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On the dynamics of randomly excited nonlinear systems

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Sommario

Nella disamina del problema di caratterizzare il comportamento dinamico di sistemi eccitati da segnali casuali, si mette in rilievo come l'approccio probabilistico, sebbene concettualmente più rigoroso, sia di difficile applicazione ai casi statistici oltre che a quelli normali. Si richiama quindi il metodo diretto di Axelby che viene applicato ad un sistema non lineare eccitato da un segnale casuale. Lo sviluppo dell'applicazione, in termini parametrici, fa riferimento ad un sistema di secondo grado e i relativi risultati numerici vengono discussi nel loro significato quantitativo.

Summary

The problem of characterising the dynamics of randomly excited systems is examined. It is shown that the probability approach, though conceptually more rigorous, is difficult to apply to statistics other than normal ones. The direct method of Axelby is recalled and applied to a nonlinear system with random excitation characterised by a statistic of great interest in real physical systems. The application is developed parametrically with reference to a second order system for which the calculations are developed and the quantitative results discussed.

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Abbreviations

x :

absolute input displacement

y :

absolute output displacement

e :

relative displacement (X−Y)

V e :

relative velocity (X−Y)

K 0 :

spring linearity constant

K 1 :

spring nonlinearity constant

a :

degree of spring nonlinearity

M :

system mass

C 0 :

damper linearity constant

C 1 :

damper nonlinearity constant

b :

degree of damper nonlinearity

σ 1 :

mean square value of the spring action

σ 2 :

mean square value of the damper action

σ e :

mean square value ofe=X−Y

σ ve :

mean square value ofV e

λ :

signal bandwidth

G(ω):

spectral width of the range of input displacement

x 1 :

nondimensional S.D.F. of the spring

x 2 :

nondimensional S.D.F. of the damper

x 3 :

nondimensional error (or relative specific displacement)

x 4 :

nondimensional velocity (or relative specific velocity)

x 5 :

nondimensional elongation (or specific output signal)

Γ :

specific bandwidth

τ x :

specific input signal

Ω :

specific frequency of spring nonlinearity

Z 0 :

specific nonlinear damping

Z 1 :

specific nonlinear damping

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Authors and Affiliations

  1. Laboratorio della Geofisica della Litosfera, Milano

    Giampiero Benevolo

  2. Istituto di Meccanica Applicata alle Macchine, Università di Genova, Italy

    Renato C. Michelini

Authors
  1. Giampiero Benevolo
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  2. Renato C. Michelini
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Benevolo, G., Michelini, R.C. On the dynamics of randomly excited nonlinear systems. Meccanica 7, 71–79 (1972). https://doi.org/10.1007/BF02129986

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  • DOI: https://doi.org/10.1007/BF02129986

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