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Vibrations of Hollow Elastic Bodies [electronic resource] / by Magomed F. Mekhtiev.

By: Mekhtiev, Magomed F [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Advanced Structured Materials: 88Publisher: Cham : Springer International Publishing : Imprint: Springer, 2018Edition: 1st ed. 2018.Description: XVII, 212 p. 12 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319743547.Subject(s): Mechanics, Applied | Solids | Materials—Analysis | Multibody systems | Vibration | Solid Mechanics | Characterization and Analytical Technique | Multibody Systems and Mechanical VibrationsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620.105 Online resources: Click here to access online
Contents:
Introduction -- 3D equations of dynamic elasticity in orthogonal co-ordinates -- Exact homogeneous and inhomogeneous solutions -- Cylinder of finite length -- Spherical layer -- Truncated cone -- Plates of variable thickness -- Free vibrations of cylinders and spheres -- Asymptotic analysis of thin-walled structures -- Validation of 2D engineering theories -- Conclusions.
In: Springer Nature eBookSummary: This book focuses on the justification and refinement of highly diverse approximate dynamic models for engineering structures arising in modern technology, including high-tech domains involving nano- and meta-materials. It proposes a classification for vibration spectra over a broad frequency domain and evaluates the range of validity of various existing 2D theories for thin-walled shells by comparing them with 3D benchmark solutions. The dynamic equations in 3D elasticity are applied to the analysis of harmonic vibrations in hollow bodies with canonical shapes. New exact homogeneous and inhomogeneous solutions are derived for cylinders, spheres and cones (including spherical and conical layers), as well as for plates of variable thickness. The book includes a wealth of numerical examples, as well as refined versions of 2D dynamic formulations. Boundary value problems for hollow bodies are also addressed.
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Introduction -- 3D equations of dynamic elasticity in orthogonal co-ordinates -- Exact homogeneous and inhomogeneous solutions -- Cylinder of finite length -- Spherical layer -- Truncated cone -- Plates of variable thickness -- Free vibrations of cylinders and spheres -- Asymptotic analysis of thin-walled structures -- Validation of 2D engineering theories -- Conclusions.

This book focuses on the justification and refinement of highly diverse approximate dynamic models for engineering structures arising in modern technology, including high-tech domains involving nano- and meta-materials. It proposes a classification for vibration spectra over a broad frequency domain and evaluates the range of validity of various existing 2D theories for thin-walled shells by comparing them with 3D benchmark solutions. The dynamic equations in 3D elasticity are applied to the analysis of harmonic vibrations in hollow bodies with canonical shapes. New exact homogeneous and inhomogeneous solutions are derived for cylinders, spheres and cones (including spherical and conical layers), as well as for plates of variable thickness. The book includes a wealth of numerical examples, as well as refined versions of 2D dynamic formulations. Boundary value problems for hollow bodies are also addressed.

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