  This paper presents a configuration design optimization method for
three-dimensional curved beam built-up structures having maximized fundamental
eigenfrequency. We develop the method of computation of design velocity field
and optimal design of beam structures constrained on a curved surface, where
both designs of the embedded beams and the curved surface are simultaneously
varied during the optimal design process. A shear-deformable beam model is used
in the response analyses of structural vibrations within an isogeometric
framework using the NURBS basis functions. An analytical design sensitivity
expression of repeated eigenvalues is derived. The developed method is
demonstrated through several illustrative examples.
