CLOSED-FORM SOLUTION FOR TRANSVERS VIBRATION OF RECTANGULAR THIN PLATES CARRYING MULTIPLE LlNE—CONCENTRATED MASSES

At the present study, the free transverse vibration of a thin rectangular plate carrying multiple inline concentrated masses is taken into consideration. The closed-formsolution is based on applying the generalized Diracs delta fiinctions in order to model the line-concentrated masses and the frequency equations and vibration modes aredirectly obtained for an arbitrary number of concentrated masses in arbitrary position on the plate . The frequency equations are extracted from a two-order determinantwhich obtained by solving goveming equations that yield the natural frequencies and mode shapes. The effects of munber, position. magnitude of concentrated masses on the value of natural frequencies are investigated and evaluated by numerical approaches. The boundary conditions are simply supported for the edges along the width of the plate and arbitrary for other edges. Obtained results introduce the procedure fast, accurate and straight-forward in comparison with those obtained by numerical proceduressuch as DQEM [9].

Keywords:

line-concentrated masses , basic functions , transverse vibration. frequency equation , Dirac’s delta function