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After analyzing existing vehicle motion data for low speed rear-end impacts, this paper develops an efficient mathematical model to simulate such testing. The proposed idealization is believed to be as simple a model as is possible for delivering reasonable time history responses of the two vehicles involved, i.e. a linear two-degree of freedom mass/spring/dashpot system. A closed-form solution of the equations is then developed and numerical results based upon it are compared to the time histories of the actual vehicle motions and peak loads. Experimental data is used to determine the effective stiffness and damping for the two degree of freedom model. Comparisons of results obtained from the analysis with scaled test data agree favorably, thus identifying the basic design parameters which could be used to minimize vehicle damage and passenger loading.

The physical origin and ambiguity of repeated frequency modes, is discussed, followed by a mathematical derivation of the governing equations for the derivatives of repeated eigenvalues. This is followed by a derivation for the associated eigenvector gradient equations and two small examples to illustrate the solution procedure. Physical interpretations are also included to help explain the analytical results. An efficient computation procedure which preserves the bandwidth for very large matrices is also proposed for systems with repeated or closely spaced eigenvalues.

Results of an analytical investigation on the influence of bond thickness upon the stress distribution in single lap adhesive joints are presented. The present work extends the basic approach for bonded joints, originally introduced by Goland and Reissner, through use of a more complete shear-strain/displacement equation for the adhesive layer. This refinement was not found to be included in any of the numerous analytical investigations reviewed. As a result of the approach employed, the present work uncovers several interesting phenomena without adding any significant complication to the analysis. Besides modifying some coefficients in the shear stress equations, completely new terms in the differential equation and boundary conditions for bond peel stress are obtained. In addition, a variation of shear stress through the bond thickness - no matter how thin it may be - is analytically predicted only by the present theory.