Journal of Engineering Mechanics

Different continuous‐time approaches have been proposed in recent years to formulate active control algorithms to reduce the response of civil engineering structures under dynamic excitations. In this paper, a general formulation of a new discrete‐time control methodology is presented and applied to structural control. This methodology, based on the concept of predictive control, is discussed and compared to the optimal control methodology by means of numerical examples.

Identification problems on dynamic parameters of a running load and beam system were investigated, using the EK‐WGI method, which is a weighted global iteration procedure incorporated with the extended Kalman filter. By suitably formulating a set of state vector equations and observation equations for the system on which this method was applied, dynamic parameters of both the running load and the beam were identified with high accuracy, where numerically simulated data were used as observation waves so that accuracy and convergency of estimated parameters might be examined.

Dealing with the issues of response variability for statically determinate structures, this study analyzes the response variability in two cases in which the spectral density function of the stochastic field takes limiting shapes. In these limiting cases, the spectral density, having a constant total area, concentrates sharply around the origin in one case and spreads thinly throughout in the other. Also, the present study derives the upper and lower bounds on the response variability. These results provide important physical as well as numerical insight into the response variability issue, whether we solve the problem by exact or numerical integration of equations of equilibrium or motion, or by other numerical methods. It is rather difficult to estimate experimentally the autocorrelation or spectral density function for the stochastic variation of material properties. In view of this, the upper bound results are particularly important, since the bounds derived here do not require knowledge of the autocorrelation function.

The propagation of axisymmetric transients in a rod, governed by the Mindlin‐McNiven theory, is treated by the method of wave‐front expansion. The transients are due to impulsive‐end loading specified in the form of stress, strain, velocity, or acceleration boundary conditions. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variable and its derivatives. These discontinuities are determined from a set of recurrence relations, which are in turn generated using time‐harmonic asymptotic series solutions to the equations of motion. Discontinuities of all orders are determined and the transient solution obtained as a series expansion behind the wave front. The entire solution procedure has been programmed and requires a minimum of input data. Numerical examples are presented to illustrate the method and the results are discussed. Distortion of the transient waves is clearly seen from the results where axial force, strain, velocity, and acceleration responses are presented.

The problem of a simple harmonic oscillator under parametric and nonhomogeneous random excitation is investigated. The governing differential equation is recast as an integral equation, and the solution is taken to be in the form of an infinite sum. The specific case considered here assumes stiffness and force to be modeled as stationary, Gaussian, nonwhite random processes. An iterative solution scheme is set up, and a symbolic manipulation code MACSYMA is used to generate the first three nonzero terms in the series. Approximate expressions are derived for the mean value and spectral density of the oscillator response. In order to obtain some measures for the validity of the method, a Monte Carlo simulation is performed. An important conclusion is that a one‐term “correction” can provide a good measure of the effect of system randomness on output statistics. In a companion paper (5), these methods are used to derive exact closed‐form solutions for the case where the system parameter is a white‐noise process. This fact, that an exact solution is possible for white‐noise parameters, will be very useful in those instances where the physical processes can be reasonably approximated as white noise. To the best knowledge of the writers, this extensive analytical/numerical simulation study has not appeared in the literature.

The results of a companion paper (1) are extended here for the case of white‐noise parameters. The problem is that of a harmonic oscillator with random force. These random processes are assumed to be stationary and Gaussian. The cases considered are: (1) In the limit as the correlation functions approach a delta function and thus the processes have white spectra; (2) where an iterative method is applied to the white‐noise case; and (3) where a noniterative, direct method is applied to the white‐noise problem. It is shown that white‐noise results can be obtained directly from the previous analysis using a limiting procedure. In addition, an exact solution is obtained using iterative and noniterative methods. This permits a simple error analysis by comparing the results of a truncated series with those of the exact solution. Qualitatively, it is possible to say that the better the white‐noise spectra approximates the physical processes, the more accurate will be the truncated solution of Ref. 1.

Trefftz's method is applied to study the vertical vibration of a rigid rectangular plate of infinite length resting on an elastic half‐space. The problem is formulated as one of diffraction of elastic waves. The method consists in using c‐complete or T‐complete (T after Trefftz) families of solutions of the governing equations in the medium to construct the diffracted displacement fields as linear combinations of such solutions. Coefficients are obtained from the treatment of boundary conditions using a collocation least‐square scheme. The relationship between the vertical contact force applied to the plate and vertical displacement is given in terms of a complex stiffness that depends on the frequency. Numerical values are given for different Poisson's ratios. They are compared with those obtained by an analytical method.

To describe the response of concrete under combined thermal and mechanical action it is necessary to abandon the usual assumption that thermal strain and mechanical strain can be treated as mutually independent, additive components. A generalized model which accounts for the thermomechanical interaction observed in tests is discussed. The basic feature of the formulation is that the thermal strain rate is considered to be a function of both rate of temperature change and the current state of stress. The problems dealt with in the paper are of great practical interest in the design of concrete structures exposed to severe thermal loading.

A beam theory which accounts for cross‐sectional warping caused by transverse shearing is presented. A stress resultant theory is formulated for elastic beams, and examples are provided to assess the effects of warping restraint. The ideas are extended to the case of elastoplastic warping. A numerical formulation for the analysis of the inelastic problem is presented and examples of elastoplastic warping are given.

A probabilistic model for length effect in long continuous components is proposed that is based upon the presence of manufacturing defects. This model, as well as some traditional serial weakest link models, are compared with high replication life data taken at eight different increasing lengths.

The C-shaped spring is a planar, very flexible elastic beam, the center axis of which is, in an undeformed configuration, i.e., a part of a circle. Its free ends are subjected to point loads of constant direction. This note presents essentials of a deformation and stability study of the C-shaped springs of various initial shapes, and comments upon results.