Journal of Engineering Mechanics

A method for analyzing the free vibration of combined linear undamped dynamical systems attached at discrete points is shown. The method uses separation of variables to exhibit the harmonic motion of the system and to derive a generalized differential equation for the normal modes. Green's functions for the vibrating component systems are used to solve the generalized differential equation and derive the characteristic equation for the natural frequencies of the system. The characteristic equation can then be solved for the exact natural frequencies and exact normal modes. The method is demonstrated for two types of dynamical systems involving beams and oscillators. For two particular systems, approximate natural frequencies determined through a Galerkin's method and the finite element method are compared to the exact natural frequencies. The generalized orthogonality relation for each system is derived.

A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam‐oscillator systems presented earlier by the writers is extended to viscously damped plate‐oscillator systems. The natural modes are expressed in terms of the Green's function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate‐oscillator system, provided the Green's function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.

A thermo‐elastic problem is analyzed for an infinite plate with a kinked crack, which occurs from an end of a linear initial crack. The plate is subjected to a uniform heat flow in an arbitrary direction. The rational mapping function of a sum of fractional expressions, thermal dislocation and the complex variable method are used in the analysis. A closed solution is obtained for the shape represented by the rational mapping function. Distributions of heat flow, temperature and stress, the stress intensity factor and singularity of heat flow are investigated, both before and after the occurrence of a kinked crack.

The spline finite strip method was developed recently as a complement to the semi‐analytical finite strip method in dealing with problems involving mixed boundary conditions, concentrated loads, and continuous spans. In this paper, the spline strip method is further extended to the analysis of arbitrary shaped general plates. The versatility and accuracy of the method are amply demonstrated through a number of numerical examples.

A two‐dimensional turbulent boundary layer flow at a low Reynolds number has been produced in a long and wide flume using rounded gravels of four different sizes. Instantaneous velocity components in the mean flow and vertical directions have been measured. Turbulent parameters (turbulent intensities, Reynolds stresses, skin friction, shape factor and the length scale), along with mean velocity profile, energy spectra and bursting events, have been determined. The results have been compared, whenever possible, with those obtained from wind tunnel experiments.

The present‐day electronic technology has made availability of a large volume of monitoring data for large projects a reality. However, such data automatically contain random noise which only when eliminated provide a reliable set of data depicting the site conditions. This paper presents a method, based on digital signal processing principles, to optimize elimination of noise from such data. The method is based on simple applications of digital signal processing techniques. The method of application is explained through an actual case study and concludes with possible application of such methods in geotechnical and structural monitoring.

A comprehensive framework is set forth for the analysis of structural reliability under incomplete probability information. Under stipulated requirements of consistency, invariance, operability, and simplicity, a method is developed to incorporate in the reliability analysis incomplete probability information on random variables, including moments, bounds, marginal distributions, and partial joint distributions. The method is consistent with the philosophy of Ditlevsen's generalized reliability index and complements existing second‐moment and full‐distribution structural reliability theories.

A computer oriented “exact” method of solution is presented for the bending problem of orthotopic rectangular plates. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could be subjected to any combination of patch, uniform, line, and concentrated loads. The plate is divided into strips whose number depends on the type and number of loads. The solution for the deflection of each plate strip is expressed as a Levy type single Fourier series, and the loads are expressed as a corresponding series. The advantage of the analytical strip method is that it overcomes the limitations of the previous “exact” methods (Navier's and Levy's), it is easy to program on a computer, and it provides an alternative to numerical, semi‐numerical, and other approximate methods. Results are presented for isotropic and orthotropic plates with different loading and boundary conditions.

Measurements of spatio-temporal pressure fluctuations on the windward and leeward faces of a typical tall building model exposed to simulated suburban flow conditions are reported. These results are utilized to examine the validity of often-used strip and quasi-steady theories in the formulation of alongwind aerydynamic loads on tall buildings. The comparison suggests that despite some individual shortcomings of the above theories, the overall load description is quite satisfactory.