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A critical, textbook-like review of the generalized modal superposition method of evaluating the dynamic response of nonclassically damped linear systems is presented, which it is hoped will increase the attractiveness of the method to structural engineers and its application in structural engineering practice and research. Special attention is given to identifying the physical significance of the various elements of the solution and to simplifying its implementation. It is shown that the displacements of a nonclassically damped n-degree-of-freedom system may be expressed as a linear combination of the displacements and velocities of n similarly excited single-degree-of-freedom systems, and that once the natural frequencies of vibration of the system have been determined, its response to an arbitrary excitation may be computed with only minimal computational effort beyond that required for the analysis of a classically damped system of the same size. The concepts involved are illustrated by a series of exqmples, and comprehensive numerical data for a three-degree-offreedom system are presented which elucidate the effects of several important parameters. The exact solutions for the system are also compared over a wide range of conditions with those computed approximately considering the system to be classically damped, and the interrelationship of two sets of solutions is discussed.function of time and then combined to yield the response history of the system; and (2) the response spectrum version, in which first the maximum values of the modal responses are determined, usually from the response spectrum applicable to the particular excitation and damping under consideration, and the maximum response of the system is then computed by an appropriate combination of the modal maxima.When damping is of the form specified by Caughey and OKelly,' the natural modes of vibration of the system are real-valued and identical to those of the associated undamped system. Systems satisfying this condition are said to be classically damped, and the modal superposition method for such systems is referred to as the classical modal method.The classical modal method has found widespread application in civil engineering practice because of its conceptual simplicity, ease of application and the insight it provides into the action of the system. The response spectrum variant of the method, which makes it possible to identify and consider only the dominant terms in the solution, is particularly useful for making rapid estimates of maximum response values.Viscously damped systems that do not satisfy the Caughey-OKelly condition generally have complexvalued natural modes. Such systems are said to be non-classically damped, and their response may be evaluated by a generalization of the modal superposition method due to Foss. ' Although well e~tablished,'-~ the generalized modal method has found only limited application in structural engineering practice. Several factors appear to have contributed to this: (a) the generalized method is Bro...

For the past few decades global attention and interest has grown in the application of Ductile Steel Plate Walls (DSPW) for building lateral load resisting systems. Advantages of using DSPWs in a building as lateral force resisting system compromise stable hysteretic characteristics, high plastic energy absorption capacity and enhanced stiffness, strength and ductility. A significant number of experimental and analytical studies have been carried out to establish analysis and design methods for such lateral resisting systems, however, there is still a need for a general analysis and design methodology that not only accounts for the interaction of the plates and the framing system but also can be used to define the yield and ultimate resistance capacity of the DSPW in bending and shear combination. In this paper an analytical model of the DSPW that characterizes the structural capacity in the shear and bending interaction is presented and discussed. This proposed model provides a good understanding of how the different components of the system interact, and is able to properly represent the system's overall hysteretic characteristics. The paper also contributes to better understand the structural capacity of the DPSW and of the shear and bending interaction. The simplicity of the method permits it to be readily incorporated in practical non-linear dynamic analyses of buildings with DSPWs. To demonstrate the effectiveness of the proposed model, its predicted response is compared with results from experimental studies performed by various researchers.