VIBRATION OF A CLASS OF SHALLOW SHELLS BOUNDED BY EDGES DESCRIBED BY POLYNOMIALS .1. THEORETICAL APPROACH AND VALIDATION

The Ritz method is used to obtain an eigenvalue equation for the free vibration of thin shallow shells of curvilinear planform defined by po lynomial expressions. The shell is discretized into four 90 degrees se ctorial elements allowing for up to four different outer curves and up to four different inner curves described by polynomials which define the planform of the shell; the elements are joined together through th e use of artificial springs. Several complicating effects are included in the analysis, such as the presence of internal point or line suppo rts, concentrated masses and stepped material thickness. In Part I of the paper, the theoretical approach is developed and its validity demo nstrated through its application to several shells previously treated in the literature. In Part II of the paper, the proposed approach is a pplied to a number of shallow shells of various different planforms, w ith and without complicating effects, both demonstrating its versatili ty and giving results for problems as yet untreated in the open litera ture.