Heliyon (Oct 2024)
Analytical solution of seismic power-based equation of motion
Abstract
This research proposes an innovative power-based equation of motion (PBEM) for the single degree of freedom (SDOF) system considering seismic excitation. The external or input frequency function, solution of time, relation between external and kinetic powers, and equation of strain-power (SP) are obtained by solving the power balance equation (PBE). The external frequency function is related to both the particular and total solutions of the PBEM. The particular solution of PBEM is applied on the shake table test of the tunnel-soil-pile interaction (TSPI) model, real-scale test of 2-storied reinforced concrete frame structure, and case study of Bolu tunnel for the verification purpose. The differences in verification (PBEM and previous works) results are found to be 21.6 % for the real-scale test and 19.5 % for the case study. These differences may represent a reasonable agreement with verification. Also, the relationship between the kinetic and external powers is verified with the previous shake table test of steel cantilever column, whereas the difference in results is found to be 5 %. Finally, a design chart is proposed for predicting the input frequency function for various frequency ratios and damping.
