Non-modal eigenfunction expansions

Ordinary and Partial Differential Equations - Lecture Notes in Mathematics ◽

10.1007/bfb0089830 ◽

1981 ◽

pp. 109-118 ◽

Cited By ~ 2

Author(s):

M. Faierman ◽

I. Knowles

Keyword(s):

Eigenfunction Expansions

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Eigenfunction Expansions of Source-excited Electromagnetic Fields on Open Cylindrical Guiding Structures in Unbounded Gyrotropic Media

PIERS Online ◽

10.2529/piers070317073215 ◽

2007 ◽

Vol 3 (8) ◽

pp. 1283-1287 ◽

Cited By ~ 1

Author(s):

Alexander V. Kudrin ◽

E. Yu. Petrov ◽

T. M. Zaboronkova

Keyword(s):

Electromagnetic Fields ◽

Eigenfunction Expansions ◽

Gyrotropic Media

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Theorems of Chernoff and Ingham for certain eigenfunction expansions

Advances in Mathematics ◽

10.1016/j.aim.2021.107815 ◽

2021 ◽

Vol 386 ◽

pp. 107815

Author(s):

Pritam Ganguly ◽

Sundaram Thangavelu

Keyword(s):

Eigenfunction Expansions

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Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8130 ◽

1999 ◽

Author(s):

Keh-Yang Lee ◽

Anthony A. Renshaw

Keyword(s):

Solution Technique ◽

Distributed Parameter ◽

Moving Mass ◽

Eigenfunction Expansions ◽

Galerkin’S Method ◽

Galerkin's Method ◽

Mass Problem ◽

Linearly Independent ◽

Large Numbers ◽

Speed Accuracy

Abstract A new solution technique is developed for solving the moving mass problem for nonconservalive, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of terms because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented in the method proposed here by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, 1997). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. A set of real differential ordinary equations in time are derived which require exactly as much work to solve as Galerkin’s method with a set of real, linearly independent trial functions. Results indicate that the proposed method is competitive with traditional Galerkin’s method in terms of speed, accuracy and convergence.

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