Statistical Dynamics and Reliability Theory for Mechanical Structures

of Systems with One Degree of Freedom.- 5.1 Free Random Vibrations of Linear Systems.- 5.2 Forced Random Vibrations of Linear Systems.- 5.2.1 Non-Stationary Vibrations.- 5.2.2 Stationary Forced Vibrations.- 5.3 Vibrations Caused by Random Kinematic Excitation.- 5.3.1 Non-Stationary Random Vibrations at Kinematic Excitation.- 5.4 The Problem of Overshoots at Random Vibrations.- 5.5 Nonlinear Random Vibrations.- 5.5.1 The Method of Statistical Linearization.- 5.5.2 The Solution of the Nonlinear Equations with the Use of Markov Processes.- 5.5.3 The Method of Statistical Trials (Monte-Carlo Method).- 6. Random Vibrations of Systems with Finite Number of Degrees of Freedom.- 6.1 Free Random Vibrations of Linear Systems.- 6.2 Vibrations at Random Pulse Loading.- 6.3 Non-Stationary Random Vibrations of Linear Systems.- 6.4 The Method of Principal Coordinates in Non-Stationary Vibrations Analysis.- 6.5 Forced Stationary Random Vibrations of Linear Systems.- 7. Random Vibrations of Strings; Longitudinal and Torsional Vibrations of Straight Rods.- 7.1 Introduction.- 7.2 Equations of Small Vibrations.- 7.3 Solving Equations of Small Vibrations.- 8. Random Vibrations of Rods.- 8.1 Nonlinear Equations of Motion of Three-Dimensional Curvilinear Rods.- 8.2 Equations of the Motion of a Rod in the Attached Coordinate System.- 8.2.1 Equation of Space Motion of a Rod.- 8.2.2 Equation of Plane Motion of a Rod.- 8.2.3 Rods Having Lumped Masses.- 8.3 Equation of Small Vibrations of Rods.- 8.3.1 Equations of Small Vibrations in the Attached Coordinate Frame.- 8.3.2 Equations of Small Vibrations about a Natural State.- 8.4 Determination of Eigenvalues and Eigenvectors.- 8.5 Non-Stationary Random Vibrations of Rods.- 8.6 Stationary Random Vibrations of Rods.- 9. Fundamentals of Reliability Theory.- 9.1 Introduction.- 9.2 Elementary Problems of Reliability Theory.- 9.3 Possible Causes of Failures.- 9.4 Determination of Numerical Values of No-Failure Operation Probability (Reliability).- 9.5 Determination of Reliability at the Linear Dependence of a Stress State on Random Loads.- 9.6 Determination of the Probability of No-Failure Operation at the Nonlinear Dependence of the Random Quantity F on External Loads.- 10. Random Processes at the Action of Random Functions Bounded in Absolute Value.- 10.1 Introduction.- 10.2 Determining the Maximum Values of the Components of the Systems State Vector.- 10.3 Areas of Possible Values of the System State Vector at the Action of Independent Excitations.- 10.4 Projections of the Area of Possible Values of the System State Vector onto Two-Dimensional Planes.- 10.5 Determination of the Maximum Values of Dynamic Reactions.- 10.6 Areas of Possible Values of the System State Vector in the Case of Several Sections of Motion.- 10.7 Areas of Possible Values of the System State Vector at the Action of Dependent Random Excitations.- 10.8 Determination of the Maximum Values of Linear Functionals at Independent Excitations.- 10.9 Maximum Value of a Linear Functional at Dependent Excitations.- 10.10Vibration Protection of Mechanical Systems.- A. Appendices.- A.1 Elementary Generalized Functions.- A.3 Correlation Functions and Spectral Densities Corresponding to Them.- A.4 Hiawatha Designs an Experiment.- References.