Mathematical model of rod oscillations with account of material relaxation behaviour

International Conference on Mechanical Engineering, Automation and Control Systems 2017

机械制造;无线电电子学;计算机科学

Kudinov, I.V.^1 ; Kudinov, V.A.^1 ; Eremin, A.V.^1 ; Zhukov, V.V.^1

Samara State Technical University, Molodogvardeyskaya St. 244, Samara

443100, Russia^1

关键词: Damped oscillations;    Low-amplitude;    Mixed derivatives;    Positive displacement;    Relaxation factors;    Separation of variables;    Space and time;    Time derivative;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/327/4/042059/pdf
DOI  :  10.1088/1757-899X/327/4/042059

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Taking into account the bounded velocity of strains and deformations propagation in the formula given in the Hooke's law, the authors have obtained the differential equation of rod damped oscillations that includes the first and the third time derivatives of displacement as well as the mixed derivative (with respect to space and time variables). Study of its precise analytical solution found by means of separation of variables has shown that rod recovery after being disturbed is accompanied by low-amplitude damped oscillations that occur at the start time and only within the range of positive displacement values. The oscillations amplitude decreases with increase of relaxation factor. Rod is recovered virtually without an oscillating process both in the limit and with any high values of the relaxation factor.