Exact method of solution of free vibrations problem for one-dimensional rheological structures

• Autorzy: Cabański J.
• Języki publikacji: EN

Abstrakty

EN

Free vibrations of one-dimensional rheological structure have been described by the system of the conjugated partial differential equations. A vector form of this system of equations allows to identify the self adjoint linear operators of inertia, damping and stiffness. These operators are not homothetic, hence the method of a separation of variables for the considered system of equations is applicable only in the introduced complex Hilbert space. Such a separation of variables leads to the system of ordinary differential equations in time and to the system of three ordinary differential equations with respect to spatial variables. Solution of the obtained boundary-value problems proceeds in a classical way, however, the results are of a complex conjugated type. Applying the fundamental principle of the general orthogonality of complex eigenvectors, the problem of free vibrations of the system with arbitrary initial conditions was solved in exact form.

Słowa kluczowe

PL

drganie; drganie własne; funkcja własna; lepkość; metoda dokładna; przestrzeń Hilberta; reologia; równanie różniczkowe zwyczajne; wartość własna; zagadnienie brzegowe

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2001
• Tom: Vol. 42, no 1
• Strony: 85--102
• Opis fizyczny: Bibliogr. 9 poz.,

Twórcy

autor

Cabański J.

• Department of Applied Mechanics, Faculty of Armament and Aviation, University of Technology and Agriculture, Kaliskiego 7, 85-791 Bydgoszcz, Poland.