The Vibration of Stepped Cantilevered Plates

摘要

A theoretical and experimental study of seven stepped cantilevered plates is presented. Four of the plates are square, with increasingly severe steps, and the remaining three are non-rectangular, formed by removing parts of the outboard corners. The first nine natural frequencies and mode shapes of each of the plates are found experimentally and are compared with results predicted using two different approximate finite element representations. It is found that a relatively coarse gridwork of finite elements (4 elements x 4 elements) will predict frequencies with an accuracy of better than 5 percent and also accurately predict mode shapes. There appears to be little difference between the results predicted using the two different methods. The energy models predict frequencies slightly closer to the experimental ones, but only the Hrennikoff model can be used to solve the non-rectangular problems. The present study serves to illustrate further the power of finite element techniques. (Author)