黏弹性地基上双模量梁受迫振动的时域微分求积法求解

Time-Domain Differential Quadrature Method Solution for Forced Vibration of Bimodular Beams on Viscoelastic Foundations

以欧拉—伯努利梁模型和黏弹性地基模型为基础,说明了黏弹性地基上双模量梁在振动过程中有效抗弯刚度不变,推导出中性层在梁内部时,双模量梁在地基上的受迫振动控制方程.利用其中性层跳变时位移和速度没有突变,用时域微分求积法求解了控制方程,并分别探讨了地基的线性刚度和剪切参数,以及双模量特性对简支双模量梁受迫振动的影响.结果表明,地基的2个参数越大,受迫振动到达稳定的时间越短;双模量比值越大,受迫振动幅值越小.

Based on the Euler-Bernoulli beam model and the viscoelastic foundation model,it is explained that the effective flexural stiffness of the bimodular beam on the viscoelastic foundation is unchanged during the vibration,and the governing equation of the bimodular beam on the foundation when the neutral layer is inside the beam is derived.Using the absence of sudden changes in displacement and velocity during the transition of the neutral layer,the governing equation is solved by the time-domain differential quadrature method,and the influence of linear stiffness,shear parameters and bimodular characteristics on the forced vibration of simply support bimodular beams is discussed respectively.Finally,the larger the two parameters of the foundation are,the shorter the time for the forced vibration to reach stability will be.The larger the dual-modulus ratio is,the smaller the forced vibration amplitude will be.