Abstract：Adjusting structural dynamic characteristics by searching reasonable structural design parameters to avoid the predominant frequencies or high energy bands corresponding to the external excitation for structures subjected to wind, earthquake or vehicle-borne excitation, which can inevitably improve the safety of structures during service. In this paper, an optimal method of structural dynamic design with dimension constraints, single frequency-prohibited band constraint and structural weight minimization is studied. A single factor iteration algorithm of second-order sensitivity of structural frequency to variables based on the Kuhn-Tucker condition and the sensitivity of frequency to variables is deduced and established by Taylor's second-order expansion formulation. The first-order and second-order sensitivity computing programs in terms of the same example are developed based on the platform of MATLAB. The example shows that the optimization results of both algorithms are identical, but the second-order sensitivity algorithm is more efficient and convergent than the first-order algorithm, and the correction factor doesn’t need to be adjusted in the whole process of optimization, which is more convenient for operators. The reasonable range of the single factor is given. It is found and preliminarily demonstrated that" no weight reduction", when all design variables do not reach the upper and lower bounds of the constraints, can only be regarded as the necessary condition for optimum, while "higher-order frequency converges to the upper limit of the frequency-prohibited band " should be a sufficient and necessary condition, which is more suitable as a convergence criterion. The conclusion can effectively discriminate the "pseudo-optimal" situation. Based on data representation in the example, it is preliminarily revealed that the modification of optimization variables is mainly dominated by frequency gradient, and the magnitude of frequency gradient is inversely proportional to the magnitude of variable modification. The work done here has important theoretical guiding value and practical significance for the design of wind resistance, earthquake resistance, dynamic reinforcement or reconstruction of structures in service.
2019, Vol. 40 
