The anomalous region of elastic-plastic beam dynamics

The anomalous response of an elastic-plastic beam may occur in a narrow region of loading parameters (Symonds, Yu. ASME J Appl Mech 1985;52:517-22). The existence and the width of the anomalous region of loading parameter depend on system parameters. When the width of the anomalous region is less than the design or experimental tolerance, experimental results are uncertain (Li, Liu. Int J Impact Engng 2003;28(6):643-51). In the present paper, an elastic, linear plastic-strain-hardening Shanley model is used to understand the dependence of anomalous region on system parameters. Results show that there exist two anomalous regions when the strain-hardening parameter R varies between 0 and 0.18. The very closeness of φ0c and φ0b indicates that the beam response is extremely sensitive to the load parameter for the specifically selected system parameters.