EFFICIENT OPTIMIZATION PROCEDURE FOR MINIMIZING VIBRATORY RESPONSE VIA REDESIGN OR MODIFICATION .1. THEORY

This paper addresses the problem of minimizing the vibrating response via structural modification. The method presented is computationally e fficient, and orders of magnitude faster than conventional approaches. Some aspects of the method's efficiency are traceable to specific pro perties of vibrating structures. The method is based on the assumption of knowledge of the excitation's power spectral density and can handl e structures modelled by an incomplete modal model. While the geometri c structural changes are represented as mass and stiffness changes, an y structural or geometrical parameter can be used. The optimization pr oblem is cast into numerically efficient subsequent stages. Also the r esponse measure, the cost function and the sensitivities with respect to structural parameter change, are calculated by using a very efficie nt scheme, exploiting the modal decomposition. The problem is formulat ed directly in terms of physical and geometrical quantities: i.e., sec tion areas, height, width and point mass. Simple constraints ensure re alizable structural changes yielding optimal performance. This helps i n presenting more viable design options. Examples are deferred to the companion paper, part II.