ON THE DETERMINATION OF PHASE CONSTANTS FOR THE STUDY OF THE FREE-VIBRATION OF PERIODIC STRUCTURES

An alternative approach for the determination of the phase constants f or use in the study of the free vibration of periodically supported st ructures is proposed. The Rayleigh-Ritz method, together with the pena lty function, is used, and its applicability and accuracy is demonstra ted through the treatment of two structures which have been studied by previous researchers: the periodically supported uniform beam and thi n flat plate. The approach is then used to obtain phase constant curve s for periodically, shear diaphragm supported, doubly curved, shallow shells, for which no results have previously been reported. The approa ch is simple in concept and straightforward in application.