The book presents an analysis of the oscillation of a harmonic oscillator forced by a sequence of pulses. The values of the pulses are described by a random variable. The moments at which the pulses act on the oscillator are also chosen at random.
W książce przedstawiono analizę drgań oscylatora harmonicznego wymuszonych ciągiem impulsów. Wartości impulsów są opisane zmienną losową. W sposób losowy wybierane są również chwile, w których impulsy działają na oscylator.
- Contents
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Preface 5
5 1. Characteristic functions of stochastic vibrations 11
1.1. Introduction 11
1.2. Characteristic functions of stochastic vibrations 13
2. Stationarity of damped stochastic vibrations 23
2.1. Introduction 23
2.2. Stationarity of damped stochastic vibrations 24
2.3. Ergodicity of damped stochastic vibrations 26
2.4. Stochastic moments of damped vibrations 30
2.5. Stochastic moments and derivatives of characteristic functions 31
3. Applications to vibratory systems 34
3.1. Damped oscillator 34
3.2. Oscillator without damping 40
3.3. Damped string 42
4. Computer simulations 44
4.1. Introduction 44
4.2. Parameters and description of simulations 48
4.2.1. Simulations for λ = 10 51
4.2.2. Simulations for λ = 103 56
4.2.3. Simulations for λ = 104 60
4.3. Statistical investigations 64
4.3.1. Histograms for λ = 10 65
4.3.2. Histograms for λ = 103 69
4.3.3. Histograms for λ = 104 73
4.3.3. Histograms for high damping 78
4.4. Remarks and conclusions 83
Appendix 103
Literature 120
