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Lecturer(s)
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Kout Jan, doc. Ing. CSc.
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Paščenko Petr, prof. Ing. Ph.D.
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Tomek Petr, doc. Ing. Ph.D.
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Course content
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Basic considerations, type of nonlinearity, mathematical models of nonlinear mechanical systems. Methods for solving of equations of motion. Single degree of freedom vibration - free vibration. Single degree of freedom vibration - forced vibration. Amplitude - resonant curves, amplitude - phase angle curves, type of resonances. Stability ( stability according to Ljapunov ),type of singular points, methods of linearization. Nonlinear elastic and elastic-plastic material, physical equations of nonlinear theory of elasticity and theory of plasticity. Conditions of plasticity (invariability of intensity of stress, invariability of maximum tangential stress). Basic system of equations of theory plasticity, solving exercises of theory plasticity, minimum principles in theory of elastic-plastics deformations. Simple exercises of elastic-plastic equilibrium.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Methods of individual activities
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Learning outcomes
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Aim of the course unit is acquaint students with bases of free and forced vibration of non-linear discrete mechanical systems as well as methods solution of non-linear equations of motion, with methods of linearization of equations of motion, with basics of theory of plasticity and its conditions and basic system of equations of theory of plasticity as with solution to the problems of theory of plasticity.
After graduation of the subject regaining student setings for solving of nonlinear exercises of mechanics and problems of plasticity.
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Prerequisites
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The following basis knowledge is supposed: mathematics (linear algebra, matrix calculus, eigenproblems, nonlinear differential equations), mechanics (dynamics, strength of materials).
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Assessment methods and criteria
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Discussion
The requirements will be defined by lecturer.
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Recommended literature
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Brepta, Rudolf. Mechanické kmitání. Praha: Sobotáles, 1994. ISBN 80-901684-8-5.
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Koloušek, V. a kol. Stavebné konštrukcie namáhané dynamickými účinkami. SVTL Bratislava, 1967.
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Němec, J., Dvořák, J., Höschl, C. Pružnost a pevnost ve strojírenství. SNTL Praha, 1989.
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Servít, L. a kol. Pružnost a pevnost ve stavitelství II. SNTL Praha, 1966.
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