Khanh C. Le

Vibrations of Shells and Rods (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book is intended for engineers who deal with vibrations of rods and shells in their everyday practice but also wish to understand the subject from the mathematical point-of-view. Particularly the results concerning high-frequency vibrations may be new to them. The book can also serve as a textbook for advanced students. It may also be interesting for mathematicians who seek applications of the variational and asymptotic methods in elasticity and piezoelectricity. Only a minimum knowledge in advanced calculus and contiuum mechanics is assumed on the part of the reader.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 423
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642599118
• Artikelnr.: 53391145

Inhaltsangabe

1 Introduction.- 2 Preliminaries.- 2.1 Tensor analysis.- 2.2 Geometry of curves and surfaces.- 2.3 Dynamic theory of elasticity.- 2.4 Dynamic theory of piezoelectricity.- 2.5 Variational-asymptotic method.- I Low-frequency vibrations.- 3 Elastic shells.- 3.1 Two-dimensional equations.- 3.2 Asymptotic analysis.- 3.3 Dispersion of waves in plates.- 3.4 Frequency spectra of circular plates.- 3.5 Dispersion of waves in cylindrical shells.- 3.6 Frequency spectra of cylindrical shells.- 3.7 Frequency spectra of spherical shells.- 4 Elastic rods.- 4.1 One-dimensional equations.- 4.2 Asymptotic analysis.- 4.3 Cross section problems.- 4.4 Dispersion of waves.- 4.5 Frequency spectra.- 5 Piezoelectric shells.- 5.1 Two-dimensional equations.- 5.2 Asymptotic analysis.- 5.3 Error estimation and comparison.- 5.4 Frequency spectra of circular plates.- 5.5 Frequency spectra of cylindrical shells.- 6 Piezoelectric rods.- 6.1 One-dimensional equations.- 6.2 Asymptotic analysis.- 6.3 Cross section problems.- 6.4 Frequency spectra.- 6.5 Longitudinal impact.- II High-frequency vibrations.- 7 Elastic shells.- 7.1 Two-dimensional equations.- 7.2 Long-wave asymptotic analysi.- 7.3 Short-wave extrapolation.- 7.4 Dispersion of waves in plates.- 7.5 Frequency spectra of plates.- 7.6 Dispersion of waves in cylindrical shells.- 7.7 Frequency spectra of cylindrical shells.- 8 Elastic rods.- 8.1 One-dimensional equations.- 8.2 Long-wave asymptotic analysis.- 8.3 Short-wave extrapolation.- 8.4 Cross section problems.- 8.5 Dispersion of waves.- 8.6 Frequency spectra.- 9 Piezoelectric shells.- 9.1 Two-dimensional equations.- 9.2 Long-wave asymptotic analysis.- 9.3 Short-wave extrapolation.- 9.4 Frequency spectra of circular plates.- 9.5 Frequency spectra of cylindrical shells.- 10 Piezoelectric rods.- 10.1 One-dimensional equations.- 10.2 Long-wave asymptotic analysis.- 10.3 Short-wave extrapolation.- 10.4 Cross section problems.- 10.5 Frequency spectra.- A.I Elastic isotropic materials.- A.2 Piezoelectric crystals.- A.3 Piezoceramic materials.- B List of notations.