New Sensitive Inverse Eigenvalue Method for Optimising Dynamic Behaviour of Steel Structures

Abstract eng:
An efficient relationship between geometric and material properties of framed and continuous structures and their eigenvalues is established. The problem is formulated as an inverse eigenvalue problem. This formulation allows the determination of the required modifications on the structural members such as bar area as well as cross section form for frames, and thickness for continuous elements in order to achieve specified eigenfrequencies. In addition to the modification of the existing structural elements, the formulation also allows addition or suppression of new structural elements to obtain the desired frequencies. The influence of inertia variation on the applicability of the inverse approach is also studied by considering two types of cross sections. The first is a rectangular one with fixed height and variable width, second is circular. This influence on the applicability of the process for framed structures seems to be unimportant. Using the proposed inverse method, two cases of plane framed structure as well as a continuous twelve elements plate are studied and the results compared with those obtained using the conventional optimization techniques adopted by commercial finite element codes. This approach provides an effective and simple algorithm to the designers, formulated so that no iteration or convergence is implied in the process for obtaining the necessary modifications. It shows high accuracy without complicated calculations.

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