Multiscale asymptotic analysis and algorithm for the quadratic eigenvalue problem in periodic composite materials
A second-order two-scale(SOTS)asymptotic analysis and computational method are developed for solving the quadratic eigenvalue problem(QEP)in periodic composited domain.A typical QEP involving the velocity-damping is considered and asymptotic expansions for the eigenfunctions are performed.Then a finite el-ement procedure is proposed and the homogenized QEPs are solved by the linearized method.Numerical ex-amples demonstrate the accuracy and efficiency of the method.It is shown that the method can effectively be ap-plied to such nonlinear eigenvalue problems in which the second-order correctors play an important role for de-scribing the local behavior of eigenfunctions and obtaining better approximation of the eigenvalues at lower cost.
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