Research On Dynamic Characteristics Analysis And Optimization For Stochastic Chain Structures

Dynamic analysis and optimization of structure plays an important role in structural design and investigation, but structural dynamic analysis and optimization for stochastic structures is a more important task which must be investigated today. In this paper, the problem of structural dynamic characteristics analysis of stochastic structures and optimal dynamic characteristics design of structure with the reliability constraints on frequency is studied. As chain structures for object, the stochastic property of physics parameter (mass density and shear elastic module) of structural material and structural dimensions is individually or meantime considered and structural dynamic characteristics analysis based on probability is analyzed. The equation to calculate natural frequency has been built, and the digit characteristics of natural frequency random variable are derived. Considering the randomness of structure parameters, the numerical value simulation of structural dynamic characteristic is derived. Based on theory discussed above, the structural optimization design model is developed with the reliability constraints of frequency forbidden or frequency domain, in which the structural dimensions are taken as design variables and the structure weight as objective function. In optimization process, the reliability constraints are equivalently displayed is that the constraints in probability form can be showed in normal form with equivalence. Finally, the structural dynamic characteristics sensitivity is analyzed and a formula for calculating the sensitivity of the reliability constraints on dynamic characteristics is developed. Several numerical examples are presented, and some conclusions are obtained.