Inhaltsangabe1 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.