<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Zhou, Q.</style></author><author><style face="normal" font="default" size="100%">Y. Chen</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Free vibration analysis of thin-walled axisymmetric structures with boundary element method</style></title><secondary-title><style face="normal" font="default" size="100%">Lixue Xuebao/Chinese Journal of Theoretical and Applied MechanicsLixue Xuebao/Chinese Journal of Theoretical and Applied MechanicsLixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics</style></secondary-title><alt-title><style face="normal" font="default" size="100%">Lixue Xuebao</style></alt-title><short-title><style face="normal" font="default" size="100%">轴对称薄壁结构自由振动的边界元分析Lixue XuebaoLixue Xuebao</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Axisymmetric structure</style></keyword><keyword><style  face="normal" font="default" size="100%">Boundary element method</style></keyword><keyword><style  face="normal" font="default" size="100%">Boundary integral equations</style></keyword><keyword><style  face="normal" font="default" size="100%">Circumferential direction</style></keyword><keyword><style  face="normal" font="default" size="100%">Dual reciprocity method</style></keyword><keyword><style  face="normal" font="default" size="100%">Dual reciprocity methods</style></keyword><keyword><style  face="normal" font="default" size="100%">Eigenvalues and eigenfunctions</style></keyword><keyword><style  face="normal" font="default" size="100%">Fourier series</style></keyword><keyword><style  face="normal" font="default" size="100%">Free vibration</style></keyword><keyword><style  face="normal" font="default" size="100%">Free-vibration analysis</style></keyword><keyword><style  face="normal" font="default" size="100%">Linear transformations</style></keyword><keyword><style  face="normal" font="default" size="100%">Nearly singular integral</style></keyword><keyword><style  face="normal" font="default" size="100%">Numerical methods</style></keyword><keyword><style  face="normal" font="default" size="100%">Radial basis function networks</style></keyword><keyword><style  face="normal" font="default" size="100%">Sailing vessels</style></keyword><keyword><style  face="normal" font="default" size="100%">Singular matrices</style></keyword><keyword><style  face="normal" font="default" size="100%">Singular matrix</style></keyword><keyword><style  face="normal" font="default" size="100%">sinh transformation</style></keyword><keyword><style  face="normal" font="default" size="100%">Thin walled structures</style></keyword><keyword><style  face="normal" font="default" size="100%">Vibration analysis</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><number><style face="normal" font="default" size="100%">1</style></number><publisher><style face="normal" font="default" size="100%">Chinese Journal of Theoretical and Applied Mechanics Press</style></publisher><volume><style face="normal" font="default" size="100%">51</style></volume><pages><style face="normal" font="default" size="100%">146-158</style></pages><isbn><style face="normal" font="default" size="100%">04591879 (ISSN)</style></isbn><language><style face="normal" font="default" size="100%">Chinese</style></language><abstract><style face="normal" font="default" size="100%">The dual reciprocity method(DRM) is extended to study the eigenvalue and eigenmode of thin-walled axisymmetric structures. First the displacement in the domain integral can be approximated by a set of radial basis functions and the domain integral can be converted to the boundary using DRM. Then the displacement and the traction can be expanded as Fourier series and integrate along the circumferential direction. The obtained boundary integral equation can be used for analysis of elastostatics of axisymmetric structure distributed body force and elastodynamics subject to asymmetric loading. The special case of the source point on the axis of symmetry is discussed in detail. New schemes are suggested for dealing with singular matrices for cases with and without body force respectively according to the degenerate form of the fundamental solution and the particular solution. For the thin walled structure, the sinh transformation is applied to improve the accuracy of evaluation of the nearly singular integrals. The developed project has been used to analyze elastostatics with body force and the free vibration of the thin axisymmetric structures. Numerical results indicate that the proposed method for dealing with singular matrices can effectively deal with the situation where the source point is on the axis of symmetry. and when the thickness ratio reaches 10-3, the relative error of the results can approach 10-3, which is better than those of FEM. © 2019, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.</style></abstract><work-type><style face="normal" font="default" size="100%">Article</style></work-type><notes><style face="normal" font="default" size="100%">Export Date: 02 November 2022; Cited By: 4; CODEN: LHHPA</style></notes><auth-address><style face="normal" font="default" size="100%">Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China</style></auth-address><remote-database-name><style face="normal" font="default" size="100%">Scopus</style></remote-database-name></record></records></xml>