Perturbation of Vibrating Systems
In this chapter we apply the perturbation methods of Chapters V and VI to study asymptotic properties of vibrating systems involving a small parameter ε. Most of the examples were considered, for fixed values of ε, in Chapters II and IV. Several kinds of stiff problems in low frequency vibration are considered in Sections 1 to 4. The case of high frequencies and other problems involving spectral families are considered in Sections 5 and 6. Sections 7 and 8 are devoted to more classical problems involving boundary layers. An example of the splitting of an eigenvalue with infinite multiplicity appears in Section 9. The rest of the chapter (Sections 10 to 13) is devoted to problems with masses concentrated in small regions. To some extent, the different sections may be read independently.
KeywordsEigenvalue Problem Holomorphic Function Dirichlet Problem Dirichlet Boundary Condition Compatibility Condition
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