Vibrations of straight pipes/beams with two-sided stops: Analytical and numerical analyzes

Abstract

The impacts on pipes or beams are of fundamental mechanical interest. These impacts can be studied analytically. This makes it easier to examine the basic effects and to compare these effects with the results of finite element analyzes (FEA). The displacements of a pipe with two-sided stops and harmonic excitation are investigated. For hard impacts many modes must be used in the analytical calculations, which leads to considerable numerical problems and sometimes chaotic behavior. The influence of a small viscose damping is small compared with the effects of the mode numbers. For plastic impacts and elastic impacts with more realistic stiffness of the stops a moderate number of modes can be used. The comparison of the displacements for hard, plastic and elastic (with high stiffness of the stops) shows a remarkable good agreement with the results of the FEA for hard impacts. This confirms the plastic impact approach in the FE software Abaqus. It is noted that for plastic impacts already two modes give an acceptable description of the displacements.

Keywords

• Vibration
• Impact
• Multiple
• Beam
• Solution
• FE analyzes