Dynamic characteristics of a structure with multiple attachments: A receptance approach

An application of the analytical approach of receptance for the analysis of vibration and stability of a structure with multiple linear and torsional springs of different stiffness attached to an axially loaded beam is described. The beam–spring combination is a typical analytical model that is often used as the benchmark to verify frequency and buckling data obtained by numerical algorithms and full structural models. Solutions of the analytical model also provide the necessary understanding of system properties in the process of establishing numerical models. Although vibration and buckling characteristics of a structural model with multiple linear and torsional components can be obtained by directly solving governing differential equations, the process can become quite complicated if there are a large number of attachments with a wide range of stiffness values. A receptance procedure proposed in the present study provides a simple and accurate alternative. The approach is an approximation method similar to sub-structuring techniques. By retaining only the essential interactions between the major structure and attached components, the analysis is much simplified. The present study illustrates the simplicity and effectiveness of this approach. A parametric study is also given and compared with the finite element result. Good agreement indicates the accuracy of the approximation.