Engineering Mechanics Dynamics II Contents:
SLOVAK UNIVERSITY of TECHNOLOGY IN BRATISLAVA FACULTY OF MECHANICAL ENGINEERING INSTITUT OF APPLIED MECHANICS AND MECHATRONICS B Sc SYLLABUS ENGINEERING MECHANICS II DYNAMICS Number of subject 2 5520 Study discipline all study program No of credit 6 Lectures 39 hour 3 hour week 13 week term Warrantor of subject Lecturer Assoc Prof M Sc PhD Stanislav iaran Year second summer Seminars 26 hour 2 hour week 2008 Key words vector mass rigid body constrain motion dynamic equilibrium work energy impulse vibration impact gyroscope reaction 1 Introduction to Dynamics Kinematics of Particles History and modern application Basic concepts Newton s laws Units Formulation and solution of dynamics problems Rectilinear motion of particles General plane curvilinear motion Rectangular co ordinates Normal and tangential co ordinates Space curvilinear motion Relative motion Constrained motion of connected particles 2 Kinetics of Particles Linear momentum of a particle Equation of motion Newton s laws of motion Dynamic equilibrium Angular momentum of a particle Equations of motion in terms of rectangular co ordinates and normal and tangential components Motion under a central force Work of a force Kinetic energy of a particle Principle of work and energy Application of the principle of work and energy Power and efficiency Potential energy Conservative force Conservation of energy Principle of impulse and momentum 3 System of Particles Introduction Application of Newton s laws Linear and angular momentum Motion of the mass centre Angular momentum Conservation of momentum Kinetic energy Work energy principle Principle of impulse and momentum 4 Mechanical Vibration Introduction vibration without damping free vibrations of particle simple pendulum free vibration of a rigid body forced vibrations Examples of application 5 Mechanical Vibration Damped vibrations damped free vibrations damped forced vibrations damped vibrations with kinematic excitation critical speeds of shaft transmission of the vibration to the foundation Examples of application 6 Impulsive Motion and Variable Systems of Particle Impact Direct central impact Oblique central impact Eccentric Impact Steady stream of particles Systems gaining or losing mass Examples of application 7 Rigid Bodies Kinematics Moment of Inertia Translation Rotation about fixed axis Equation defining the rotation of a rigid body about fixed axis General plane motion Absolute and relative velocity Instantaneous centre of zero velocity Absolute and relative acceleration Analysis of plane motion in terms of parameters Rate of change of a vector with respect to a rotating frame Coriolis acceleration Motion about a fixed point General plane motion Moments of inertia of masses moment of inertia of a mass product of inertia ellipsoid of inertia 8 Plane Motion of Rigid Bodies Equations of motion Angular momentum D Alambert s principle Translation motion Centroidal rotation motion Noncentroidal rotation General plane motion Constrained plane motion Rolling motion Principle of work and energy for a rigid body in plane motion Kinetic energy of a rigid body in plane motion Principle of impulse and momentum Impulsive motion 9 Kinetics of Rigid Bodies in Three Dimensions Three dimensional motion of a particle relative to a rotating frame Coriolis acceleration Frame of reference in general motion Angular momentum Inertia tensor Application of the principle of impulse and momentum Kinetic energy of a rigid body Motion of a rigid body in three dimensions Euler s equations Motion of a rigid body about a fixed point 10 Gyroscope Motion of gyroscope Eulerian angels Steady precession of a gyroscope Motion of an axisymetrical body under no force Application of gyroscope s moment Examples of application 11 Systems of Rigid Bodies Kinematic analyse of the plane machines Analytical methods of kinematic analyse of the plane machines Conservation of energy Conservation of angular momentum Unconstrained and constrained motion System of interconnected rigid bodies Method of dismemberment method of reduction constant and non constant ratio Examples of application 12 Dynamic Reactions Rotation of unbalanced body principle inertia axes static unbalance couple unbalance dynamic unbalance balancing of rigid rotors single plane static balancing two plane dynamic balancing calculation of amount of unbalance Critical speed of a rotor Examples of application 13 Basis of theory of analytical dynamics Generalised co ordinates principle of virtual work generalised force development of Lagrange s equation Examples of application Literature McGill D J King W W Engineering mechanics DYNAMICS Boston 1989 Beer F P Johnston E R Vector mechanics for engineers DYNAMICS New York 1988 Meriam J L Kraige L G Engineering mechanics DYNAMICS New York 1992 Thomson W T Theory of vibration with applications London 1981 Hibbeler R C Engineering mechanics DYNAMICS New York 1997 Z horec O Caban S DYNAMIKA SjF TU Ko ice 2002 Z horec O Michal ek M iaran S DYNAMIKA Zbierka pr kladov Alfa Bratislava 1991
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