Kernel function for nonplanar oscillating surfaces in supersonic flow

t;(0) =. w>(0) = t;'(0) =' w'(0) = */'(!) = w"(l) = t;'"(l) = w'"(l} = 0 (12) Equations (10) and (11) are now solved by Galerkin's method,4 utilizing the known, uncoupled modes of vibration which are also the solutions for no preconing or vanishing ft. This permits a direct comparison and evaluation of the signifi- cance of the Coriolis coupling. Let W(x) ^ (13) Associated with Wi and Vi, the ith modes of uncoupled out-of- plane and in-plane vibrations are the uncoupled natural fre- quency ratios vwi and vvi, respectively. Substituting Eqs. (13) and (14) into Eqs. (10) and (11), multiplying through by Wj and Vjj respectively, and integrating over the dimension- less span there results the 2n homogeneous algebraic equa- tions n