A modal element is defined as a body or substructure described solely through its natural vibration properties: angular eigenfrequencies ω{sub}n, modal masses m{sub}n, and a number of pertinent eigenmode translations and rotations (p{sub}j){sup}n at discrete positions of interest (with n=1,2,...,N and j=1,2,...,J). These modal parameters may have been found experimentally or theoretically. Modal damping will not be included in the present study. The built-up structure analyzed in the following may consist of modal elements, standard finite elements (beams, plates, etc), and so-called exact finite elements (each characterized by a dynamic stiffness matrix whose elements are transcendental functions of the angular frequency ω). The evaluation of the eigenfrequencies of such a built-up structure constitutes a nonlinear eigenvalue problem The Wittrick-Williams algorithm will here be applied to numerically solve that problem. Modal elements with N>J are considered as are modal elements having rigid-body eigenmodes (ω{sub}n=0 for some n). Static loading (ω=O) of the structure will also be discussed. The computer program SFVIBAT-II for space frame analysis has been extended to include modal elements. A numerical example is given. The results are compared with those from a parallel computation by use of the general-purpose program MSC/NASTRAN. A list of NOTATION is given at the end of the paper.
展开▼
