Dynamic Scaling of Flexible Structures With Viscoelastic Components

Laboratory dynamic testing of large and complex space structures can be difficult and expensive, if practical at all. The use of dynamically scaled test articles is a standard approach to laboratory testing which helps to avoid these problems. The theory and practice of dynamic scaling for elastic structures are well established and validated; however, the issue of scaling structures with viscoelastic components has not been thoroughly investigated. In a structure that is “replica scaled” by a factor 1/λ, the natural frequencies are each scaled by a factor λ. For proper dynamic scaling, each corresponding damping ratio should be unchanged from that of the original full scale structure. The difficulty that arises with structures incorporating viscoelastic components is that the viscoelastic material properties vary with frequency in a nonlinear fashion. Thus, for a particular mode of a scaled model, the viscoelastic material’s damping properties are evaluated at a frequency which is modified by a factor 1/λ and as a consequence the damping ratio does not scale properly. To solve this problem, the authors propose taking advantage of the temperature dependence of viscoelastic material properties. By appropriately controlling the experimental temperature of the scaled structure, it is possible to obtain accurate dynamic scaling results. In this paper, the proposed frequency-temperature compensation method of dynamic scaling for viscoelastically damped structures is developed and experimentally validated.