Pseudovelocity modal stress velocity proportionality

Abstract

The fact that maximum modal stress is proportional to maximum modal velocity is the foundation of Pseudo Velocity Shock Spectrum analysis of mechanical shock. This proof is very easy to overlook and very important. Neither Raleigh nor Timoshenko observed it. Few modern shock and vibration authors understand it. This misunderstanding has caused incorrect emphasis to be placed dynamic accelerations. In this paper, I try to collect the proof elements for rods and beams. I also prove that shock excitation of a simply supported beam causes a peak modal velocity equal to a participation factor times the PVSS (pseudovelocity shock spectrum) level at the modal frequency. For the first mode this participation factor is 1.27 or 27% higher than the corresponding PVSS value. This is a reference document that repeats all of the proofs elements so that the reader need not refer to the documented literature to follow the explanation. © The Society for Experimental Mechanics, Inc. 2012.