Abstract：One of the essential characteristics of the dynamic response of the soil-structure interaction system is that the elastic foundation in a limited range and its supporting structure motion together. The dynamic equations that introduce soil motion into the system can reflect its effect on the system's dynamic characteristics. On the basis of the nonlinear equation of motion of the finite-length beam on Winkler foundation with the consideration of finite-depth soil mass motion, the Galerkin method and the multiple scales method were employed to obtain the frequency response equation and the second-order approximation solution of the 1/2 order sub-harmonic resonance of the beam. Then, through numerical calculation, the frequency-response curves of the 1/2 order sub-harmonic resonance of the beam are obtained. Meanwhile, the effects of foundation depth, soil mass, elastic modulus, Winkler parameter, and damping on the 1/2 order sub-harmonic resonance response of beams on elastic foundation were investigated. The results show that the effect of the finite-depth soil mass motion on the 1/2 order sub-harmonic resonance of the beam on Winkler foundation was significant. When the influence of soil mass motion is introduced into the equation of motion of the beam, the range of 1/2 order sub-harmonic resonance of the system is significantly reduced. With the change of the depth, mass, and elastic modulus of foundation, there are some quantitatively changes that were observed in the frequency-response curves of the 1/2 order sub-harmonic resonance of beam on elastic foundation, such as the degree of deflection, resonance range, and response amplitude. When the stiffness of the elastic foundation increased to a specific value, the effect of changes in the Winkler foundation parameters on the system’s 1/2 order sub-harmonic resonance response was significantly weakened. Because the damping inhibited the dynamic response of the system, when the parameter η increased to a specific value, the non-trivial solution of the 1/2 order sub-harmonic resonance would not appear.
王满,马建军,韩书娟. 考虑有限深度土体运动的Winkler地基梁1/2次谐波共振响应分析[J]. 振动与冲击, 2020, 39(11): 165-170.
WANG Man, MA Jianjun, HAN Shujuan. 1/2 sub-harmonic resonance of beams on Winkler foundation with consideration of finite-depth soil motion. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(11): 165-170.
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