弹性地基上加热梁受简谐激励的主共振响应

英文篇名：The main resonance response of a heating beam on elastic foundation under simple harmonic energizing
中文刊名：青海大学学报(自然科学版)
英文刊名：Journal of Qinghai University(Nature Science)
作者：赵伟东 ; 杨亚平
英文作者：ZHAO Weidong ; YANG Yaping (Civil Engineering Department of Qinghai University ; Xining 810016 ; China)
中文关键词：梁 ; 热 ; 弹性地基 ; 非线性受迫振动 ; 主共振
英文关键词：beam ; heat ; elastic foundation ; nonlinear forced vibration ; main resonance
出版日期：2010-02-20
机构：青海大学建筑工程系;
年：2010
期：01
出版单位：青海大学学报(自然科学版)

摘要

基于Hamilton原理,得到了弹性地基上加热梁受简谐激励作用的非线性强迫振动控制方程。运用Kantorovich平均法将非线性偏微分方程转化成一组常微分方程,考虑不可移夹紧边界条件,采用打靶法得到了主共振的数值结果。考察了不同参数对主共振响应的影响。
Based on the Hamilton principle,the governing equations of the nonlinear forced vibration of a heated beam on an elestic foundation under simple harmonic energization were obtained in this paper and the nonlinear partial differential equations were converted into a set of ordinary ones by using Kantorovich average methed.Considering immovable clamped boundary conditions,the numerical results of the main resonance were obtained by employing a shooting method.At last,the influence of different parameters on the main resonance is examined too in details.

引文

[1]李世荣,程昌钧.加热弹性杆的热过屈曲分析[J].应用数学和力学,2000,21(2):119-125.
    [2]Li Shirong.Nonlinear Free Vibration of Thermally Buckled Beam with Both Ends Immovable and Simply Supported[J].Journal of GansuUniversity of Technology,2001,5(1):111-114.
    [3]Li S R.Batra R C.Thermal Buckling and Postbuckling of Euler-Bernoulli Beams Supported on Nonlinear elastic Foundations[J].AiaaJournal,2007,45(3):712-720.
    [4]赵伟东,杨亚平.弹性地基上简支梁在热载荷作用下的自由振动[J].青海大学学报:自然科学版,2008,26(4):14-18.
    [5]赵伟东.弹性地基上固支梁在热载荷作用下的自由振动[J].青海大学学报:自然科学版,2009,27(1):3-6.
    [6]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[J].地震工程与工程振动,2006,26(3):91-93.
    [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[J].地震工程与工程振动,2006,26(5):239-242.
    [8]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[J].地震工程与工程振动,2006,26(4):132-135.
    [9]赵伟东,卞敬玲.弹性地基梁在温度场中受简谐激励的主共振响应[J].宁夏大学学报,2009,30(3):244-247.