Dynamics of Continuum

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Materials

Synopsis:

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.

Requirements:

Lectures on mathematical solution of ordinary and partial differential equations.

Lectures on vibration of linear systems.

Syllabus of lectures:

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.

Syllabus of tutorials:

Study Objective:

Knowledge:

Obtaining of knowledge on basic dynamical characteristics of continues elastic bodies, on ways and methods of their solution related to dynamical loading of structural elements and possible fatigue failures of materials.

Skills:

Development of abilities for performing individual solution and analyses of dynamical stresses in structures, and estimation of dynamical behavior of elastic bodies in special more complicated cases.

Study materials:

Key references:

[1] Brdička M., Samek L. Sopko B.: Mechanics of continua, Academia, Prague, 2000 - selected chapters.

[2] Brepta R., Půst L., Turek F.: Mechanical vibrations, Technický průvodce 71, Sobotáles, 1994 - selected chapters.

Recommended references:

[1] Kunz J.: Vibration of linear systems, Textbook, ČVUT, Prague, 2009.

[2] Půst L.: Applied mechanics of continua II. Textbook, FJFI, ČVUT, Prague, 1986

[3] Bolotin V. V. (Ed.), Vibrations in Engineering. A Handbook in 6 Volumes. Vibrations of Linear Systems, Vol. 1. Mashinostroyeniye, Moscow, 1978. - - selected chapters

[4] Rektorys, K.: Variational methods in engineering problems and problems of mathematical physics, issue 6, Prague: Academia 1999. - selected chapters

[5] Juliš K., Brepta R.: Mechanics I. a II. Prague SNTL 1987. - selected chapters.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: