Study On Dynamic Optimization Design Of Structures With Frequency-prohibited Bands

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,based on Kuhn-Tucker condition and sensitivity of frequency to variables,a two-factor iteration method of first-order sensitivity of frequency to variables with internal iteration is presented by using Taylor’s first-order expansion,and the calculation program is compiled on the platform of MATLAB,aiming at the optimization design of structural dynamics with size constraints,single frequency-prohibited band constraint and structural weight minimization.According to the shortcomings of the first-order sensitivity algorithm,the second-order sensitivity single-factor iteration method of structural frequency to variables is deduced and established by using Taylor’s second-order expansion.The example shows that it is more efficient and convergent than the first-order sensitivity 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 value range of the single factor is given.It is found and preliminarily demonstrated that when all design variables do not reach the upper and lower bounds of the constraints,"no weight reduction" 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 it is found that the magnitude of frequency gradient is inversely proportional to the magnitude of variable modification.The existing optimization methods of single frequency-prohibited band mainly solve the problem of single predominant frequency or single high-energy frequency band,and the effect of solving the problem of broader high-energy frequency band or multiple high-energy frequency bands is not ideal,and the overall applicability of the method is poor.In response to this situation,in this paper,the first-order sensitivity and the second-order sensitivity of frequency to variables are used to establish the structural optimization calculation method of multiple high-energy bands.Examples verify the accuracy of the optimization method.It is found that in the first order sensitivity optimization method,reducing the number of lower order optimization frequencies in the frequency-prohibited bands is an effective way to improve the efficiency of structural optimization.The first and second order sensitivity optimization methods with multiple variables based on criterion method are extended.According to the optimization examples of I-shaped and rectangular sections,it is revealed that the sensitivity of frequency to different parameter variables of the same section is the main factor affecting the final optimization value of each parameter,and also the basis for distinguishing primary and secondary parameters;a proposal for reducing the number of variables and the variable factor in the first-order sensitivity algorithm is proposed,in order to improve the programming efficiency.It is pointed out that reducing the high-order frequency of the structure,relaxing the lower limit of variable constraints corresponding to minor factors or increasing the upper limit of variable constraints corresponding to major factors are effective ways to improve the engineering economy when the section satisfies the static requirement.In order to adapt to the frequency optimization of complex structures and complex external loading conditions,a high-order sensitivity structural optimization design method with multiple frequency-prohibited bands and variables is established,which greatly improves the application scope of structural dynamic optimization.Based on the first and second order sensitivity optimization algorithm of structural frequency,the design dimension of 24 m simple-supported single-track high-speed railway bridge structure is optimized,and the bamboo-like main girder model under the excitation of measured frequency spectrum is obtained,and its causes are analyzed.The work has certain reference value for dynamic selection of high-speed railway bridge structureThe work done has important theoretical guiding value and practical significance for the design of wind resistance,earthquake resistance,dynamic reinforcement or reconstruction of structures in service.