AN ANALYTIC MODEL FOR THE FREE INPLANE VIBRATION OF BEAMS OF VARIABLECURVATURE AND DEPTH

In this study a flexible and powerful model is presented for the in-pl ane vibration of a beam whose curvature and depth are arbitrary, const rained only to such smoothness as can be accommodated by a quartic pol ynomial in the centerline arc length. The model includes the effects o f shear deformation, rotary inertia, and centerline extensibility. The equations of motion are solved by an extension of the classic Galerki n method wherein the effect of boundary residuals is included. Timoshe nko models are compared to other theoretical models and to experimenta l results; the comparisons are done for a variety of support schemes. A detailed study of a cantilever beam of variable curvature and depth is done and, finally, the utility and flexibility of the model is demo nstrated for an arch whose shape is given only by a scale drawing, dev oid of any other information except material properties.