- STRUCTURAL MECHANICS
- Exact Analytical Solutions To Non-Stationary Problems For Rods Based On S. P. Timoshenko Theory
- UDC 624.04:534.11 DOI: 10.33622/0869-7019.2020.07.16-25
Alexander L. ZONENBERG, e-mail: email@example.com
Moscow State University of Civil Engineering (National Research University), Yaroslavskoe shosse, 26, Moscow 129337, Russian Federation
Abstract. Based on the theory of S.P. Timoshenko, exact analytical solutions of non-stationary problems for rods in general form are given. Such solutions are necessary for the study of transient wave processes of deformation in rods under transverse short-term and fast-changing effects. The work uses operational calculus based on the integral Laplace- Carson transformation, methods of structure dynamics, Mathcad program (drawing of graphs). Exact formulas are given in general form, including integrals from Bessel functions, to determine efforts in semi-infinite rods of various types, as well as in an infinite rod when solving an auxiliary problem. For each task, a conclusion is made on the existence of discontinuities. The situation where force impacts are pulsed is highlighted. As an illustration, graphs of changes in time of efforts in rods calculated according to the given formulas under effects of special type are given. The results of the work can be used in the practice of calculating buildings and structures for the effect of impact and explosive loads, with a refined assessment of the parameters of oscillations excited by industrial enterprises, vehicles, etc.
Key words: Transient wave processes, S.P. Timoshenko theory, rods, traveling waves, operational ratio, Bessel functions.
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- For citation: Zonenberg A. L. Exact Analytical Solutions to Non-Stationary Problems for Rods Based on S. P. Timoshenko Theory. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2020, no. 7, pp. 16-25. (In Russian). DOI: 10.33622/0869-7019.2020.07.16-25.