Journal of Engineering Mechanics

Probability density functions, mean crossing rates, and other descriptors are developed for the response of linear systems to squares of Gaussian excitations. The analysis is based on discrete approximations of the spectrum of the Gaussian excitation. Accordingly, the response can be expressed as a finite quadratic form in Gaussian variables, whose characteristic function has a closed form. The characteristic function can be inverted by Fast Fourier Transform algorithms to find the first order probability of the response. Several approximations are applied to determine crossing and peak characteristics of the response. The proposed methodology is applied to estimate structural response to wind loads and the mean failure rate of systems subjected to bivariate Gaussian stress processes.

The antiplane response of a rigid semicircular cylinder embedded in a homogeneous, isotropic half space due to a step function incident stress is considered. A Fourier synthesis technique is used, in which the admittance function is obtained from the corresponding steady state solution. The influence of the angle of incidence and the mass of the cylinder on the interfacial stresses are examined. The studies carried out indicate that for cylinders with a mass density larger than that of the surrounding half space, the interfacial stresses at the first point of contact between the nonvertically incident stress wave and the cylinder attain their maximum value not at the initial moment of impact but at some later time. A cylinder with a higher mass density would develop a higher maximum stress and take a longer time to reach this maximum stress. The angular distribution of shear stress at different times are also examined.

Random vibration of rotating machines subjected to seismic excitations is analyzed in which the six‐component earthquake ground motions are modeled as nonstationary random processes. The six‐component earthquake inputs including the rotational components of base excitations, result in not only nonhomogeneous excitations but also parametric excitations. Thus, the classical spectral analysis of random vibration is not applicable. Furthermore, both nonhomogeneous and parametric random excitations are correlated random processes, making the problem even more difficult to solve analytically. To date random vibration of such a complicated problem has not been investigated. The method of Monte Carlo simulation is used to simulate the six‐component nonstationary earthquake ground motions and to determine the statistics of the response of rotating machines. The significance of seismic base rotations on the overall structural response is examined. A numerical example is worked out to demonstrate the methodology employed.

This paper discusses the fracture processes of concrete and fiber reinforced cementitious composites with special focus on the development of the fracture process zone with respect to the stress‐separation constitutive relation of such materials. The suggestion is that the overall mechanical behavior of a concrete or FRC structure could be strongly influenced by the stress‐separation constitutive relation, which in turn could be altered by engineering the microstructure of the material, especially in FRC. The process zone length is found not be a material property, but depends on the geometry of the specimen and the loading configurations. All these results are shown explicitly by a simple numerical model of a center‐cracked panel subject to remote edge loading or to wedge loading on the crack faces. These calculations also provide further understanding to the validity of certain failure criteria.

The method of singular surfaces was used in a recent paper to develop a numerical procedure for calculating the growth and decay of the amplitude of shock waves propagating into a one‐dimensional nonlinearly elastic body. Here we extend this approach to estimate the influence of such external effects as elastic support and viscous friction on the propagation of shocks. We conclude that even in the case of a homogeneous linearly elastic material these external effects account for some attenuation of the amplitude of the shock and/or the secondary waves. Further analysis of a nonlinear elastic material readily shows that an increase in the viscosity produces, among other things, a slower growth of the shock amplitude and that for some critical value it will even start with a decay. Numerical examples illustrate the applicability of the technique in the case of a homogeneous nonlinear elastic body subjected to external viscous friction.

The elastic nonlocal moduli are first determined from an auxiliary problem involving longitudinal waves in an infinite nonlocal medium. A comparison of the dispersion equation obtained with that derived in the lattice dynamics of Born and von Kármán is made. Constitutive equations of Kroener and Eringen are introduced, and an extended Euler-Bernoulli approach is used in combination with the Rayleigh-Timoshenko corrections. The field equations obtained represent a system of two coupled difference-differential equations for the displacements of the beam generated by bending and shear. A solution of the system provides the frequency equation of the problem discussed in some detail in the cases of purely flexural waves and of flexural waves with the effect of rotation. In the limit of long waves the nonlocal approach furnishes the classical results. In the short wave limit the results: (1) Do not diverge too drastically from the predictions of the lattice dynamics; (2) enable one to study the domain of short waves, a task outside the possibilities of the classical theory; and (3) help to circumvent the classical paradox of an infinite velocity of short waves.

A framework is developed within which linguistic assessments of seismic loads and structural damage can be assigned fuzzy set representations. This involves a set of rules in the form of a language organized in an algorithmic manner. Factors that affect the function of language elements are discussed and the use of the language is shown in an example. It is concluded that the developed framework enables linguistic assessments about seismic loads and associated structural damage to be concisely and consistently represented in terms of fuzzy sets.

A simple formula, valid over a wide range of systems, that can easily be used during preliminary design stages to estimate the maximum dynamic response of light equipment in structures subjected to impact or ground shock is presented. The formula is developed by smoothly matching results for the response at or near tuning to those at gross deturning. The derived results are compared to results from a Newmark time marching scheme. Excellent correlation is achieved for all systems considered.