Closed-form solutions of dynamic vibration equations of seismically excited structures

Abstract Novel closed-form solutions of the dynamic vibration equations of seismically excited structures are derived by using the Laplace transform. Structures with single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) are considered and modelled as lumped mass systems. Several earthquake records with different peak ground accelerations (PGAs) are used to excite such systems. To be compared, time-history responses are obtained numerically by using Newmark’s step-by-step iteration method and analytically by the proposed approach. After conducting such comparisons, the proposed approach successfully computes the exact responses of seismically excited structures.