Numerical scheme approximating solution and parameters in a beam equation

[摘要] We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed. (C) 2003 Elsevier B.V. All rights reserved.

[发布日期] 2003-12-15

[关键词] beam equation;finite element;Galerkin;inverse problem;parameter estimation