In this study, through novel drift-based equations of motion in the frequency domain, optimum placement and characteristics of linear velocity-dependent dampers are investigated. In this study, the sum of the square o...In this study, through novel drift-based equations of motion in the frequency domain, optimum placement and characteristics of linear velocity-dependent dampers are investigated. In this study, the sum of the square of the absolute values of transfer matrix elements for interstory drifts is considered as the optimization index. Optimum placement and characteristics of dampers are simultaneously obtained by minimizing the optimization index through an incremental procedure. In each step of the procedure, a predefined value is considered as the damper characteristic. The optimum story for this increment is selected such that it leads to a minimum value for the optimization index. The procedure is repeated for the next increments until the optimization index meets its target value, which is obtained according to the desired damping ratio for the overall structure. In other words, the desired overall damping ratio is the input to the proposed procedure, and the optimal placement and characteristics of the dampers are its output. It is observed that the optimal placement of a velocitydependent damper depends on the damping coefficient of the added damper, frequency of the excitation, and distribution of the mass, stiffness, and inherent damping of the main structure.展开更多
The authors would like to thank the discusser for his considerations and comments. The discusser believes that some of the derived formulations need to be referred to his previously published works and also some relat...The authors would like to thank the discusser for his considerations and comments. The discusser believes that some of the derived formulations need to be referred to his previously published works and also some related studies have not been cited.展开更多
The authors presented an interesting aspect in viscous or visco-elastic damper optimization under earthquake excitation. They also reviewed the research development in the field of passive damper optimization.
It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsform...It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.展开更多
In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane unde...In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane under the sole influence of gravity;our current investigation is its natural extension. As shown in [1] even for the simplest case where gravity is the only acting external agent literature overlooked reveling the characteristics of the envelope such as its arc-length, the surface area of the enclosed surface and etc. Calculation leading to these has carried out mostly longhand [1]. The current extended version embodies a realistic scenario where the projectiles in addition to gravity encounter linear velocity-dependent media resistance. In order to fulfil objectives similar to [1], we develop two distinct strategies obtaining the analytic equation for the envelope. On one hand, we solve the equations of motion applying traditional longhand approach. On the other hand, we adopt a Computer Algebra System (CAS), e.g. <em>Mathematica</em> [2] [3]. Having these outputs at hand, via mixed-mode calculation—some longhand and some via CAS—we explore its global geometric characteristics such as its arc-length, the surface area of the enclosure. Because of the calculation complexities we could not have achieved our set goals.展开更多
基金National Natural Science Foundation of China Under Grant No.50638010the Foundation of Ministry of Education for Innovation Group Under Grant No.IRT0518
文摘In this study, through novel drift-based equations of motion in the frequency domain, optimum placement and characteristics of linear velocity-dependent dampers are investigated. In this study, the sum of the square of the absolute values of transfer matrix elements for interstory drifts is considered as the optimization index. Optimum placement and characteristics of dampers are simultaneously obtained by minimizing the optimization index through an incremental procedure. In each step of the procedure, a predefined value is considered as the damper characteristic. The optimum story for this increment is selected such that it leads to a minimum value for the optimization index. The procedure is repeated for the next increments until the optimization index meets its target value, which is obtained according to the desired damping ratio for the overall structure. In other words, the desired overall damping ratio is the input to the proposed procedure, and the optimal placement and characteristics of the dampers are its output. It is observed that the optimal placement of a velocitydependent damper depends on the damping coefficient of the added damper, frequency of the excitation, and distribution of the mass, stiffness, and inherent damping of the main structure.
文摘The authors would like to thank the discusser for his considerations and comments. The discusser believes that some of the derived formulations need to be referred to his previously published works and also some related studies have not been cited.
文摘The authors presented an interesting aspect in viscous or visco-elastic damper optimization under earthquake excitation. They also reviewed the research development in the field of passive damper optimization.
文摘It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.
文摘In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane under the sole influence of gravity;our current investigation is its natural extension. As shown in [1] even for the simplest case where gravity is the only acting external agent literature overlooked reveling the characteristics of the envelope such as its arc-length, the surface area of the enclosed surface and etc. Calculation leading to these has carried out mostly longhand [1]. The current extended version embodies a realistic scenario where the projectiles in addition to gravity encounter linear velocity-dependent media resistance. In order to fulfil objectives similar to [1], we develop two distinct strategies obtaining the analytic equation for the envelope. On one hand, we solve the equations of motion applying traditional longhand approach. On the other hand, we adopt a Computer Algebra System (CAS), e.g. <em>Mathematica</em> [2] [3]. Having these outputs at hand, via mixed-mode calculation—some longhand and some via CAS—we explore its global geometric characteristics such as its arc-length, the surface area of the enclosure. Because of the calculation complexities we could not have achieved our set goals.
