The possibility of using a response spectra method (RSM) for the calculation of structures with mass dampers (MD) is considered. It is shown that the Guide Lines SP 14.13330.2014 allows us to take into account the MD behavior and estimate its efficiency. However, it is impossible to optimize damping in the mass damper elements. To take into account the damping RSM, including amendments to the damping and the mode correlation, may be modified. In this case, satisfactory results are obtained when the relative weight of MD less than 0.7 and the construction damping of less than 0.3 (15% of the critical value). For the great mass of the MD optimum damping is more than 20% of the critical, and there is a need to consider the effect of modal damping.

The comments consider the possibility of using the response-spectra method (RSM) taking damping into account in seismic calculations. The results of the paper under consideration are fair if the influence of damping on the shape modes has not been taken into consideration. At present there exists a variant of RSM, which takes into account the damping influence on shape modes. This variant of RSM has been described in the comments. In this case complex eigenvalues and eigenvectors of the damped system are calculated. The imaginary part of the eigenvalues determines the modal frequency, and the real part of the eigenvalues determines the modal damping. Seismic forces are calculated taking into account the amendments caused by modal damping.

The problem of calculating harmonic oscillations of a linear damped system with inhomogeneous damping is considered. Along with the solution available in literature, which requires the inversion of the matrix that determines the eigenvalues of the undamped system, the authors propose a new solution that does not require the inversion of the above mentioned matrix, but requires the inversion of the system damping matrix. The cases of hysteretic, viscous and mixed damping are considered. It is shown that the known solution gives an error near the resonance. At the resonance point, the result is not defined at all, and near the resonance it may be incorrect. An example of building the amplitude-frequency characteristic of a system with two mass tuned dynamic dampers and three peaks in the amplitude-frequency characteristic is given. The proposed formulas for calculating displacements are convenient for constructing the amplitude-frequency characteristics of damped systems with viscous, hysteretic and mixed types of damping.

The paper is devoted to studying the influence of the method of accounting the system damping on the mass damper optimal parameters and their effectiveness under seismic impacts. Steady harmonic oscillations of a damped system with the mass damper are considered. The calculation model is represented by two masses connected by springs. Optimal damping parameters are determined by minimizing peak displacements in the frequency response of the system under consideration.

Four ways of accounting the damping are considered: hysteresis damping in the structure and the damper spring, equivalent viscous damping in the structure and the damper spring, hysteresis damping in the structure and damper spring and additional viscous damping in the damper spring and setting the damping in proportion to the shape mode energy. It has been established that the type of the model for taking into account the resistance forces significantly affects selecting the optimal parameters of the mass damper and its design efficiency

The aim of the research is to assess the influence of the method accounting damping on the mass damper efficiency and selecting their optimal parameters for seismic impact. Particular attention is paid to the behavior of mass dampers of large mass. The steady-state harmonic oscillations of a damped system with a mass damper are considered. The design model is represented by two masses connected by springs. The mass damper optimal parameters are determined by minimizing the peak displacements on the amplitude-frequency characteristic. Three methods of damping accounting are considered: hysteresis in the structure and damper spring, equivalent viscous in the structure and in the damper spring, as well as hysteresis in the structure and in the damper spring and additional viscous in the damper spring. It has been established that when the mass of the damper is less than 10% of the mass of the protected structure, the method of accounting for energy losses in the structure and in the mass damper spring is not essential. With a damping mass of more than 50% of the structure weight, the method of damping accounting becomes fundamental important. It is noted that for highly damped systems, the efficiency of mass damper is noticeably reduced. Apparently, the ambiguity and inconsistency of recommendations on the damping selection for mass dampers available in the literature is associated with a significant influence of the way system damping is taken into account. It is recommended to consider the damping in the damper spring and in the structure separately. In a structure, damping does not usually exceed 15% of the critical one and the way it is taken into account is not important, but special dampers are used in the damper spring and their consideration must correspond to the actual damper loading diagram.

The results of the paper of Prof. Tan “An improved response spectrum method for non-classically damped systems”, previously published in Bulletin of Earthquake Engineering, are analyzed. It is noted that the paper contains important material which allows one to analyze systems with arbitrary damping. According to the authors, the method of constructing the velocity spectra of damped systems is important for calculating damped systems. The material presented in the paper is a kind of basis for explicitly taking damping into account in regulatory documents. To do this, it is necessary to link the existing regulatory documents with theoretical studies. Relevant proposals are set out in the presented response and are illustrated by an example. At present the most difficult thing is to carefully construct damping equations, in particular, to take account of internal friction in the material