Evaluation of Rayleigh damping coefficients for laminated rubber bearing using modal analysis / Ahmad Idzwan Yusuf

Laminated rubber bearing is a significant device found in structures such as bridges and buildings. It is used to isolate the foundation and the superstructure from seismic loads. Since it is made up from a combination of rubbers and steel shim plates in alternate layers which make the laminated rubber bearing a complex material, the measurements of damping of the laminated rubber bearing is difficult in practice. Damping is a dissipation of energy or energy losses in the vibration of the structure when the structures are excited with external dynamic loading. An accurate value of damping is very important as damping plays a crucial role in fixing the borderline between stability and instability in many structural systems. A small amount of damping will have a big influence on the systems. Therefore, it is essential to determine the accurate value of damping in structural analysis especially in finite element analysis. Modal analysis is one of the methods that can be used to determine dynamic properties including damping in any structures. Hence, the main objectives of this research are to determine the Rayleigh's damping coefficients, α andβ and to evaluate the performance of the laminated rubber bearing using modal analysis. There are two methods of modal analysis which are the finite element modal analysis and the experimental modal analysis. Initially, the natural frequencies and mode shapes from both methods are compared and validated. When the natural frequencies and mode shapes are well correlated, the damping ratio values from the experimental modal analysis are used to determine the Rayleigh's damping coefficients α and β. The Rayleigh's damping coefficients that have been determined by experiment are then inserted in the finite element modal analysis to evaluate the performance of the laminated rubber bearing in term of natural frequencies, mode shapes, minimum displacement and maximum displacement with the addition of Rayleigh's damping coefficient. Based on the finding, the finite element modal analysis with the added Rayleigh's damping coefficients α and β shows a good agreement with the experimental modal analysis in term of natural frequencies and mode shapes. The value of natural frequencies reduces after the Rayleigh's damping coefficients are added into the finite element modal analysis and the minimum and maximum displacement are found to be unaffected by the Rayleigh's damping coefficients. It can be concluded that modal analysis method can be used to estimate the accurate values of damping ratio and to determine the Rayleigh's damping coefficients α and β as well. The damping ratio of the first mode from the experimental modal analysis can also be used to determine the Rayleigh's damping coefficients α and β.