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The conception of effective vibrodynamic properties of heterogeneous media is presented, enabling one to solve various problems on vibration of elastic systems containing liquid and a large number of identical inclusions. The idea of the conception consists in that the liquid with the inclusions for example, a rod bundle being affected by vibration is considered a continuous medium with the special dynamic properties — vibrodensity and vibroviscosity.

These properties are dependent both on the properties of liquid and inclusions and on the frequency of vibration impacts.

Free and Forced Longitudinal Vibrations of Rods

It is these vibrodynamic properties upon which the vibration performance of elastic systems containing heterogeneous media is dependent. General equations of vibrodensity and vibroviscosity are used in studying natural and forced vibrations of shell containing liquid and a bundle of elastic rods.

It is established that natural frequencies and amplitudes of shell resonance vibrations depend on rod bundle parameters. The result obtained on vibrodensity was used as well for determination of natural frequencies of free-surfacc liquid vibration in cylindrical vessel enclosing rod bundle. It is demonstrated that the natural frequencies of liquid vibration in vessel with rod bundle are lower than in vessel without rods. Comparison of theory with experimental data is made.

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Google Scholar. The book serves equally well as an advanced textbook, while remaining of interest to mathematicians who seek applications of the variational and asymptotic methods in elasticity and piezoelectricity. Only a minimum knowledge in advanced calculus and continuum mechanics is assumed on the part of the reader. Product details Format Paperback pages Dimensions x x Back cover copy 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.

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Particularly the results concerning high-frequency vibrations may be new to them. The book can also serve as a textbook for advanced students.

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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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Table of contents 1 Introduction. I Elastic isotropic materials. Learn about new offers and get more deals by joining our newsletter.