Features of application of simplified method of power calculation of plane trusses under conditions of forced oscillations
Abstract
Kholodniak Yu. S., Podliesnyi S. V., Kaporovych S. V. Features of application of simplified method of power calculation of plane trusses under conditions of forced oscillations // Herald of the DSEA. – 2019. – № 2 (46). – Р. 103–113.
The analysis of existing methods of power calculation of trusses under the influence of forced oscillations is performed. When considering the forced oscillations of flat trusses, two-dimensional models are used, which are complex for wide practical use. Their implementation requires in-depth mathematical training and complex computational tools. Therefore, they are difficult to apply in normal engineering practice. Simplified techniques oscillating force analysis of trusses does not exist. The aim of this work is to develop a simplified two-dimensional mathematical model of forced oscillations of flat trusses, followed by the use of this model in their power calculations. The mathematical model proposed in this paper describes the oscillations of a weightless truss with a point mass with simultaneous action of vertical and horizontal harmonic disturbing forces on them. The model is based on the method of forces, establishes a link between the movements of the trusses and the forces that act on it. Together with the model, the dependences for calculating the resonant frequencies of the oscillatory system are obtained. The performed developments allow to determine the dynamic characteristics of the oscillatory process and to calculate the strength, stiffness and stability of the truss. The method of such calculation is implemented in Mathcad15 and has been successfully tested on a number of educational tasks. The results of the work can be useful for students and teachers of technical universities, as well as practitioners performing power calculations.
References
Kovtun V.V. Resistance of materials. Design work. Lviv: Poster. 2002, 280 p. (in Ukrainian).
Itskovich G.M., Minin L.S., Vinokurov A.I. Guide to solving problems of resistance of materials. Moscow: High school. 2001, 592 p. (in Russian).
Darkov A.V., Spiro G.S. Resistance of materials. Moscow: High school. 1989, 624 p. (in Russian).
Pisarenko G.S., Kvitka O.L., Umansky E.S. Resistance of materials. Kyiv: High School. 2004, 655 p. (in Ukrainian).
Shevchenko F.L. Course of resistance of materials. Tips for learning theory and solving problems. Donetsk: DonNTU. 2013, 260 p. (in Ukrainian).
Lamcy B.B. et al. Collection of tasks and exercises on the dynamics of core systems. Nizhny Novgorod: NNGASU. 2016, 96 p. (in Russian).
Dovnar E.P., Klimova L.B. Calculation of frames on static and dynamic loads. Minsk: BNTU. 2004, 186 p. (in Russian).
Polyakov A.A., Lyalina F.G., Ignatov R.G. Construction mechanics. Yekaterinburg: UrFU. 2014, 424 p. (in Russian).
Gaijurov P.P. Calculation of core systems for stability and oscillations. Novocherkassk: SRSTU. 2009, 195 p. (in Russian).
Kholodnyak Yu.S., Podlesny S.V., Kaporovich S.V. Simplified method of force calculation of flat frames under forced oscillations. Herald of the DSEA. Kramatorsk: DSEA. 2018, 1 (43), pp. 198-213 (in Russian).
Kholodnyak Yu.S., Podlesny S.V., Kaporovich S.V. Development of methodology of power calculations of flat frames in conditions of forced oscillations Scientific Herald of the DSEA [Online]. Kramatorsk: DSEA. 2018, 1 (25E), pp. 96-97. http://www.dgma.donetsk.ua/science_public/science_vesnik/%E2%84%961(25%D0%95)_2018/article/16.pdf (in Ukrainian).
Kholodniak Yu.S., Kaporovych S.V., Korotenko Ye.D. Elaboration of a Methodology of Pover Calculations of Flat Frames Under Conditions of Forced Oscillations. Contemporary Innovation Technique of Engineering Personnel Training for the Mining and Transport Industry 2019. Conference Proceedings (2019). Ukraine, Dnipro: NTUDP, pp. 92100.
Kutovyi L.V. et al. Collection of calculation and graphical tasks from the course "Resistance of materials. Kramatorsk: DSEA. 2007, 220 p. (in Ukrainian).
Nikitin N.N. Course in theoretical mechanics. Moscow: Higher School. 1990, 607 p. (in Russian).
Pisarenko G.S. et al. Reference book on the resistance of materials. Kyiv: Naukova Dumka. 1988. 704 p. (in Russian).
