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SUMMARYMany real systems such as moving vehicles on roads, missiles following trajectories and ships in sea water have asymmetric mass, damping and stiffness matrices. Eigen-sensitivity analysis methods for the symmetric damped system cannot be used in the asymmetric damped case. Therefore, a method for calculating eigenpair sensitivity of the asymmetric damped system is needed. To do this, a modal method employing a modal superposition idea was recently developed. Since the accuracy of the modal method is dependent on the number of modes used in calculation, the modal method needs higher eigenvectors to guarantee the accuracy. In large-scale systems, however, only a few lower modes are generally considered for the dynamic analysis. Hence, if the modal method is used to obtain the eigen-sensitivity of the large-scale system, the significant errors could not be avoided due to the lack of the information of higher modes. In this paper, the modified modal methods for computing the sensitivities of the eigenpairs of asymmetric damped system using a few lowest sets of modes are proposed. Numerical example shows that the proposed methods achieve better calculating efficiency than the previous modal method.

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In the evaluation of crashworthiness of roadside safety features, full-scale impact tests are generally required according to the established test protocols. Since the tests are expensive, it is useful to predict the crash responses of a vehicle from the other size test vehicles. This concept was used in the Manual for Assessing Safety Hardware (MASH) of American Association of State Highway and Transportation Officials (AASHTO) to decide whether mid-size vehicle tests are necessary for an attenuator system design in addition to the small car and pickup truck tests. The general applicability of this procedure in the estimation of impact responses of one vehicle from the tested vehicle is studied using the crash test data of 11 crash cushions tested by the Korea Expressway Corporation Research Institute (KECRI). Each of the 11 crash cushions has two sets of test data from 1.3 and 0.9 ton vehicles tested with an impact speed of 80 or 100 km/h depending on the class of each system. Using the procedure, for each of the 11 systems, 1.3 ton crash data were transformed into the 0.9 ton crash data, then the estimated 0.9 ton crash data were compared with the 0.9 ton test data. It was found that the crash data predictions deviated from the test data, leading to overly conservative estimation of safety risk factors. The procedure was also found inapplicable in estimating crash data of a large vehicle (1.3 ton) from the test data of a small vehicle (0.9 ton). New procedure to estimate the crash data of a vehicle from the test vehicle regardless of their relative mass size was developed and the method was validated using the crash test data of 11 different crash cushions. In the new procedure developed, pivoting the velocity trace of test vehicle was utilised. The new procedure showed favourable results in estimating the crash data of a small vehicle (0.9 ton) from the crash data of a large test vehicle (1.3 ton). It can also be applied in reverse case estimation where the predicting vehicle (1.3 ton) was larger than the test vehicle (0.9 ton).