Dynamics of Longitudinal Impact in the Variable Cross-Section Rods

4th International Conference on Advanced Engineering and Technology

Stepanov, R.^1 ; Romenskyi, D.^1 ; Tsarenko, S.^2

Department of Structural and Theoretical Mechanics, National Research University Moscow, State University of Civil Engineering, 26 Yaroslavskoye Shosse, Moscow

129337, Russia^1

Department of Strength of Materials, Donetsk National Technical University, 58 st. Artema, Donetsk

83001, Ukraine^2

关键词: Cross sectional area;    Dynamic effects;    Fourier methods;    Orthogonality properties;    Recurrence relations;    Special functions;    Stress strain state;    Variable cross section;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/317/1/012029/pdf
DOI  :  10.1088/1757-899X/317/1/012029

来源: IOP

【 摘 要 】

Dynamics of longitudinal impact in rods of variable cross-section is considered. Rods of various configurations are used as elements of power pulse systems. There is no single method to the construction of a mathematical model of longitudinal impact on rods. The creation of a general method for constructing a mathematical model of longitudinal impact for rods of variable cross-section is the goal of the article. An elastic rod is considered with a cross-sectional area varying in powers of law from the longitudinal coordinate. The solution of the wave equation is obtained using the Fourier method. Special functions are introduced on the basis of recurrence relations for Bessel functions for solving boundary value problems. The expression for the square of the norm is obtained taking into account the orthogonality property of the eigen functions with weight. For example, the impact of an inelastic mass along the wide end of a conical rod is considered. The expressions for the displacements, forces and stresses of the rod sections are obtained for the cases of sudden velocity communication and the application of force. The proposed mathematical model makes it possible to carry out investigations of the stress-strain state in rods of variable and constant cross-section for various conditions of dynamic effects.