On the sensitivity analysis of dynamic characteristics for structural modification

Abstract

Recently, lots of improvement in design structure has been made through experiments and experience of engineers. This process is wasteful in terms of time consumption, expenses and resources, especially when considering the trend towards reducing weight in manufacturing products. Hence, it is important to understand well the dynamic characteristics of the products precisely before production commences. One of the steps in understanding the characteristics is to conduct the sensitivity analysis which requires a numerical skill for the optimum design. Besides that, the sensitivity analysis may predict the influence of some effects on the total structure system due to the modification of the design. For instance, Nelson[1] presented a direct method of sensitivity analysis, which is found splendidly practical by many researchers. Mills-Curran[2] had investigated the possibility of iterative eigenvalue application. However, in practical use, this method has a problem. Rudisill[3] determined the change rates for the first eigenvalue and eigenvector. The change rates for the second eigenvalue were also determined. Fox and Kapoor[4] linear combination for non-modified structure amount of changes of an eigenvector and determined the sensitivity coefficient from the normalised mass and orthogonal condition and calculated the change rates for the first eigenvector. Wang[5] applied mode summation technique of accelerated mode on the sensitivity analysis and improved the estimation accuracy. Min, Hyun-Gi et. al.[6] used direct differential method and studied the kinematics of an automobile suspension system with the sensitivity analysis. The sensitivity analysis methods explained above are widely used by most of the researchers; however none of them considered the sensitivity analysis can determine the location of the modification and the modified value, but the analysis itself is a key problem. Once the modifications are made, the structure correspondently changes the natural frequency and the result may not be the optimum value. For instance, if we intend to change the original structure but with less modified points and less subsequent on the dynamic parameters in achieving the desired value, what should we do? To overcome such problems, a sensitivity analysis method by determining the most sensitive point, direction of parameter change and modified value for modification was proposed. Besides that, the sensitivity method in determining natural frequency using partial differential equation is derived with respect to physical parameter to calculate the structure modification. The method is applied to the 3 degrees of freedom lumped mass model by modelling the mass and stiffness and applies the method to a real crankshaft system. The position, direction of parameter change and modified value is predicted for modification of the crankshaft system and the result is used to investigate the magnitude of vibration level.