第46卷第4期浙江师范大学学报(自然科学版)Vol.46,No.42023年11月JournalofZhejiangNormalUniversity(Nat.Sci.)Nov.2023DOI:10.16218/j.issn.1001-5051.2023.023均匀弹性杆弯曲振动的机电等效电路李凤鸣1,2,刘世清1,许龙2,陈赵江1(1.浙江师范大学应用声学研究所,浙江金华321004;2.中国计量大学理学院,浙江杭州310018)摘要:为简化弯曲振动系统的设计,基于Shear梁和Euler-Bernoulli梁理论与机电类比原理,推导了均匀弹性杆弯曲振动的机电等效电路及其共振频率方程.在此基础上,探讨了杆的前10阶弯曲振动共振频率与其几何尺寸之间的依赖关系,并对其弯曲振动特性进行了数值仿真计算与分析.结果表明:均匀弹性杆两端横向力与振速之间满足互易关系,其弯曲振动亦可用机电类比T型等效电路来描述;杆的弯曲振动共振频率随其振动阶次的增加而增大;相同阶次的弯曲共振频率随其长高比的增加而减小;对于考虑剪切变形影响的Shear梁,在较高的振动阶次及较小的长高比范围内,其弯曲振动共振频率的理论与仿真结果吻合较好.研究结果可为弯曲振动及其耦合振动系统的设计及应用提供一种有效的等效电路分析方法.关键词:均匀弹性杆;弯曲振动;机电等效电路;共振频率;振动阶次中图分类号:O426.9文献标识码:A文章编号:1001-5051(2023)04-0395-07TheelectromechanicalequivalentcircuitoftheuniformsectionelasticrodinflexuralvibrationmodeLIFengming1,2,LIUShiqing1,XULong2,CHENZhaojiang1(1.AppliedAcousticsInstitute,ZhejiangNormalUniversity,Jinhua321004,China;2.CollegeofSciences,ChinaJiliangUniversity,Hangzhou310018,China)Abstract:Inordertosimplifythediesignoftheflexurelvibartionsystem,theelectro-mechanicalequivalentcircuitandtheresonancefrequencyequationoftheuniformsectionelasticrodinflexuralvibrationwerederivedbasedonthetheoryoftheShearbeamandtheEuler-Bernoullibeamaswellastheelectro-mechanicalanalogy.Therelationshipbetweentheresonantfrequencyoftherodinthefirsttenordersflexuralvibrationmodeanditsgeometricaldimensionswereanalyzed,andtheflexuralvibrationcharacteristicsoftheuniformelasticrodweresimulatedandinvetigated.Itwasshowedthatthereciprocalrelationshipbetweentransverseforceandvibrationvelocityatthebothendsoftheuniformsectionelasticrodwassatisfied,andtheelectro-mechanicalequivalentcircuitoftherod...
