In this study, a robust adaptive controller is designed to be used in an active tuned mass damper system that can be used to damp undesired vibrations that occurred on the multistory buildings during the earthquake. To realize the controller design, all of the system parameters are assumed to be unknown, and the adaptive structure of the designed controller is obtained by designing adaptive compensation rules for system parameters. A backstepping control design approach is utilized for the control design by considering the appropriateness of the system’s structure of multistory buildings having an active tuned mass damper system at the top of the structure. The proposed control design is supported with a Lyapunov-based stability analysis where it is proven that the designed controller is able to protect the overall system’s stability while reaching the main control purpose. In addition to these, in the simulation studies realized for a nine-story building under the effect of a major earthquake, it is shown that the designed controller can be used to reach the main control purpose efficiently.

The effects of crack depth and crack location on the in-plane static and dynamic stability of cracked multi-bay frame structures subjected to periodic loading have been investigated numerically by using the finite element method. For the rectangular cross-section beam, a crack element is developed by using the principles of fracture mechanics. In addition, the effect of the number of spans and static and dynamic load parameters on static and dynamic stability analysis are also investigated. For buckling and dynamic stability analyses, the results obtained by using the present model are presented in three-dimensional graphical forms and tables.

The objective of this paper is to investigate the effects of laminate scheme, crack ratio ( a/h) and crack position ( L₁/L) on the free vibration and lateral buckling of a cantilever slender rectangular beam such as an airplane wing or a wind turbine blade with a single edge crack. The local flexibility approach is adopted to model the crack, based on linear fracture mechanics and the Castigliano theorem. The governing matrix equations for free vibration and buckling load are derived from the standard beam element and cracked beam element combined with the local flexibility concept. The results are obtained numerically using the finite element method, based on the energy approach and are given for crack ratios up to 0.5 at crack positions up to 0.9 ratio. Polynomial approximation for displacements gives results with reasonable accuracy.

In this study, in-plane natural frequencies and the dynamic stability of a curved beam subjected to a uniformly distributed periodic axial load with suspended spring–mass systems are investigated by using the FEM. The natural frequency results obtained from the developed FE code are compared with the ANSYS model results to verify the accuracy of the present model. The effect of the stiffness coefficients, the position of the spring–mass system, static and dynamic load parameters on the natural frequencies and the dynamic instability regions are investigated for a various subtended angle. The results are presented by tables and graphics.