Izuru Takewaki

Optimal damper placement for minimum transfer functions

The purpose of this paper is to propose an efficient and systematic procedure for finding the optimal damper placement to minimize the sum of amplitudes of the transfer functions evaluated at the undamped fundamental natural frequency of a structural system subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper placement is determined based upon those criteria without any indefinite iterative operation. The present procedure can be applied to any structural system so far as it can be modelled with finite-element systems. The present procedure also enables one to treat structural systems with an arbitrary damping system (for example, proportional or non-proportional) in a unified manner. Due to employment of a general dynamical property, i.e. the amplitude of a transfer function, the results are general and are not influenced by characteristics of input motions.

Optimal damper placement for critical excitation

Since earthquake ground motions are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new probabilistic critical excitation method is proposed. Different from the conventional critical excitation methods, a stochastic response index is treated as the objective function to be maximized. The energy (area of power spectral density function) and the intensity (magnitude of power spectral density function) are fixed and the critical excitation is found under these restrictions. It is shown that the resonant characteristic of ground motions can be well represented by the proposed critical excitation. An original steepest direction search algorithm due to the present author is applied to the problem of optimal damper placement in structures subjected to the critical excitation. Closed-form expressions of the inverse of the coefficient matrix (tri-diagonal matrix) enable one to compute the transfer function and its derivative with respect to design variables very efficiently. A numerical example of a 6-DOF shear building model is presented to demonstrate the effectiveness and validity of the present method.

Non-monotonic optimal damper placement via steepest direction search

An efficient and systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a 3-D shear building model. The dynamic compliance is expressed in terms of the transfer function amplitudes of the local interstorey drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper positioning is determined via an original steepest direction search algorithm. This algorithm enables one to find an optimal damper positioning sequentially for gradually increasing damper capacity levels. A non-monotonic design path with respect to the total damper capacity level often appears in the application of this algorithm. A new augmented algorithm via parameter switching is devised to find this non-monotonic design path. Copyright

Effects of support stiffnesses on optimal damper placement for a planar building frame

An efficient and systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a planar building frame. The dynamic compliance is expressed in terms of the transfer function amplitudes of the interstory drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper positioning is determined via an original steepest direction search algorithm. This algorithm enables one to find an optimal damper positioning sequentially for gradually increasing damper levels. The influences of support-member stiffnesses on the response suppression level and on the optimal damper positioning are also disclosed numerically. Copyright

Application of an optimum design method to practical building frames with viscous dampers and hysteretic dampers

An innovative optimum design system for structures with passive-type dampers is proposed. The design system depends on the type of dampers. A realistic application example is presented first of the optimum structural design method to practical building frames with hysteretic dampers. A computer program based on the gradient projection algorithm is used for initial design of a 100 m-high building frame located at Osaka, Japan. The effect of hysteretic dampers is incorporated in the calculation of design horizontal loads. The present method has the flexibility that manual modification by structural designers can be added to the initial design in order to satisfy multiple design conditions specified in the Japanese building structural design codes. Subsequently another practical method is presented for optimum structural design of building frames with viscous dampers. This method is a two-step design procedure. The first step consists of the stiffness design of a reduced shear-building model with viscous dampers. The second step is the optimum design for building frames subjected to static design loads. The design horizontal static loads are determined in the first step. Several design examples are presented to demonstrate the usefulness of the proposed design method.

Optimal placement of viscoelastic dampers and supporting members under variable critical excitations

The concept of performance-based design has recently been introduced and is well accepted in the current structural design practice of buildings. In earthquake-prone countries, the philosophy of earthquake-resistant design to resist ground shaking with sufficient stiffness and strength of a building itself has also been accepted as a relevant structural design concept for many years. On the other hand, a new strategy based on the concept of active and passive structural control has been introduced rather recently in order to provide structural designers with powerful tools for performance-based design.

Stiffness‐damping simultaneous identification using limited earthquake records

A new method of stiffness-damping simultaneous identification of building structures is proposed using limited earthquake records. It is shown that when horizontal accelerations are recorded at the floors just above and below a specific storey in a shear building model, the storey stiffness and the damping ratio can be identified uniquely. The viscous damping coefficient and the linear hysteretic damping ratio can also be identified simultaneously in a numerical model structure. The accuracy of the present identification method is investigated through the actual limited earthquake records in a base-isolated building. It is further shown that an advanced identification technique for mechanical properties of a Maxwell-type model can be developed by combining the present method with a perturbation technique. Copyright

Critical excitation for elastic-plastic structures via statistical equivalent linearization

Abstract Since earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method for single-degree-of-freedom (SDOF) elastic–plastic structures is proposed. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and related simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except elastic–plastic time-history response analysis. Statistical equivalent linearization is utilized to estimate the elastic–plastic stochastic peak responses approximately. The critical excitations are obtained for two examples and compared with the corresponding recorded earthquake ground motions.

An approach to stiffness-damping simultaneous optimization

An approach is proposed to stiffness-damping simultaneous optimization of structural systems. The sum of mean square responses to stationary random excitations is minimized subject to the constraints on total stiffness capacity and total damper capacity. Optimality conditions are derived and a two-step optimization method using the optimality conditions is devised. In the first step, the optimal design is found for a specified set of total stiffness capacity and total damper capacity. In the second step, a series of optimal designs is found with respect to a varied set of total stiffness capacity and total damper capacity. An incremental inverse problem approach proposed by the present author is taken full advantage of. It is shown through numerical examples that the proposed method is efficient and reliable.

Optimal damper positioning in beams for minimum dynamic compliance

Abstract The purpose of this paper is to propose an efficient and systematic procedure for finding the optimal damper positioning to minimize the dynamic compliance of a cantilever beam. The dynamic compliance is expressed in terms of the amplitude of a transfer function of the tip deflection evaluated at one of the undamped natural frequencies. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper positioning is determined via a new steepest direction search algorithm. Due to employment of a general dynamical property, i.e. the amplitude of a transfer function, the results are general and are not influenced by characteristics of disturbances.