Study of dynamic end effects in an elastic strip with sliding boundary conditions

The dynamic response of an elastic, semi-infinite strip with sliding surfaces, subjected to various forms of end excitations, was solved analytically employing the property of bi-orthogonality of wave modes. An explicit relation between the amplitudes of evanescent waves and the form of the excitation was obtained. Quantitative measure for dynamic end effects was suggested, termed Saint-Venant ratio (SVR). It was shown that two qualities of that ratio are useful for monitoring the health of structural joints (SHM): being that ratio not affected by the intensity of the end excitation and its high sensitivity to small variations in the form of the excitation. The axial behavior of the strip subjected to several forms of end excitations was further used to demonstrate the validity of a previously suggested dynamic version of Saint-Venant’s principle.