A numerical procedure, which lies between Rayleigh-Ritz and the nite element method so far applied only to aeronautical structures in both two-and three-dimensional space, is utilized for the dynamic analysis of periodic truss space structures, typical of appendices of arti cial satellites. The structural components are unidimensional tube-type elements with circular cross sections. They are considered as beam elements, for which a complete model for the internal strain energy has been utilized. Three different numbers of component bays of these structures are assumed in the numerical applications, and the obtained results are analyzed. The advantages of the proposed method as the number of the component bays increases, particularly with respect to the CPU time, are pointed out comparing the obtained results with the ones of a classical nite element method numerical program, such as MSC/NASTRAN. Nomenclature A = beam cross-sectional area E = modulus of elasticity E f 0 = parameter containing the modulus of elasticity e e , e de , e ded = occurring integrals determined by the local describing functions G = shear rigidity modulus G t 0 , G d = parameters containing the shear rigidity modulus g (n) ia ib ic , g (r ) ia ibic , = global describing functions g ja j b jc (s ) coef cients of the generic variable S n J f = exural moment of inertia J t = torsional moment of inertia K = stiffness matrix L = length of the generic beam L = nondimensional length of the generic beam L 0 = reference length l ( Ib ) nie , l ( Ib ) rie , l ( Ib) s j e = local describing functions coef cients of the generic variable S n in the I b th beam M = mass matrix N = number of Lagrangian degrees of freedom N a , N b , N c= number of global describing functions along the axes X , Y , and Z , respectively N el = number of local describing functions P e , P de , = occurring mixed integrals determined P ed , P ded by the global and local describing functions coupling P p , P d p , P d pd = occurring integrals obtained by the global describing functions q i = generic Lagrangian degree of freedom R i j = rotation matrix element connecting the axis x i with the axis X l j S d a = parameter containing the modulus of elasticity S m t , S m f , S m a = parameters containing the mass density and J t , J f , and A, respectively S n = generic independent variable = kinetic energy U, V , W ; = nondimensional displacements along U 1 , U 2 , U 3 the axes of the main reference system U l , V l , W l ; = nondimensional displacements along U l1 , U l2 , U l3 the axes of the local reference system a = axial strain energy f = exural strain energy T = total strain energy
