Keywords: dynamic stiffness matrix, lambda matrices, self-adjoint operators, approximation in frequency domain..

The aim of the study, described in this paper, is an alternative analysis for the structure response or modal properties. The structure consists of one-dimensional bars (rectior curvi-linear). Analysis is considered on a full abstract basis as a problem of a differential system of an oriented graph. This graph is a geometric representation of the investigated mechanical system, where elements of the graph are individual bars of the system, recti- or curvilinear. The system as a whole is fixed through boundary conditions or interconnected with other sub-systems. Hence the paper can be taken as a follow up to an earlier work where a full mathematical background dealing with a general problem has been discussed. This paper is focused to the problem of dynamics of a system with straight prismatic bars with uniformly distributed mass. Any dissipation is omitted to keep the formulation in the real domain. The detailed assembling algorithm of the dynamic stiffness matrix (DSM) in local coordinates and its transformation into global coordinates is outlined and demonstrated. Conventional methods of eigenvalues searching by means of a discrete alternative of the Newton- Raphson method is sketched out and later two possibilities based on polynomial and hyperbolic approximations of the DSM elements are pointed out. Lambda matrices are introduced, as a tool, together with a couple of application possibilities. Finally, an illustrative example of the eigenvalue analysis of a structure is included. Strengths and shortcomings of the approach are discussed. Some open problems and directions for further investigation are briefly outlined.

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