考虑非黏性阻尼的黏弹性DDA解法

Viscoelastic DDA solution considering non-viscous damping

将非黏性阻尼引入到DDA方法中,用以分析非黏性阻尼对于非连续黏弹性结构的影响。首先,将非黏性阻尼引入到块体系统的运动方程中,发现微分形式运动方程难以求解的问题。其次,通过黏弹性结构的力与位移的关系以及Newmark积分方案,推导得到具有对称系数矩阵的含有非黏性阻尼的等价DDA运动方程。最后,结合具体算例,分别分析在恒力作用下和谐振激励作用下的块体位移响应,通过比较DDA计算值和理论值,验证提出的含有非黏性阻尼的黏弹性结构DDA解法的正确性。研究结果表明该考虑非黏性阻尼的DDA方法是一种高效的处理黏弹性问题的解法,这为分析黏弹性结构的非连续变形提供了新思路。

The non-viscous damping is introduced into the DDA method in this article for analysing the influence of non-viscous damping on discontinuous viscoelastic structure.Firstly,the non-viscous damping is introduced into the motion equations of block system,and the difficulty of solving the differential motion equations was found.Secondly,with the relationship between force and displacement and the Newmark integration algorithm,the equivalent DDA motion equations considering non-viscous damping with the symmetrical coefficient matrix was derived.Finally,with specific examples,the block displacement response under constant force or resonant excitation was analyzed,and through comparing DDA calculated value and theoretical value,the correctness of the viscoelastic DDA solution considering non-viscous damping proposed in the article was verified.Thus,the DDA solution considering non-viscous damping is a highly effective method to deal with viscoelastic problem,and it provides a new idea for analysing the discontinuous deformation of viscoelastic structure.