阻尼连续体简谐基础振动的有限元实现方法
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摘要
针对简谐基础激励下,阻尼连续体响应结果数值计算存在刚体位移、约束方式、载荷施加方式和数值算法稳定性等限制,依据连续体基础振动原理和有限元数值计算实现过程推导,提出一种求解简谐基础振动响应的有效方法——静力等效载荷法。该方法依据连续体等效载荷形式,结合通用有限元软件和自编数据处理程序,将简谐基础振动问题转化为固定基础的载荷简谐振动。通过某航空涡轮发动机气流测温探针简谐基础振动试验和仿真结果对比表明,静力等效载荷法能够有效地求解阻尼连续体简谐基础振动问题,具有实现简单、结果准确和响应结果直观的特点,且克服了时间历程法和反映谱法的诸多限制,为复杂阻尼结构简谐基础振动、基础冲击和非简谐基础振动等问题求解提供了新思路。
There are lots of restrictions to numerical simulation of continua vibrations from the base,including rigid-body motion,constrains,loading mode,stability of numerical algorithm and so on. By theoretical deduction and FEM calculation of the structural response under harmonic vibration of the base,a new effective approach called static inertia method is proposed. Based on the equivalent form of base load,general FEM software and self-developed data processing program,the new method transforms the original problem into an ordinary harmonic vibration problem with fixed base. Both of experimental and numerical results with the probe for detecting the temperatures inside turboprop indicate that the static inertia method is an effective method with simple implementation and accurate response results. It overcomes the restrictions of existing methods and provides a new approach to solving the problems such as harmonic vibration,flush and anharmonic vibration from the base.
There are lots of restrictions to numerical simulation of continua vibrations from the base,including rigid-body motion,constrains,loading mode,stability of numerical algorithm and so on. By theoretical deduction and FEM calculation of the structural response under harmonic vibration of the base,a new effective approach called static inertia method is proposed. Based on the equivalent form of base load,general FEM software and self-developed data processing program,the new method transforms the original problem into an ordinary harmonic vibration problem with fixed base. Both of experimental and numerical results with the probe for detecting the temperatures inside turboprop indicate that the static inertia method is an effective method with simple implementation and accurate response results. It overcomes the restrictions of existing methods and provides a new approach to solving the problems such as harmonic vibration,flush and anharmonic vibration from the base.
引文
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[2]任建峰,仇原鹰,段宝岩,等.一种基础加速度冲击的仿真新方法[J].现代机械,2006,2:21-23.REN Jianfeng,QIU Yuanying,DUAN Baoyan,et al.A new idea to access the simulation of a shock from thebase[J].Modern Mechanic Machine,2006,2:21-23.
[3]HAN Wei,HU Haiyan,JIN Dongping.Vibrao-impacts of a slender cantilever beam with a lumped tip mass between two rigid stops[J].Transactions of Nanjing University of Aeronautics&Astronautics,2001,18(2):137-143.
[4]宋宇,王本利,马兴瑞.伸展柔性附件对简谐激励的响应分析[J].航空学报,1999,20(1):8-10.SONG Yu,WANG Benli,MA Xingrui.Dynamic response of flexible appendages to the harmonic excitation during extension[J].Acta Aeronautica et Astronautica Sinica,1999,20(1):8-10.
[5]COLLIER C J,ELNASHAI A S.A procedure for combining vertical and horizontal seismic action effects[J].Journal of Earthquake Engineering,2001,5(4):521-539.
[6]徐平,夏唐代.P1波入射角对建筑基础振动的影响[J].振动与冲击,2006,25(5):58-61.XU Ping,XIA Tangdai.Influence of incident angle of P1wave on vibration of building foundation[J].Journal of Vibration and Shock,2006,25(5):58-61.
[7]张富有,刘汉龙,崔艺斌.并联基础隔震结构的地震随机响应分析[J].岩土力学,2006,27(11):1927-1934.ZHANG Fuyou,LIU Hanlong,CUI Yibin.Analysis of random resposes to earthquake of parallel base isolated structure[J].Rock and Soil Mechanics,2006,27(11):1927-1934.
[8]邵长江,钱永久.Koyna混凝土重力坝的塑性地震损伤响应分析[J].振动与冲击,2006,25(4):129-131.SHAO Changjiang,QIAN Yongjiu.Seismic plastic damage response analysis of Koyna concrete gravity dam[J].Journal of Vibration and Shock,2006,25(4):129-131.
[9]POLITOPOULOS I,AXISA F.On the earthquake re-sponse of rotors[J].Journal of Earthquake Engineering,2006,10(5):641-664.
[10]CHOPRA Anil K.结构动力学理论及其在地震工程中的应用[M].谢礼立,吕大刚,译.北京:高等教育出版社,2005.CHOPRA Anil K.Dynamics of structures-Theory and applications to earthquake engineering[M].Translated by XIE Lili,LüDagang.Beijing:Higher Education Press,2005.
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