As one of the most representative passive control devices, tuned mass dampers (TMDs) are widely used in civil engineering, aerospace, machinery, and other fields, after years of research and improvement. However, due to their large displacement and the use of a limiting device, they inevitably exhibit some nonlinear characteristics in practical engineering applications. This nonlinearity is often ignored; however, neglecting it in the design process can adversely affect the control performance. Therefore, considering the nonlinearity of a TMD while designing TMD parameters can make the calculation results closer to reality and benefit the structural design. In this paper, we derived the approximate analytical solution of TMD amplitude using the complex variable averaging method by considering the nonlinearity generated by a TMD in the vibration process. Theoretical optimal design parameters were obtained by analytical comparison, and we compared the computational time consumption of this method and the numerical method. The results showed that the optimized parameters of the TMD obtained by nonlinear design possessed a good vibration reduction effect both before and after the TMD generated nonlinear characteristics. Additionally, the complex averaging method generated frequency response curves tens of times faster than the numerical method.

The tuned mass damper (TMD), as a representative passive control device, has been widely used in various fields such as mechanical vibration and civil engineering. In practical engineering applications, nonlinear characteristics of the TMD inevitably occur due to the installation of limiting devices or large displacements. Neglecting such nonlinearity may adversely affect the control performance of the TMD. Based on this situation, the parameters of the nonlinear tuned mass damper (NTMD) were analyzed, considering the linear and cubic nonlinear stiffness of the TMD, in order to improve its control performance. In this paper, a numerical model of a single-degree-of-freedom controlled structure using an NTMD was established, and the complex variable averaging method was employed to derive the response expression of the structure under the 1:1 resonance condition. Subsequently, the nonlinear design equation for the NTMD frequency was obtained. Based on this nonlinear design formula, the design accuracy was analyzed under 1:1 resonance, undamped and softened stiffness conditions. The results indicate that the NTMD based on a nonlinear design exhibits good control performance.

Tuned mass dampers (TMDs) are widely used as vibration damping devices in engineering practice. However, during use, TMDs inevitably exhibit some nonlinear characteristics that may negatively impact engineering applications. To improve the practical performance of TMDs, the cubic nonlinear stiffness of the TMD is considered, and a nonlinear design is implemented. A numerical model of a single-degree-of-freedom main structure controlled by an NTMD is developed, and the steady-state amplitude solution of the system is obtained using the complex variable averaging method. The results show that a jump phenomenon may occur in the structure. To address this, a multivalued solution discrimination formula based on the complex variable averaging method is proposed. The discriminant formula for the jump phenomenon obtains the frequency ratio and nonlinear coefficient curves of the critical jump state, and four different system response areas are obtained. This helps the structure avoid the jump phenomenon while ensuring stability of the main structure and improving the control performance of the NTMD.

The diamond buckling restrained braced frame (DBRBF) structure is a novel form of an anti--lateral force support system. A design method for DBRBF structures suitable for various structural types is proposed based on the equilibrium of normal forces in column joints. Taking into account the...

With the development of modern structures in the direction of higher and more complexity, the existence of multiple factors in the design and requirements of structures can lead to structures prone to nonlinear properties. The tuned mass damper (TMD), a widely implemented passive control mechanism, plays a crucial role in the engineering field by effectively reducing vibrations within primary structures. Nevertheless, its deployment frequently induces nonlinear dynamics due to the substantial displacements resulting from TMD operation or the integration of limiting devices. This research delineates a computational framework for a single-degree-of-freedom nonlinear primary system regulated by a nonlinear tuned mass damper (NTMD), designed to emulate near-fault seismic phenomena via a sinusoidal load. The study concentrates on the nonlinear attributes of both the NTMD and the primary system. Utilizing the complex variable averaging method in conjunction with the multiscale technique, complex variable equations and slow invariant manifolds are formulated for the system under 1:1 resonance conditions, with their accuracy and validity substantiated through numerical simulations. Expanding upon the derived complex variable equations and slow invariant manifolds, this study examines the impact of nonlinear coefficients within the NTMD and the primary system on both the damping performance of the NTMD and the stability of the primary system. Furthermore, this research delves into the effects of mass ratio fluctuations on the damping effectiveness of the TMD and the control efficiency of the primary system, as well as the emergence of jump phenomena in the presence of significant nonlinear coefficients. The analytical outcomes underscore the critical need to account for the inherent nonlinearities in both the TMD and the primary system, which can have detrimental effects. By considering the mass ratio as a key design parameter, optimizing it can enhance the TMD’s vibration suppression capabilities and the primary system’s control behavior, while also reducing the likelihood of jump phenomena and improving overall structural stability.