An analytical model to study the coupled transverse and longitudinal vibrations of a single lap adhesive joint is described in this paper, which includes partial differential form of the motion equations. A joint consists of two identical adherents of mild steel that are lap jointed over a certain length by a viscoelastic material, epoxy resin (araldite). Adherents are modeled as Euler-Bernoulli free-free beam. Both transverse and axial deformation of adherents and longitudinal shear and transverse peel stresses at the adhesive joint interface are considered in deriving the equations of motion. The numerical solutions of the governing equations for free vibrations yield the system’s natural frequency and mode shapes. Experimentation was carried out on both monolithic and adhesively jointed beams to observe the effect of the joint; natural frequencies of the system were measured experimentally and compared with those obtained theoretically. The fundamental frequency of a free-free jointed beam was more sensitive to joint overlap ratio. However natural frequency depended on the accelerometer location in the system, which was attributed to its mass contribution to the overall system mass. Theoretical frequency response function is generated for a beam with and without accelerometer mass to show the mass loading effect of the transducer (accelerometer).
In engineering applications, almost all structures are composed of substructures and parts that are joined together with a multitude of different connections (e.g., bolted, riveted, welded, etc.). It is known that the added flexibility introduced by the joint to a structure significantly affects its dynamic behavior. The need for accurate prediction of the dynamic characteristics of complex structures has led to extensive research on the identification of joint dynamic characteristics. In the present work, a structural joint have been modeled as a pair of translational and rotational springs and the frequency equation of the overall system has been developed using sub-structure synthesis. It is shown that by using the first few natural frequencies of the system, one can estimate the unknown stiffness parameters. The estimation procedure has been developed first for a two parameter joint model and then for a three parameter model in which cross coupling terms are also included. The validity of the proposed method is demonstrated numerically and experimentally.
In this study, a method is developed for parametric identification of nonlinear element in structure. A concept of sub-structure synthesis is used to derive the frequency equation in terms of linear and nonlinear stiffness parameters. The derived equation is exploited for inverse analysis, wherein nonlinear parameter is estimated from theoretically obtained data. The method is demonstrated numerically for cantilever beam with nonlinear boundary condition. It is also shown that the method is robust against measurement errors and gives accurate estimates for a wide range of stiffness values.
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