This paper deals with the problem of a cantilever truss space structure optimization under a frequency constraint. The considered structure, with an attached rigid body at the external free end, is typical of satellite appendages. The same value of the lowest vibration frequency of the reference truss structure, with uniform thickness over all the component beams, has been prescribed to prevent possible resonances between satellite and appendages. A minimum value of the thickness over each component beam of the analyzed truss has been established a priori. Focusing attention on the dynamic behavior, a numerical procedure (based on the classical Rayleigh-Ritz method but combined with the finite element method) has been used. Polynomial power series expansions have been used both for the dynamic variables (displacements and rotations) and for the thickness axial distribution over each component beam of the truss structure. The classical Euler-Lagrange optimality criterion has been used to find the requested solution of each optimization operation, which consists of the search for stationary conditions of the Lagrangian functional. A series of repeated optimization operations have been performed to arrive at the thickness optimized profile within each structural component, with the preestablished minimum value of the beams' thickness. It has also been possible to evaluate the weight reduction. Nomenclature g n i a i b i c = global describing functions coefficients of the generic variable S n I b = identification number of the generic beam i bay = identification number of a generic bay k ij , k ij;i et = stiffness matrix elements and stiffness matrix elements components L I b = nondimensional length of a generic beam L t = sum of the dimensionless lengths of the component beams considered for the optimization operations L 0 = reference length l I b n ie = local describing functions coefficients of the generic variable S n in the I b th beam l 1 , l 1 , l 2 = longitudinal lines containing aligned beams m ij , m ij;i et = mass matrix elements and mass matrix elements components N = whole number of unknown variables N a , N b , N c = number of dynamic variables global describing functions along the axes X, Y, and Z, respectively N bays = number of the truss structure component bays N beams = number of truss structure component beams considered for the dynamic analysis N el = number of local describing functions of the dynamic variables in each beam N et = number of coefficients of all the beams thickness series expansions N opt = number of all the beams considered in optimization process N qt = number of coefficients and describing functions of all the independent dynamic variables series expansions N t = number of coefficients and describing functions of the nondimensional thickness series expansion in each beam q i , q j = generic Lagrangian degrees of freedom R I b ij= rotation matrix element connecting the axis X i with the axis X lj in the I b th beam S n = generic independent variable T = dimensionless relative co...