Extremely strong convergence of eigenvalue-density of linear stochastic dynamical systems

摘要: Eigenvalue problems play a crucial role in the stability and dynamics of engineering systems modeled using linear mechanical theory. When uncertainties, either parameters or modelling, are considered, eigenvalue problem becomes random problem. Over past half century, have received extensive attentions from physicists, applied mathematicians engineers. Within context civil, aerospace engineering, significant work has been done on perturbation method based approaches conjunction with stochastic finite element method. The methods very well low frequency region which is often sufficient for many applications. In high however, necessary some practical applications, these fail to capture physics, such as veering modal overlap. this one needs consider complete spectrum eigenvalues opposed individual considered paper we density discrete discretised continuous system uncertainty. It rigorously proved that dynamical reaches non-random limit large systems. This fact demonstrated by numerical examples. implications result response calculation structural highlighted.