Winkler地基梁在温度场中受简谐激励作用下的主共振和主参数共振分析
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摘要
研究在温度场中受简谐激励作用的Winkler地基梁的响应问题。为考虑温度场中Winkler地基上受简谐激励梁的响应问题,应用弹性理论和伽辽金方法,导出温度场Winkler地基上受横向、纵向激励的梁的非线性动力学方程。通过多尺度法得到系统主共振和主参数共振的近似解,并进行数值计算,分析各种参数对共振系统的影响。
The response problem of a harmonically driven beam with respect to the influence of Winkler foundation in temperature field is considered. By applying elastic theory and Galerkin's method,the nonlinear dynamical equation is derived for a beam on Winkler foundation in temperature field,driven by vertical and horizontal harmonic excitations.By the method of multiple scales, the first approximation solutions for primary resonance and primary parametric resonance of the system are obtained.Then,it is followed by a detailed numerical analysis on influence of all kinds of parameters on the resonant responses of the system.
The response problem of a harmonically driven beam with respect to the influence of Winkler foundation in temperature field is considered. By applying elastic theory and Galerkin's method,the nonlinear dynamical equation is derived for a beam on Winkler foundation in temperature field,driven by vertical and horizontal harmonic excitations.By the method of multiple scales, the first approximation solutions for primary resonance and primary parametric resonance of the system are obtained.Then,it is followed by a detailed numerical analysis on influence of all kinds of parameters on the resonant responses of the system.
引文
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9曹志远.板壳振动理论.北京:中国铁道出版社,1989.CAO ZhiYuan.Vibration theory of plates and shells.Beijing:ChinaRailway Press,1989(In Chinese).
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2杨志安,赵雪娟,席晓燕.非线形弹性地基上矩形薄板的主参数共振.岩土力学,2005,26(12):1 921~1 925.YANG ZhiAn,ZHAO XueJuan,XI XiaoYan.Primary parametricresonance of thin rectangular plate on nonlinear elastic foundation.Rockand Soil Mechanics,2005,26(12):1 921~1 925(In Chinese).
3杨志安,席晓燕,李文兰.弹性直杆在温度场中的非线性振动与奇异性.工程力学,2006,23(6):50~53.YANG ZhiAn,XI XiaoYan,LI WenLan.Singularities and nonlinearvibration of the elastic straight bar under thermal with harmonicexcitation.Engineering Mechanics,2006,23(6):50~53(InChinese).
4吴晓,张龙庭,马建功.弹性直杆热膨胀状态下的非线性振动.工程力学,1996,13(4):129~133.WU Xiao,ZHANG LongTing,MA JianGong.The nonlinear vibrations ofelastic straight column in state of thermal expansion.EngineeringMechanics,1996,13(4):129~133(In Chinese).
5彭震,杨志安.Winkler地基梁在温度场中受简谐激励的主共振分析.地震工程与工程振动,2006,26(3):91~93.PENG Zhen,YANG ZhiAn.Analysis of primary resonance of a beamexternally excited on the Winkler foundation in temperature field.Earthquake Engineering and Engineering Vibration,2006,26(3):91~93(In Chinese).
6彭震,杨志安.Winkler地基梁在温度场中受简谐激励的1/3次亚谐共振分析.地震工程与工程振动,2006,26(4):132~135.PENG Zhen,YANG ZhiAn.Analysis of 1/3 subharmonic resonance of abeam externally excited on the Winkler foundation in temperature field.Earthquake Engineering and Engineering Vibration,2006,26(4):132~135(In Chinese).
7彭震,杨志安.Winkler地基梁在温度场中受简谐激励的3次超谐共振分析.地震工程与工程振动,2006,26(5):239~242.PENG Zhen,YANG ZhiAn.Analysis of 3 superhamonic resonance of abeam externally excited on the Winkler foundation in temperature field.Earthquake Engineering and Engineering Vibration,2006,26(5):239~242(In Chinese).
8付宝连.弯曲薄板功的互等新理论.北京:科学出版社,2003.FU BaoLian.The reciprocal new theory of bending plates.Beijing:Science Press,2003(In Chinese).
9曹志远.板壳振动理论.北京:中国铁道出版社,1989.CAO ZhiYuan.Vibration theory of plates and shells.Beijing:ChinaRailway Press,1989(In Chinese).
10胡海岩.应用非线性动力学.北京:航空工业出版社,2000.HU HaiYan.Applied nonlinear dynamics.Beijing:Aviation IndustryPress,2000(In Chinese).
11杨志安,彭震,程英辉.受简谐激励弹簧测力机构的主共振与奇异性分析.机械强度,2006,28(5):664~669.YANG ZhiAn,PENG Zhen,CHENG YingHui.Primary resonance andits singularities analysis of a dynamometer subjected to harmonicexcitation.Journal of Mechanical Strength,2006,28(5):664~669(InChinese).
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