Summary
The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.
Übersicht
Behandelt wird der Leipholz-Stab, dessen Elastizitätsmodul, Masseverteilung und tangential folgende Streckenlast stochastisch sind. Die nicht selbstadjungierte Differentialgleichung und die Randbedingungen werden als solche mit Zufallskoeffizienten betrachtet und die übliche Störungsmethode benutzt. Im Regularitätsbereich werden die nicht selbstadjungierten Operatoren benutzt. Hergeleitet wird die vollständige Kovarianz-Struktur der Eigenwerte der freien Schwingung und kritischen Lasten als Funktionen der Eigenschaften zweiter Ordnung der zufälligen Eingangsgrößen, die die Schwankungen der Systemparameter charakterisieren. Der Mittelwert der kritischen Last wird aus dem gemittelten Problem berechnet und die zugehörige Eigenwert-Statistik wird gesucht. Über die Frequenzgleichung wird eine Transformation vorgenommen, um die Statistik des Lastparameters zu erhalten. Eine numerische Studie illustriert die Leistungsfähigkeit der hergeleiteten Ausdrücke.
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Ramu, S.A., Ganesan, R. Stability of stochastic Leipholz column with stochastic loading. Arch. Appl. Mech. 62, 363–375 (1992). https://doi.org/10.1007/BF00804597
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DOI: https://doi.org/10.1007/BF00804597