Frequency response of pre-stressed structures with nonlinear cohesive interfaces

This paper explores two different methods to extract information about localized nonlinear shear cohesive behavior of interfaces from linear elastodynamic response. Both formulations are based on the concept of loading a cohesive interface statically into the nonlinear region and then superposing small amplitude vibrations or wave motions on the statically pre-loaded state. To a first order approximation the cohesive interface’s small amplitude dynamic behavior is assumed to be linearly compliant with the stiffness interpreted as the local slope of the cohesive law at the static pre-load level. The first investigation considers the vibrations of a beam made up of two sections partially bonded together through the depth of the beam to create a cracked interface. The dependence of the natural frequencies on the spring stiffnesses of a beam with the cracked interface replaced by bending and shear springs is calculated using first order beam theory. The dependence of the spring stiffnesses used in the vibration analysis on crack length, static pre-load, and yield stress of a Dugdale–Barenblatt cohesive zone in the interface is determined through a 2D elasto-static boundary element analysis of a cracked beam element, which treats the boundary nonlinearities directly. The second investigation concerns the dispersion relations for time-harmonic guided waves in a layer connected to a rigid substrate by a very thin interface layer of material with nonlinear and softening behavior. The interfacial spring stiffness which, is directly included in the dynamic layer boundary conditions, is again interpreted as the local slope of the cohesive law at the static pre-load level. The spring stiffnesses inferred from the dispersion relations of either SH or generalized Rayleigh–Lamb waves from a series of measurements taken at multiple pre-load levels could then be integrated to obtain the cohesive law.