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利用三次B样条函数的线性组合模拟柔性支撑梁的位移振型函数,根据拉格朗日方程建立了动力计算模型,模型考虑了弹性支撑和阻尼支撑等情况;研究了爆炸冲击荷载作用下柔性支撑对梁动力响应的影响;提出了短时荷载和长时荷载的定量界定建议。分析结果表明:在短时荷载(爆炸冲击持续时间小于简支梁半个自振周期)作用下,弹性支撑可有效降低梁跨中截面的弯矩,从而提高梁的抗爆承载力,且弹性系数越小,减振效果越好;在长时荷载(爆炸冲击持续时间大于简支梁半个自振周期)作用下,弹性支撑的减振效果是有条件的,只有弹性系数较小时才能降低梁的动力效应,若弹性系数超过某一限值,在残余振动阶段会出现振动反弹,反而会降低梁的抗爆承载力,这种情况下加设阻尼支撑,可使结构振动快速衰减,阻尼系数越大,振动衰减越快。
A linear combination of cubic B-spline functions was used to simulate the displacement mode function of the flexible support beam. The dynamic calculation model was established according to the Lagrange equation. The elastic support and the damping support were considered in the model. The effects of flexural load The influence of support on the dynamic response of the beam is proposed. The quantitative definition of short-term load and long-term load are proposed. The analysis results show that the elastic support can effectively reduce the bending moment of the mid-section of the beam and improve the anti-blast bearing capacity of the beam under the effect of short-time load (the duration of the impact is less than half the natural period of the simple supported beam) The smaller the coefficient is, the better the damping effect is. Under the action of long-term load (the duration of the impact is greater than half the free-vibration period of the beam), the vibration damping effect of the elastic support is conditional and can be reduced only when the elastic coefficient is small The dynamic effect of the beam, if the elastic coefficient exceeds a certain limit, will appear in the residual vibration phase vibration rebound, but will reduce the anti-blast bearing capacity of the beam, in this case the addition of damping support, the structure can quickly attenuate vibration damping The larger the coefficient, the faster the vibration decays.