移动简谐力激励非线性无限长地基梁稳态响应

STEADY STATE RESPONSE OF AN INFINITE BEAM ON A NONLINEAR FOUNDATION TO A MOVING HARMONIC LOAD

同时计入地基中的非线性弹性、黏性以及剪切作用的影响,研究移动集中简谐力作用下无限长地基梁稳态响应问题.假设基础非线性弹性为立方非线性.通过Adomian多项式分解方法和Fourier变换得到梁稳态响应的Green函数,再运用Fourier逆变换得到梁稳态响应近似解析解的积分表达式.最后对解析积分表达式应用留数定理得到复数域上的解.通过数值算例,考察了移动集中简谐力的频率和移动速度对无限长地基梁稳态响应的影响.另外,还通过算例对比研究了地基的非线性弹性系数和剪切系数对无限长地基梁稳态响应的影响.

This paper studied the steady state response of infinite beams supported by nonlinear viscoelastic foundations with 4- parameters. A moving harmonic concentrated load was considered,and the nonlinear foundation was assumed to be cubic. The domain decomposition method was used to deal with the nonlinear term of the foundation reaction,and the complex Fourier transformations,Green＇ s function,and the theorem of residues were employed to determine the steady state response of the infinite beam on a nonlinear foundation. The numerical examples were used to investigate the effects of the frequency and the speed of moving harmonic load on the steady state responses of infinite beams supported by nonlinear foundations. Moreover,the influences of the nonlinear elastic parameter and the shear modulus of foundations on the steady state responses were also studied.