Effect of soil mass motion on 1/3 sub-harmonic resonance of beams on Winkler foundation

Subjects: Physics >> Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics submitted time 2023-12-18 Cooperative journals: 《应用力学学报》

MA Jianjun

Abstract：
The effect of the finite-depth soil mass motion on the dynamic characteristics and nonlinear response of the beam on an elastic foundation is significant.To enhance and deepen the scope of related research,based on the nonlinear equation of motion of the finite-length beam on Winkler foundation with the consideration of soil mass motion,the study focuses on examining how finite-depth soil motion impacts the behavior of an elastic foundation beam under 1/3 order subharmonic resonance conditions.Then,the frequency-response equation and the second-order approximation solution of the 1/3 order sub-harmonic resonance of the beam are derived through the application of the Galerkin method and the multiple scales method.The effects of parameters closely related to soil mass motion(foundation depth,soil mass,elastic modulus,stiffness,and damping,etc.)and excitation amplitude on the sub-harmonic resonance of the beam are investigated by the response equation.The numerical results show that when the effect of soil mass motion is introduced into the equation of motion of the beam,the range and amplitude of the 1/3 order sub-harmonic resonance of the beam decrease.With the change of the depth,mass,and elastic modulus of foundation,some quantitative differences are observed in the frequency-response curves,such as the degree of deflection,resonance range,and amplitude.Excitation’s amplitude does not affect the characteristics of the 1/3 order sub-harmonic resonance of the beam.Still,it has a significant effect on the response amplitude and resonance region.On the other hand,the damping of the foundation has apparent inhibition on the 1/3 order sub-harmonic resonance of the beam.

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