Applied Dynamics of Continuum

Garant předmětu:

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Department of Materials

Synopsis:

Abstract:

Natural, free, transient and forced vibrations of continuous systems (strings, rods, beams, membranes, plates, shells), equations of motion, method of solution and basic dynamical characteristics.

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Outline:

1. Main differences between discrete and continuous dynamical systems and between linear and nonlinear systems; vibration of strings. 2. Application of variational principles on natural, free and excited vibrations of continua. 3. Galerkin's method. 4. Longitudinal and torsional vibrations of thin rods. 5. Bending vibrations of thin beams; various types of boundary and initial conditions; natural, free, transient and excited vibrations. 6. Natural frequencies and orthogonality of natural mode shapes of vibration; Krylov?s functions. 7. Transfer matrix method. 8. Fundamentals of elastic waves (longitudinal, shear and bending) propagation in continua. 9. Mathematical models of damping, consideration of material non-homogeneity and non-uniformity. 10. Influence of damping and static pre-stress on dynamical properties of continuous systems; corrections on shear and perpendicular deformations and on rotations of cross sections. 11. Vibrations of rectangle and circular membranes. 12. Vibration of thin-walled rectangle and circular plates. 13. Fundamentals of vibrations of thin-walled cylindrical shells. 14. Nonlinear phenomena in dynamical systems, their main origins and consequences.

Keywords:

Dynamics of continuous systems, vibration of strings, rods, beams, membranes, plates and shells; natural, transient and excited vibrations, natural frequencies and mode shapes of vibration, wave propagation in solids.

Syllabus of tutorials:

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Key references:

[1] S.S. Rao: Vibration of Continuous Systems, John Wiley and Sons, 2007.

[2] S. G. Kelly: Fundamentals of Mechanical Vibrations, 2nd. ed., McGraw-Hill, 2000.

Recommended references:

[3] M. Kružík nd T. Roubíček: Mathematical Methods in Continuum Mechanics of Solids. Springer, 2019

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Fyzikální inženýrství materiálů (compulsory course in the program)