Boundary integral education methods in eigenvalue problems - download pdf or read online

By Michihiro Kitahara

ISBN-10: 0444417583

ISBN-13: 9780444417589

ISBN-10: 0444424474

ISBN-13: 9780444424471

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Adjoint pair, U: Unknown -47- Φ t Table 3 . 3 . 2 Homogeneous boundary integral equations and eigenfunctions for the third boundary value problem Formulation of Problem Eigenfunction u= (St)9Di-(Du)9l>7 (St)9Dl-(K*u)9Dt ! o 1- X + Km)u]3D, = 0 = 0 o n <9Z)2 on dDx h G (u, t) {Kt)dDi-(Dnu)3D2-0 •2 •o <υ i on dDx =0 (St)9Dl-(K*u)9Dt ! P. ; Identity Pair, U: Unknown -48- The blanks in the tables show the fact that there exists no eigenfunction in the exterior problems. 5, it is adequate to express the mutual relations among integral equations of the interior and the exterior problems more explicitly on the basis of the results stated in the last section.

Integral equations for determining eigenvalues of the third interior boundary value problem. -46- Table 3 . 3 . P. A3 K)t-0 m u) US) K* 5" ιζ 1 »~ LP. : Adjoint pair, U: Unknown -47- Φ t Table 3 . 3 . 2 Homogeneous boundary integral equations and eigenfunctions for the third boundary value problem Formulation of Problem Eigenfunction u= (St)9Di-(Du)9l>7 (St)9Dl-(K*u)9Dt ! o 1- X + Km)u]3D, = 0 = 0 o n <9Z)2 on dDx h G (u, t) {Kt)dDi-(Dnu)3D2-0 •2 •o <υ i on dDx =0 (St)9Dl-(K*u)9Dt ! P. ; Identity Pair, U: Unknown -48- The blanks in the tables show the fact that there exists no eigenfunction in the exterior problems.

24) from eq. 22). Substituting eqs. 24) into eq. 25) eik v= ei — t€2 Fig. 4 . 2 . 28) where eq. 5 and the following formula (p. 74 in Ref. 11) = 2Η(„1)\Ζ) Η^\{Ζ)-Η^ΛΖ) are used. 2, we can check the jump condi­ tions of simple and double layer potentials. 32) (Β)ΞΒ+-Β-, where B+ and B~ denote the limit values when X approaches a point x on dD while re­ maining within D+ and D-, respectively. 33) for each n. 34) for each n, where the following formula (p. 76 in Ref. 35) is used.

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Boundary integral education methods in eigenvalue problems of elastodynamics and thin plates by Michihiro Kitahara


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