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Theory of waves in materials by Jeremiah Rushchitsky

Theory of waves in materials by Jeremiah Rushchitsky

On the auditory. Goals of chapters-lectures presented. Three basic parts of the book. Structure of the single chapter-lecture. On comments. On bibliography. On questions. Waves in the world around. Materials in the world around.

The book is proposed for the auditory moderately educated in the field of mechanics and mathematics. It does not assume that the presence of elementary knowledge only will be sufficient for its understanding. In the field of mechanics, the knowledge of fundamentals of continuum mechanics will be required, which in turn are available on conditions that elements of a row of other divisions of mechanics are known. In the field of mathematics, the elements of knowledge of the full university course (mathematical analysis, analytical and differential geometry, theory of functions of complex variable, vector and tensor calculation, higher algebra) will be required.

The main goal is the coherent treatment of the theory of waves propagating in materials. The unabridged presentation of such a theory is practically impossible because of the huge number of accumulated observations and published theoretical results.

The wave motion as a subclass of motion in general is observed very frequently. As a result of the observation, a description of the wave phenomenon is becoming, as a rule, well known. It is considered sometimes that the description characteristics do not need a theoretical conception. Though the last one has always to give rise to doubt. The fact is that in such a description some criterion of distinction of wave motions from other motions is present deliberately or not. Practically everyone has seen waves on water, sand or somewhere else. And it going seems that it is not very difficult to determine purely by the description that we are observing the waves.

The macro-description of materials was predominant in mechanics of materials up to 20 century, when meso-description and micro-description were proposed and developed (the first one owing mainly the in-depth analysis of metals; the second one owing to the wide fabrication and application of composite materials in the second half of 20 century). Both new descriptions are based on understanding the materials as having the internal structure of meso- and microlevel substance and on assumption that this structure can not be neglected in mechanical processes studying in meso- and micromechanics. Recently the thriving development of nanomechanics of materials is observed and this fact will be discussed in next lectures.

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