Secondary Subsystems Research Articles

Stochastic response of combined primary‐secondary structures under seismic input

AbstractA technique for non‐stationary stochastic analysis of linear combined primary and secondary subsystems subjected to a zero‐mean Gaussian base excitation is presented. The proposed technique, based on the use of the Taylor's expansion in evaluating the operators which appear in the step‐by‐step procedure, does not require the evaluation of the complex eigenproperties of the combined system. Operating in this way, even though the numerical procedure is a conditionally stable one, appears to be more efficient than existing methods to evaluate the dynamic response of such composite systems. It is also shown that the proposed procedure is available whether the seismic input is idealized as a filtered white noise or it is defined by means of its autocorrelation function.

Combined dynamic response of primary and multiply connected cascaded secondary subsystems

AbstractA method is proposed for the deterministic and stochastic non‐stationary analysis of linear composite systems with cascaded secondary subsystems subjected to a seismic input. This method makes it possible to evaluate, by means of a unitary formulation, the deterministic and non‐stationary stochastic response of both classically and non‐classically damped subsystems and of secondary subsystems multiply supported on the primary one, as well as the ground. The proposed procedure is very efficient from a computational point of view, because of the Kronecker algebra systematically employed. Indeed, by using this algebra, it is possible to obtain in a very compact and elegant form the eigenproperties of the composite system as a function of the eigenproperties of the two subsystems taken separately. Moreover, it is possible to write the first order differential equations governing the evolution of the second order moments of the response and to solve them in a simple way.

Effect of damping on the predicted seismic response of tertiary subsystems

Many factors affect the seismic response of a structural system. A study was carried out to determine the effect of different combinations of damping on the predicted response of secondary and tertiary subsystems. To simplify the results and to allow for easier interpretation, two- and three-degree-of-freedom structural systems were investigated. The study involved determining the "best estimate" seismic responses for 12 historic earthquake time histories and comparing them to the predicted responses obtained by using two simplified methods of analysis which have been in common use. Curves have been developed which specify the expected average error for the simplified methods by mass ratio(s) and damping. These results provide an overview as to the ranges of parameters where upper level interaction and nonproportional damping effects are significant. Key words: nonproportional damping, complex modal analysis, dynamic, seismic, equipment, tertiary subsystems.

Floor response spectrum method for seismic analysis of multiply supported secondary systems

AbstractFundamental principles from structural dynamics, theory of random processes and perturbation techniques are used to develop a new method for seismic analysis of multiply supported secondary subsystems, such as piping attached to primary structures. The method provides a decoupled analysis of the secondary subsystem wherein the response is given in terms of response spectra associated with the attachment points (‘floors’). In order to account for correlations between modal responses and between support motions, an extension of the conventional floor response spectrum, denoted crossoscillator, cross‐floor response spectrum, is introduced. Important effects of tuning, interaction, non‐classical damping and spatial coupling, which are inherent characteristics of combined primary–secondary systems, are included through the extended spectra. An efficient method for generation of the extended spectra directly in terms of a ground response spectrum is developed.Numerical comparisons with exact results are used to examine the accuracy of the proposed method and to demonstrate the importance of the characteristics mentioned above. In all cases examined, the proposed method shows excellent agreement with exact results. By accounting for the effect of interaction, the proposed method leads to more realistic and economical design criteria for secondary subsystems.

Earth Orbital Mission Requirements for Secondary Propulsion Systems and Their Impact on Colloid Systems

This paper develops the earth synchronous orbital mission requirements for secondary propulsion subsystems (SPS) involving positioning of satellites in orbit and station keeping when in position. It also discusses the orbital requirements associated with attitude control and touches on the requirements for SPS pulsing, thrust vector alignment, and thrust vector control. After developing the earth-orbital mission requirements for SPS, the implications of using low-thrust colloid SPS are discussed. Conclusions are then presented regarding use of colloid, SPS for synchronous earth-orbital operations.