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给出了基于Hertz接触理论的冲击体与梁结构之间的局部接触力-接触变形关系。根据弯曲理论,建立了具有粘弹性支座钢筋混凝土梁在低速冲击作用下的弹塑性动力响应计算方法,并通过算例分析了冲击速度、支座刚度和支座阻尼对动力响应的影响。分析发现:梁的总位移随冲击速度增大而增大,当冲击速度足够大时梁将出现塑性变形。支座条件对梁的动力响应有较大影响,梁的总位移最大值随支座刚度增大而减小,而相对位移最大值随支座刚度增大而增大,振动频率随支座刚度增大而明显增大;梁的总位移最大值随支座阻尼增大而减小,相对位移最大值随支座阻尼变化不明显,位移幅值衰减值随支座阻尼增大而增大,但振动频率不受支座阻尼影响。结果表明:采用粘弹性支座既能减小钢筋混凝土梁的相对位移幅值,又能加速梁的位移幅值衰减,提高了梁结构的抗冲击能力。
The local contact force-contact deformation relationship between the impact body and the beam structure based on the Hertz contact theory is given. According to the bending theory, the elastic-plastic dynamic response of a reinforced concrete beam with viscoelastic support under low velocity impact is established. The influences of impact velocity, bearing stiffness and bearing damping on dynamic response are analyzed. The analysis shows that the total beam displacement increases with the impact velocity and the plastic deformation occurs when the impact velocity is large enough. The bearing conditions have a great influence on the dynamic response of the beam. The maximum total displacement of the beam decreases with the increase of bearing stiffness, while the maximum value of relative displacement increases with the increase of bearing stiffness. The vibration frequency increases with the stiffness of bearing The maximum value of the total displacement of the beam decreases with the increase of the damping of the support, the maximum value of the relative displacement does not change obviously with the damping of the support, the attenuation value of the displacement increases with the increase of the damping of the support, However, the vibration frequency is not affected by the support damping. The results show that the viscoelastic bearing can not only reduce the relative displacement amplitude of the reinforced concrete beam, but also accelerate the amplitude attenuation of the beam and improve the impact resistance of the beam structure.