ferrero, Filippo GazzolaAbstract:We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic equation describing the dynamics of the bridge. In order to emphasize the Structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a Structural Instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of Instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.
Maochun Hong - One of the best experts on this subject based on the ideXlab platform.
-
designing a beryllium free deep ultraviolet nonlinear optical material without a Structural Instability problem
ChemInform, 2016Co-Authors: Sangen Zhao, Yaoguo Shen, Muhammad Adnan Asghar, Siyuan Zeng, Yingying Xu, Lei Kang, Xiaodong Wang, Maochun HongAbstract:K3Ba3Li2Al4B6 O20F is prepared by solid state reaction of a stoichiometric mixture of K2CO3, BaCO3, Li2CO3, Al2O3, LiF, and H3BO3 (1.
-
designing a beryllium free deep ultraviolet nonlinear optical material without a Structural Instability problem
Journal of the American Chemical Society, 2016Co-Authors: Sangen Zhao, Yaoguo Shen, Muhammad Adnan Asghar, Siyuan Zeng, Yingying Xu, Lei Kang, Xiaodong Wang, Maochun HongAbstract:A beryllium-free deep-ultraviolet (deep-UV) nonlinear optical (NLO) material K3Ba3Li2Al4B6O20F is developed mainly by the element substitution of Be for Al and Li from Sr2Be2B2O7 that was considered as one of the most promising deep-UV NLO materials. K3Ba3Li2Al4B6O20F preserves the Structural merits of Sr2Be2B2O7 and thus exhibits no layering growth tendency and possesses the optical properties required for deep-UV NLO applications, including deep-UV transparency, phase-matchability, and sufficiently large second-harmonic generation (1.5 × KH2PO4). Furthermore, it overcomes the Structural Instability problem of Sr2Be2B2O7, which is confirmed by the obtainment of large single crystals and phonon dispersion calculations. These attributes make it very attractive for next-generation deep-UV NLO materials. The substitution of Be for Al and Li in beryllium borates provides a new opportunity to design beryllium-free deep-UV NLO materials with good performance.
Elvise Erchio - One of the best experts on this subject based on the ideXlab platform.
-
Structural Instability of nonlinear plates modelling suspension bridges mathematical answers to some long standing questions
Nonlinear Analysis-real World Applications, 2016Co-Authors: Elvise Erchio, Alberto Ferrero, Filippo GazzolaAbstract:Abstract We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic-like equation describing the dynamics of the bridge. In order to emphasize the Structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a Structural Instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of Instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.
-
Structural Instability of nonlinear plates modelling suspension bridges mathematical answers to some long standing questions
arXiv: Analysis of PDEs, 2015Co-Authors: Elvise Erchio, Alberto Ferrero, Filippo GazzolaAbstract:We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic equation describing the dynamics of the bridge. In order to emphasize the Structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a Structural Instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of Instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.
Shiv P Halasyamani - One of the best experts on this subject based on the ideXlab platform.
-
deep ultraviolet nonlinear optical material k3sr3li2al4b6o20f addressing the Structural Instability problem in kbe2bo3f2
Inorganic Chemistry, 2017Co-Authors: Shilie Pan, Shiv P HalasyamaniAbstract:A beryllium-free deep-ultraviolet (DUV) nonlinear-optical (NLO) material, K3Sr3Al4Li2B6O20F, has been synthesized and characterized. Unlike KBe2BO3F2 (KBBF), the reported NLO material does not require the use of toxic BeO in the synthesis, and through the judicious selection of cations, strong interlayer interactions are observed that facilitate the crystal growth. K3Sr3Al4Li2B6O20F exhibits second-harmonic generation (SHG) at both 1064 and 532 nm with efficiencies of 1.7KH2PO4 and 0.3β-BaB2O4 and has an absorption edge of 190 nm. Because of the strong interlayer interactions, we were able to grow well-faceted large crystals, 8 × 8 × 5 mm3, through a top-seeded-solution-growth technique. With these crystals, we determined a birefringence of 0.0574 at 1064 nm and a type I phase-matching SHG limit of 224 nm.
Sangen Zhao - One of the best experts on this subject based on the ideXlab platform.
-
designing a beryllium free deep ultraviolet nonlinear optical material without a Structural Instability problem
ChemInform, 2016Co-Authors: Sangen Zhao, Yaoguo Shen, Muhammad Adnan Asghar, Siyuan Zeng, Yingying Xu, Lei Kang, Xiaodong Wang, Maochun HongAbstract:K3Ba3Li2Al4B6 O20F is prepared by solid state reaction of a stoichiometric mixture of K2CO3, BaCO3, Li2CO3, Al2O3, LiF, and H3BO3 (1.
-
designing a beryllium free deep ultraviolet nonlinear optical material without a Structural Instability problem
Journal of the American Chemical Society, 2016Co-Authors: Sangen Zhao, Yaoguo Shen, Muhammad Adnan Asghar, Siyuan Zeng, Yingying Xu, Lei Kang, Xiaodong Wang, Maochun HongAbstract:A beryllium-free deep-ultraviolet (deep-UV) nonlinear optical (NLO) material K3Ba3Li2Al4B6O20F is developed mainly by the element substitution of Be for Al and Li from Sr2Be2B2O7 that was considered as one of the most promising deep-UV NLO materials. K3Ba3Li2Al4B6O20F preserves the Structural merits of Sr2Be2B2O7 and thus exhibits no layering growth tendency and possesses the optical properties required for deep-UV NLO applications, including deep-UV transparency, phase-matchability, and sufficiently large second-harmonic generation (1.5 × KH2PO4). Furthermore, it overcomes the Structural Instability problem of Sr2Be2B2O7, which is confirmed by the obtainment of large single crystals and phonon dispersion calculations. These attributes make it very attractive for next-generation deep-UV NLO materials. The substitution of Be for Al and Li in beryllium borates provides a new opportunity to design beryllium-free deep-UV NLO materials with good performance.
