Spectral convergence for vibrating systems containing a part with negligible mass
Eugenia Pérez · Mathematical Methods in the Applied Sciences · 2005
We consider a set of Neumann (mixed, respectively) eigenvalue problems for the Laplace operator. Each problem is posed in a bounded domain ΩR of ℝn, with n=2,3, which contains a fixed bounded domain B where the density takes the value 1 and 0 outside. ΩR has a diameter depending on a parameter R, with R⩾1, diam(ΩR) →∞ as R→∞ and the union of these sets is the whole space ℝn (the half space {x∈ℝn/xn<0}, respectively). Depending on the dimension of the space n, and on the boundary conditions, we describe the asymptotic behaviour of the eigenelements as R→∞. We apply these asymptotics in order to derive important spectral properties for vibrating systems with concentrated masses. Copyright © 2005 John Wiley & Sons, Ltd.