Free longitudinal vibrations of an elastically connected double – rod system

• Autorzy: Oniszczuk Z.
• Konferencja: Dynamika Konstrukcji / Sympozjum (XII ; 28-30 września 2005 ; Rzeszów-Bystre, Polska)
• Języki publikacji: EN

Abstrakty

EN

In this work, the theoretical longitudinal vibration analysis of an elastically connected double-rod system is presented. The double-rod system is the model of a complex continuous system, which is composed of two straight, uniform elastic rods attached together by a Winkler elastic layer. The motion of the system is described by a coupled set of two non-homogeneous partial differential equations, which can be solved by using the classical mathematical methods. Solutions of undamped free vibrations are formulated by applying the modal expansion method. Two infinite sequences of the natural frequencies and corresponding mode shape functions expressing synchronous and asynchronous vibrations of the system are determined. The initial-value problem is considered to find the final form of free vibrations.

Słowa kluczowe

EN

vibration system; double-rod system; free vibration; Winkler elastic layer; elastic rod

PL

układ drgający; drganie swobodne; powierzchnia winklerowska; pręt sprężysty

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
• Rocznik: 2005
• Tom: z. 65 [222]
• Strony: 303--310
• Opis fizyczny: Bibliogr. 33 poz., rys.

Twórcy

autor

Oniszczuk Z.

• Rzeszów University of Technology, Faculty of Mechanical Engineering and Aeronautics

Bibliografia

• [1] Ziemba S., Vibration Analysis, Vol. II, PWN, Warsaw, 1959 (in Polish).
• [2] Nowacki W., Dynamics of Elastic Systems, Chapman and Hall, London, 1963.
• [3] Solecki R., Szymkiewicz M., Rod-like and Surface-like Systems. Dynamical Calculations, Arkady, Warsaw, 1964 (in Polish).
• [4] Kaliski S., Vibrations and Waves in Solids, IPPT PAN, Warsaw, 1966 (in Polish).
• [5] Vernon J.B., Linear Vibration Theory, Wiley, New York, 1967.
• [6] Skudrzyk E., Simple and Complex Vibratory Systems, The Pennsylvania State University Press, University Park, PA, 1968.
• [7] Timoshenko S.P., Young D.H., Weaver Jr. W., Vibration Problems in Engineering, Wiley, New York, 1974.
• [8] Osiński Z., Vibration Theory, PWN, Warsaw, 1978 (in Polish).
• [9] Craig Jr. R.R., Structural Dynamics, Wiley, New York, 1981.
• [10] Rao S.S., Mechanical Vibrations, Addison-Wesley, Reading, MA, 1995.
• [11] de Silva C. W., Vibration: Fundamentals and Practice, CRC Press, London, 1999.
• [12] Ginsberg J.H., Mechanical and Structural Vibrations: Theory and Applications, Wiley, New York, 2001.
• [13] Oniszczuk Z., Vibration Analysis of Compound Continuous Systems with Elastic Constraints, Publishing House of Rzeszów University of Technology, Rzeszów, 1997 (in Polish).
• [14] Oniszczuk Z., "Transverse vibrations of elastically connected double-string complex system, Part 1: free vibrations", Journal of Sound and Vibration, 232, 2000, 355-366.
• [15] Oniszczuk Z., "Damped vibration analysis of an elastically connected complex double-string system", Journal of Sound and Vibration, 264, 2003, 253-271.
• [16] Kukla S., Przybylski J., Tomski L., "Longitudinal vibration of rods coupled by translational springs", Journal of Sound and Vibration, 185, 1995, 717-722.
• [17] Mermertas V., Gürgöze M., "Longitudinal vibrations of rods coupled by a double spring-mass system", Journal of Sound and Vibration, 202, 1997, 748-755.
• [18] Gürgöze M., "Alternative formulat ions of the frequency equation of longitudinally vibrating rods coupled by a double spring-mass system", Journal of Sound and Vibration, 208, 1997, 331-338.
• [19] Li Q.S, Li G.Q., Liu D.K., "Exact solutions for longitudinal vibration of rods coupled by translational springs", International Journal of Mechanical Sciences, 42, 2000, 1135-1152.
• [20] Inceoğlu S., Gürgöze M ., "Longitudinal vibrations of rods coupled by several spring-mass systems", Journal of Sound and Vibration, 234, 2000, 895-905.
• [21] Gürgöze M., Erdoğan G., Inceoğlu S., "Bending vibrations of beams coupled by a double spring-mass system", Journal of Sound and Vibration, 243, 2001, 361-369.
• [22] Inceoğlu S., Gürgöze M., "Bending vibrations of beams coupled by several double spring-mass systems", Journal of Sound and Vibration, 243, 2001, 370-379.
• [23] Erol H., Gürgöze M., "Longitudinal vibrations of a double-rod system coupled by springs and dampers", Journal of Sound and Vibration, 276, 2004, 419-430.
• [24] Jemielita G., Szcześniak W., "The foundation models", Scientific Works of Warsaw University of Technology, Civil Engineering, 120, 1993, 5-49 (in Polish).
• [25] Oniszczuk Z., "Transverse vibrations of elastically connected rectangular double membrane compound system", Journal of Sound and Vibration, 221, 1999, 235-250.
• [26] Oniszczuk Z., "Free transverse vibrations of elastically connected simply supported double-beam complex system", Journal of Sound and Vibration, 232, 2000, 387-403.
• [27] Oniszczuk Z., "Free transverse vibrations of an elastically connected rectangular simply supported double-plate complex system", Journal of Sound and Vibration, 236, 2000, 595-608.
• [28] Oniszczuk Z., "Free transverse vibrations of an elastically connected complex beam-string system", Journal of Sound and Vibration, 254, 2002, 703-715.
• [29] Oniszczuk Z., "Free transverse vibrations of an elastically connected rectangular plate-membrane complex system", Journal of Sound and Vibration, 264, 2003, 37-47.
• [30] Weinberger H.F., Partial Differential Equations, Wiley, New York, 1976.
• [31] Polyanin A.D., Handbook of Linear Partial Differential Equations for Engineers and Scientists, CRC Press, London, 2002.
• [32] Kamke E., Differentialgleichungen: Losungsmethoden und Losungen, Chelsea, New York, 1971 (in German).
• [33] Birkhoff G., Rota G.-C., Ordinary Differential Equations, Wiley, New York, 1989.