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Summary This paper investigates the optimal design of the tuned viscous mass damper (TVMD) with linear and nonlinear viscous damping properties for a single degree‐of‐freedom structure subjected to harmonic excitation. The TVMD consists of a parallel‐connected inerter and viscous damper, and a spring that mounts them to the structure. To examine the vibration control performance of the TVMD, both theoretical analysis and numerical optimization are conducted to obtain the optimal parameters of the TVMD with either linear or nonlinear viscous damping. The influence of the damping exponent of the nonlinear viscous damper on the optimal parameters and performance of the TVMD is analyzed. The results show that much better control effectiveness and robustness can be achieved by the TVMD when compared with tuned mass damper (TMD). Furthermore, it is also of great practical importance to show that the static deformation of the supporting spring due to the self‐weight of the inerter is only a small fraction of the traditional TMD in case of vertical vibration control. Compared with the linear TVMD, the nonlinear TVMD can achieve comparable or even slightly better control performance. The optimal damping coefficient depends largely on the damping exponent, and the loading intensity fluctuation also has an influence on the performance of the nonlinear TVMD. Moreover, it is shown that that the nonlinear TVMD with damping exponent ν = 2 has the best control performance on the peak displacement response of the main structure, and the TVMD with linear viscous damping optimized for the harmonic excitation can also effectively suppress the wind‐induced vibration.

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In this article, the continuous integral terminal sliding mode control problem for a class of uncertain nonlinear systems is investigated. First of all, based on homogeneous system theory, a global finite-time control law with simple structure is proposed for a chain of integrators. Then, inspired by the proposed finite-time control law, a novel integral terminal sliding mode surface is designed, based on which an integral terminal sliding mode control law is constructed for a class of higher order nonlinear systems subject disturbances. Furthermore, a finite-time disturbance observer-based integral terminal sliding mode control law is proposed, and strict theoretical analysis shows that the composite integral terminal sliding mode control approach can eliminate chattering completely without losing disturbance attenuation ability and performance robustness of integral terminal sliding mode control. Simulation examples are given to illustrate the simplicity of the new design approach and effectiveness.