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The structural model is typical of single or multistory buildings with floor, ceiling, or wall-supported equipment assemblies. Attention is especially focused on the random properties of the earthquake environment and structural response. The method is applied to the problem of protecting industrial equipment in the vicinity of an active fault. When compared to conventional earthquake design and deterministic methods of analysis, the advantages of this approach are: (1) The random properties of the ground motion are analyzed at all earthquake intensity levels; (2) the results reflect the location, protection level, and service life of the building; (3) earthquake damage cost, protection cost, and reliability are important design factors; and (4) cost-effective and optimal design configurations are disclosed.

Based upon the concept of infinite impulse trains, the paper introduces a physically realizable stochastic model defined as an impulse process. This model allows the random amplitudes to be correlated. The input-output dynamics of linear filtering of the impulse process is investigated and the response spectral density, correlation and variance functions are derived and their behavior closely examined. Time series modelings by spectral and correlation approaches are described and digitally simulated samples for the impulse process and its response are presented. The analysis indicates that the impulse process and its filtered response process are very flexible and may be used to model a large class of random phenomena in engineering physics. The results of the analysis are also described with emphasis on their application in earthquake simulations.

Presented are analytic results of study on site properties and their use in ground-motion prediction and simulation. Spectral simulations of random-type ground motions based on modal contributions are formulated. Linear filters representing ground transfer characteristics of seismic stations are investigated. Single-mode and two-mode stochastic models are developed to permit prediction of random-type ground motions and the induced response statistics of structures. From the viewpoint of stochastic simulation, the autocorrelation function or the power spectral density function derived from the recorded accelerogram can be used to characterize the specific ground motion. By matching the power spectral density function of an existing ground-motion record to that of the appropriate output of a linear single- (or multi-) degree-of-freedom system subject to white noise, the predominant modal ground frequencies and dampings can be determined.

A simple approach using a Fast Fourier Transform (FFT) algorithm for obtaining the transient structural response to earthquakes is presented. Two different foundation models are used, a rigid circular plate and a rigid two-dimensional strip bonded to the elastic soil half space. A numerical procedure is used to obtain all pertinent transfer functions which are subsequently used in conjunction with FFT subroutines to obtain the response time histories. It is shown that over a range of scaled wave numbers which characterize the soil properties, significant base rocking can be expected only when either the slenderness parameter or the mass-ratio parameter is small. The specific advantages of the new approach are: (1) it is computational efficient; (2) it can take into account the frequency-dependent interaction forces; and (3) it is general, readily adaptable in practical applications, and can be used with any linear structure or interaction model.

An approach to the time-varying spectral analysis for shock and vibration data is presented. The approach follows and extends Page’s concept of instantaneous power spectra. Various input-output relations for simple linear systems are derived. The error involved in the evaluation of the time-varying spectra of the response and conditions that reduce it are discussed in some detail. Numerical spectra and energy distribution function of four shock functions are provided and their significance is discussed.

A stationary, Gaussian random process, having a prescribed nonuniform power spectral density function determined by a special simulation procedure which realizes the local site geology is used to analyze the response statistics of nonlinear yield type structures subjected to earthquake excitations. The structures investigated are single-mode oscillators covering long and short periods, high and low viscous dampings, and having history-dependent and -independent interanal energy dissipation mechanisms as represented respectively by stiffness degrading and ordinary elasto-plastic models. Emphasis of the analysis is placed on the probability distribution of the single highest displacement (SHD) response of structures and the accumulation of damages caused by consecutive earthquake loadings.