Jp. Charpie et Cb. Burroughs, AN ANALYTIC MODEL FOR THE FREE INPLANE VIBRATION OF BEAMS OF VARIABLECURVATURE AND DEPTH, The Journal of the Acoustical Society of America, 94(2), 1993, pp. 866-879
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.