✍ Scribed by Eugenia Pérez
No coin nor oath required. For personal study only.
We consider a set of Neumann (mixed, respectively) eigenvalue problems for the Laplace operator. Each problem is posed in a bounded domain R of R n , with n = 2; 3, which contains a ÿxed bounded domain B where the density takes the value 1 and 0 outside. R has a diameter depending on a parameter R, with R¿1, diam( R ) → ∞ as R → ∞ and the union of these sets is the whole space R n (the half space {x ∈ R n = 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.
📜 SIMILAR VOLUMES
In this paper, single-mode vibration suppression of an elastic beam "xed on a moving cart and carrying a concentrated or moving mass is considered. A modi"ed pulse sequence method with robust internal-loop compensator (RIC) is proposed to suppress single-mode residual vibration and to get accurate p