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
The stability of the roof in coal mining is crucial for ensuring safe extraction.Studying the mechanical behavior of rock beams under various conditions is essential for improving coal mining safety.However,research o...The stability of the roof in coal mining is crucial for ensuring safe extraction.Studying the mechanical behavior of rock beams under various conditions is essential for improving coal mining safety.However,research on the dynamic response of rock beams under sudden unloading remains limited.This study utilized a self-developed bidirectional loading and unilateral unloading test system to simulate how sudden lower strata subsidence induces the fracture of upper hard rock beams.Bottom unloading experiments were performed on rock beams with varying thicknesses and spans.The experiments recorded surface crack development and internal damage evolution using high speed photography and acoustic emission monitoring.The results show that rock beams experience multiple stress reductions after unloading,with the largest reduction occurring in the first stage.Flexural deformation was observed,becoming more pronounced as the thickness-span ratio decreased.Greater thickness increased shear cracks and crack expansion angles,while larger spans promoted tensile cracks,arched crack formation,and notable rock spalling.Acoustic emission analysis showed that signal count and energy increased with thickness and span.Finally,discrete element numerical simulations revealed the critical controlling role of harder rock strata in rock beam failure:when the harder strata are at the top,cracks are sharp,and shear failure is more likely;when they are at the bottom,the overall failure range expands,and cracks tend to form arches.These findings improve the understanding of dynamic rock beam fracture under sudden unloading and offer theoretical guidance for roof stability control in deep mining.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.
基金Project(TD20240003)supported by the Ordos Science&Technology Plan,ChinaProjects(52174096,52304110)supported by the National Natural Science Foundation of China。
文摘The stability of the roof in coal mining is crucial for ensuring safe extraction.Studying the mechanical behavior of rock beams under various conditions is essential for improving coal mining safety.However,research on the dynamic response of rock beams under sudden unloading remains limited.This study utilized a self-developed bidirectional loading and unilateral unloading test system to simulate how sudden lower strata subsidence induces the fracture of upper hard rock beams.Bottom unloading experiments were performed on rock beams with varying thicknesses and spans.The experiments recorded surface crack development and internal damage evolution using high speed photography and acoustic emission monitoring.The results show that rock beams experience multiple stress reductions after unloading,with the largest reduction occurring in the first stage.Flexural deformation was observed,becoming more pronounced as the thickness-span ratio decreased.Greater thickness increased shear cracks and crack expansion angles,while larger spans promoted tensile cracks,arched crack formation,and notable rock spalling.Acoustic emission analysis showed that signal count and energy increased with thickness and span.Finally,discrete element numerical simulations revealed the critical controlling role of harder rock strata in rock beam failure:when the harder strata are at the top,cracks are sharp,and shear failure is more likely;when they are at the bottom,the overall failure range expands,and cracks tend to form arches.These findings improve the understanding of dynamic rock beam fracture under sudden unloading and offer theoretical guidance for roof stability control in deep mining.
