## A green's function approach to the vibration of thin spherical shell segments |

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Appendix applied load boundary condition residuals complete sphere contour definite integral denoted differential equations displacement components displacement vector displacements and stress eigenvalue elastic foundation elastic law equating coefficients equation 28 equilibrium equation expressed in terms fixed system force couple force per unit foundation reaction Fundamental Problem integral equations introduced latitudinal load vector MECHANICS OF SOLUTION meridian circle mode shape Number numerical integration operations polar axis polar coordinate pole proportional to displacement reciprocal theorem rectangular recurrence relations relationships relative coordinate system relative system required Green's functions respectively response point sample point series solutions sign conventions simplified specified boundary conditions SPHERICAL GEOMETRY spherical surface stimulus point stress resultants substituted into equation superposition surface element symmetric problem tangent vector tangential directions thin spherical shell unit couple unit force unit load unit normal load unit surface area unit vector vector at point vector or tensor verified vibration problem