%0 Journal Article %1 du_topological_2007 %A Du, Jianbin %A Olhoff, Niels %D 2007 %J Structural and Multidisciplinary Optimization %K ({CAD}, Applied Bound Computational Computer-Aided Design, Eigenfrequency Engineering Engineering, Mechanics, Methods Multiple Numerical Theoretical Topology and design, eigenvalues, formulation, in optimization {CAE)} %N 2 %P 91--110 %R 10.1007/s00158-007-0101-y %T Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps %U http://link.springer.com/article/10.1007/s00158-007-0101-y %V 34 %X A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a given interval for external excitation frequencies. This can be achieved by, e.g., maximizing the fundamental eigenfrequency, an eigenfrequency of higher order, or the gap between two consecutive eigenfrequencies of given order. This problem is often complicated by the fact that the eigenfrequencies in question may be multiple, and this is particularly the case in topology optimization. In the present paper, different approaches are considered and discussed for topology optimization involving simple and multiple eigenfrequencies of linearly elastic structures without damping. The mathematical formulations of these topology optimization problems and several illustrative results are presented.

@article{du_topological_2007, abstract = {A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a given interval for external excitation frequencies. This can be achieved by, e.g., maximizing the fundamental eigenfrequency, an eigenfrequency of higher order, or the gap between two consecutive eigenfrequencies of given order. This problem is often complicated by the fact that the eigenfrequencies in question may be multiple, and this is particularly the case in topology optimization. In the present paper, different approaches are considered and discussed for topology optimization involving simple and multiple eigenfrequencies of linearly elastic structures without damping. The mathematical formulations of these topology optimization problems and several illustrative results are presented.}, added-at = {2013-01-26T11:35:39.000+0100}, author = {Du, Jianbin and Olhoff, Niels}, biburl = {https://www.bibsonomy.org/bibtex/2a61cd4b722473655ee79bcdc024ea700/bhessen}, doi = {10.1007/s00158-007-0101-y}, file = {Full Text PDF:C:\Users\hessenauer\AppData\Roaming\Mozilla\Firefox\Profiles\1h9szxht.firefox4\zotero\storage\TVT4FTEC\Du und Olhoff - 2007 - Topological design of freely vibrating continuum s.pdf:application/pdf;Snapshot:C:\Users\hessenauer\AppData\Roaming\Mozilla\Firefox\Profiles\1h9szxht.firefox4\zotero\storage\HC6XFTIZ\10.html:text/html}, interhash = {c9a964946b0f184a3293248133d3b8b6}, intrahash = {a61cd4b722473655ee79bcdc024ea700}, issn = {1615-{147X}, 1615-1488}, journal = {Structural and Multidisciplinary Optimization}, keywords = {({CAD}, Applied Bound Computational Computer-Aided Design, Eigenfrequency Engineering Engineering, Mechanics, Methods Multiple Numerical Theoretical Topology and design, eigenvalues, formulation, in optimization {CAE)}}, language = {en}, month = aug, number = 2, pages = {91--110}, timestamp = {2013-01-26T11:35:57.000+0100}, title = {Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps}, url = {http://link.springer.com/article/10.1007/s00158-007-0101-y}, urldate = {2013-01-24}, volume = 34, year = 2007 }