Dynamic analysis of structures is of significant importance in a variety ofapplications. Modal parameters identification can be utilized in resonance frequency estimation, fault detection and its diagnostics in many industrial applications from automobile to aerospace and satellite industries. To perform the vibration tests utilizing shaker, test sample should be connected to shaker using fixture. No fixture can reproduce a perfectly rigid boundary condition; at some frequencies the interaction between the fixture and the structure will become important, causing the modes of the assembly to be considerably different from the fixed-base modes that would be predicted by an idealized finite element model. However, it would be very convenient to be able to estimate the fixed-base modes of a structure experimentally so they could be used to update or validate the model for the structure. In this paper, two degree of freedom model is considered for the system and optimal shape for fixture is designed based on the analytical analysis. Mode shapes and frequencies of fixture are investigated numerically and compared with experimental results. Effect of connection torques on the system dynamics such as power spectral density and natural frequencies is studied by performing different experimental analyses.