Training Manual . - Odessa: OGPU, 2000. - 302 s. Practical methods for calculating torsional, and bending oscillations, as well as stretching-compression oscillations. are presented. Methods for calculating systems with finite and infinite degrees of freedom are described Methods of formation of mechanical models with a finite number of degrees of freedom . Classification of forces acting under fluctuations. Classification of oscillations. Methods of obtaining differential equations of motion. Free Fluctuations. General information about free fluctuations. Free oscillations of a system with one degree of freedom without friction. Examples of calculations. Free oscillations of a system with one degree of freedom in the presence of friction. Viscous friction . Dry friction . Positional friction. Free oscillations of systems with a finite number of degrees of freedom (general case). Solving equations of motion in the general case. Solution of equations of motion for the simplest system. Orthogonality of its own forms of oscillation. Multivariate and zero roots of the frequency equation. Effect of friction on free oscillations of a system with N-degrees of freedom. Free oscillations of rod systems. Curve fluctuations of the shafts. Examples of calculations. Free Vehicle Fluctuations. Forced fluctuation . Systems with one degree of freedom in the absence of friction. Forced Excitation of Fluctuations . Kinematic oscillation excitation. General solution of the standard equation. Action of non-recurrent perturbing force. The action of harmonic force. Action of two harmonic forces with close beat frequencies. Action of an arbitrary periodic perturbing force (method of decomposition into harmonic components). Effects of periodic pulses. Systems with one degree of freedom under the action of forces of inelastic resistance . Effect of viscous friction. Influence of arbitrarily defined forces of inelastic resistance. Examples of calculations. Systems with a finite number of degrees of freedom . Core systems with a finite number of degrees of freedom under harmonic load. Curve fluctuations of the shafts. Examples of calculations. Parametric oscillations. The basic equation (Matthieu's equation). Cases of periodic rigidity change. Cases of periodic changes in parametric loads. Pendulum with swinging point of suspension. Auto fluctuation. General provisions and examples of auto-oscillation systems. Frictional vehicular oscillations. Wing flutter in airflow. Free oscillations of systems with distributed parameters. Longitudinal oscillations of rods. Curve fluctuations of the shafts. Bending Bracket Fluctuations. The basic equation. Boundary conditions. Frequency equation and eigenforms. Definition of initial conditions of motion. Effect of constant longitudinal force. Impact of chain efforts. Effect of viscous friction. Variable cross-sectional rod oscillations. Circular Ring Fluctuations . Fluctuations in the plane of the ring. Fluctuations perpendicular to the plane of the ring. Approximate Methods for Calculating Fluctuations . Rayleigh's Theorem and Method . Ritz Method. Grammel Method. Donkerley Formula . The method of successive approximations. Forced oscillations of systems with distributed parameters. Longitudinal oscillations of rods. Bending Bracket Fluctuations. Fluctuations of plates and shells . Constant Thickness Plate Movement Equation. Rectangular plate of constant thickness. Plate hinged on opposite sides. Asymptotic method of calculating plates . Round plate of constant thickness. Determination of the forms and frequencies of oscillations. Running Waves in Round Plates. Application of the Rayleigh-Ritz method to the determination of the frequencies of own oscillations of plates . Fluctuations of shells. Theory of Oscillations of Shells Without Stretching the Median Surface. The equations of motion of shells. Technical applications of oscillation theory. Basics of Vibration Insulation Calculation. Automatic balancing of rotating shafts. Critical conditions of helicopter rotor. Fluctuations of turbomachine blades. The concept of a dynamic oscillator. Literature.