Spectral properties of the laplacian with attractive boundary conditions

2005 ◽  
pp. 194-202
Author(s):  
Manfred Schröder
Keyword(s):  
Boundary Conditions ◽  
Spectral Properties

Pencils of differential operators containing the eigenvalue parameter in the boundary conditions

2003 ◽  
Vol 133 (4) ◽  
pp. 893-917 ◽  
Author(s):  
Marco Marletta ◽  
Andrei Shkalikov ◽  
Christiane Tretter
Keyword(s):  
Boundary Conditions ◽  
Spectral Properties ◽  
Differential Operators ◽  
Finite Interval ◽  
Linear Operators ◽  
Riesz Bases ◽  
Ordinary Differential Operators ◽  
Associated Functions ◽  
Eigenvalue Parameter

The paper deals with linear pencils N − λP of ordinary differential operators on a finite interval with λ-dependent boundary conditions. Three different problems of this form arising in elasticity and hydrodynamics are considered. So-called linearization pairs (W, T) are constructed for the problems in question. More precisely, functional spaces W densely embedded in L2 and linear operators T acting in W are constructed such that the eigenvalues and the eigen- and associated functions of T coincide with those of the original problems. The spectral properties of the linearized operators T are studied. In particular, it is proved that the eigen- and associated functions of all linearizations (and hence of the corresponding original problems) form Riesz bases in the spaces W and in other spaces which are obtained by interpolation between D(T) and W.

scholarly journals Effects of Boundary Conditions on the Modal and Spectral Properties of the Shaft

2020 ◽  
Vol 22 (1) ◽  
pp. 42-47
Author(s):  
Petr Hruby ◽  
Tomas Nahlik ◽  
Dana Smetanova
Keyword(s):  
Boundary Conditions ◽  
Spectral Properties ◽  
Rotating Shaft ◽  
The Real ◽  
Vibration Problem ◽  
Modal Properties ◽  
Fixed End

Influence of boundary conditions (i.e. mounting type of shafts ends) on spectral and modal properties is studied in this paper. Cases with joints at both ends and with joint at one end and fixed end are described in detail. The vibration problem of rotating shaft is generalized to problem of vibration of the shaft in the rotating plane. The problem is illustrated on testing models. The real mounting type of shafts is presented.

Sign in / Sign up

Export Citation Format

Share Document