title: The boundedness of Gorman’s Superposition method for free vibration analysis of plates

authors: Mochida, Yusuke

subjects: superposition method

abstract: Gorman’s Superposition method is known as one of the most efficient methods to solve the eigenvalue problems of plates because of its excellent convergence rate. However, there are few published results available that provide sufficient information on its boundedness. Here we have considered the nature of convergence of the eigenvalues for rectangular plates with the following sets of boundary conditions, completely free, fully clamped and cantilever. This paper shows numerically, the boundedness of the Superposition method for undamped vibration problems of rectangular isotropic plates subjected to different boundary conditions. The Superposition method gives upper bound results for eigenvalues of plates if the building blocks used in the Superposition method are subjected to stiffer boundary conditions than those of the original system being modelled. In contrast, the Superposition method yields lower bound results if the boundary conditions of building blocks are more flexible than those of the original system. The results would be useful to estimate the maximum possible error if the other bound can be obtained by another method.

text: The boundedness of Gorman’s Superposition method for free vibration analysis of plates Gorman’s Superposition method is known as one of the most efficient methods to solve the eigenvalue problems of plates because of its excellent convergence rate. However, there are few published results available that provide sufficient information on its boundedness. Here we have considered the nature of convergence of the eigenvalues for rectangular plates with the following sets of boundary conditions, completely free, fully clamped and cantilever. This paper shows numerically, the boundedness of the Superposition method for undamped vibration problems of rectangular isotropic plates subjected to different boundary conditions. The Superposition method gives upper bound results for eigenvalues of plates if the building blocks used in the Superposition method are subjected to stiffer boundary conditions than those of the original system being modelled. In contrast, the Superposition method yields lower bound results if the boundary conditions of building blocks are more flexible than those of the original system. The results would be useful to estimate the maximum possible error if the other bound can be obtained by another method.

year: 2012

title: Pushing the boundaries with bdrmapIT: mapping router ownership at internet scale

authors: Marder, Alexander

subjects: computer science

abstract: Two complementary approaches to mapping network boundaries from traceroute paths recently emerged [27,31]. Both approaches apply heuristics to inform inferences extracted from traceroute measurement campaigns. bdrmap [27] used targeted traceroutes from a specific network, alias resolution probing techniques, and AS relationship inferences, to infer the boundaries of that specific network and the other networks attached at each boundary. MAPIT [31] tackled the ambitious challenge of inferring all AS-level network boundaries in a massive archived collection of traceroutes launched from many different networks. Both were substantial contributions to the state-of-the-art, and inspired a collaboration to explore the potential to combine the approaches. We present and evaluate bdrmapIT, the result of that exploration, which yielded a more complete, accurate, and general solution to this persistent and central challenge of Internet topology research. bdrmapIT achieves 91.8%-98.8% accuracy when mapping AS boundaries in two Internet-wide traceroute datasets, vastly improving on MAP-IT’s coverage without sacrificing bdrmap’s ability to map a single network. The bdrmapIT source code is available at https://git.io/fAsI0.

text: Pushing the boundaries with bdrmapIT: mapping router ownership at internet scale Two complementary approaches to mapping network boundaries from traceroute paths recently emerged [27,31]. Both approaches apply heuristics to inform inferences extracted from traceroute measurement campaigns. bdrmap [27] used targeted traceroutes from a specific network, alias resolution probing techniques, and AS relationship inferences, to infer the boundaries of that specific network and the other networks attached at each boundary. MAPIT [31] tackled the ambitious challenge of inferring all AS-level network boundaries in a massive archived collection of traceroutes launched from many different networks. Both were substantial contributions to the state-of-the-art, and inspired a collaboration to explore the potential to combine the approaches. We present and evaluate bdrmapIT, the result of that exploration, which yielded a more complete, accurate, and general solution to this persistent and central challenge of Internet topology research. bdrmapIT achieves 91.8%-98.8% accuracy when mapping AS boundaries in two Internet-wide traceroute datasets, vastly improving on MAP-IT’s coverage without sacrificing bdrmap’s ability to map a single network. The bdrmapIT source code is available at https://git.io/fAsI0.

year: 2018

title: Kia kāpuia te reo o Tāmaki ki te Tonga: Tāmaki Makaurau ki te Tonga

authors: Lee-Morgan, Jenny Bol Jun

abstract: Mai i te Papakuratanga o Mataoho tae noa ki tona Ipu. Mai i Pukaki Tapu o Poutiikeka ki Te Puketapapatanga a Hape. Mai i te tahuna o Torea i nga wai o Mokoia, mawhiti atu ki Te Arapueru e karekare mai na ko Te Manukanuka a Hoturoa, kei reira a Taramainuku raua ko Kaiwhare. Ka kawea ki nga.hau o Mangere, e topa ai taku manuhokahoka ki Te Manurewatanga a Tamapahore. Whakaterawhiti taku haere ki Otara-a-nuku, ki Otara-a-rangi koia te tikapatanga o toku tiipuna o Marutuahu. Hoki whenei mai au ki Te Pane o Mataoho, tiro kau ake au ki aku pa whakairo ko Matatukutureia, ko Matukurua nga nohoanga tapu o Huakaiwaka, o Nga Tini-o-toitehuatahi, o Maruiwi kua ngaro katoa ki te reinga.

text: Kia kāpuia te reo o Tāmaki ki te Tonga: Tāmaki Makaurau ki te Tonga Mai i te Papakuratanga o Mataoho tae noa ki tona Ipu. Mai i Pukaki Tapu o Poutiikeka ki Te Puketapapatanga a Hape. Mai i te tahuna o Torea i nga wai o Mokoia, mawhiti atu ki Te Arapueru e karekare mai na ko Te Manukanuka a Hoturoa, kei reira a Taramainuku raua ko Kaiwhare. Ka kawea ki nga.hau o Mangere, e topa ai taku manuhokahoka ki Te Manurewatanga a Tamapahore. Whakaterawhiti taku haere ki Otara-a-nuku, ki Otara-a-rangi koia te tikapatanga o toku tiipuna o Marutuahu. Hoki whenei mai au ki Te Pane o Mataoho, tiro kau ake au ki aku pa whakairo ko Matatukutureia, ko Matukurua nga nohoanga tapu o Huakaiwaka, o Nga Tini-o-toitehuatahi, o Maruiwi kua ngaro katoa ki te reinga.

year: 2017