Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections.For the special geometry characteristic,the beam was modelled as the combination of long equal-le...Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections.For the special geometry characteristic,the beam was modelled as the combination of long equal-length uniform Euler-Bernoulli beam segments and short equal-length uniform Timoshenko beam segments alternately.By using continuity conditions,the hybrid beam unit(ETE-B) consisting of Euler-Bernoulli beam,Timoshenko beam and Euler-Bernoulli beam in sequence was developed.Classical boundary conditions of pinned-pinned,clamped-clamped and clamped-free were considered to obtain the natural frequencies.Numerical examples of the equal-length composite beam with 1,2 and 3 ETE-B units were presented and compared with the equal-length and equal-cross-section Euler-Bernoulli beam,respectively.The work demonstrates that natural frequencies of the composite beam are larger than those of the Euler-Bernoulli beam,which in practice,is the interpretation that the inner-welded plate can strengthen a hollow beam.In this work,comparisons with the finite element calculation were presented to validate the ETE-B model.展开更多
基金Projects(51605138,U1508210)supported by the National Natural Science Foundation of ChinaProject(BK20160286)supported by the Natural Science Foundation of Jiangsu Province,ChinaProject(2015B30214)supported by the Fundamental Research Funds for the Central Universities,China
文摘Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections.For the special geometry characteristic,the beam was modelled as the combination of long equal-length uniform Euler-Bernoulli beam segments and short equal-length uniform Timoshenko beam segments alternately.By using continuity conditions,the hybrid beam unit(ETE-B) consisting of Euler-Bernoulli beam,Timoshenko beam and Euler-Bernoulli beam in sequence was developed.Classical boundary conditions of pinned-pinned,clamped-clamped and clamped-free were considered to obtain the natural frequencies.Numerical examples of the equal-length composite beam with 1,2 and 3 ETE-B units were presented and compared with the equal-length and equal-cross-section Euler-Bernoulli beam,respectively.The work demonstrates that natural frequencies of the composite beam are larger than those of the Euler-Bernoulli beam,which in practice,is the interpretation that the inner-welded plate can strengthen a hollow beam.In this work,comparisons with the finite element calculation were presented to validate the ETE-B model.
