International Journal of Structural Stability and Dynamics

This paper presents the new type of head loading the columns, comprising of elements making a side surface of circular cylinders. It demonstrates a constructional solution of forcing and receiving heads, as well as theoretical considerations related to the determination of boundary conditions, taking into account the loading of needle rolling bearings or rigid elements in the loading heads. Results of experimental investigations of the free vibration of columns having various constructions of receiving heads were presented. In the case of columns for which rigid elements were installed in the receiving heads, the rigidity of equivalent rotational spring is determined, which takes into account the rigidity of the free end of the column caused by sliding friction existing in the loading head elements. The value of critical force and the course of the natural frequency against external load for given geometry and physical constants of the column are determined.

This paper uses a recently developed technique, known as the differential transformation, to determine the critical buckling load of axially compressed heavy columns of various support conditions. In solving the problem, it is shown that the differential transformation technique converts the governing differential equation into an algebraic recursive equation, which must be solved together with the differential transformation of the boundary conditions. Although a fairly large number of terms are required for convergence of the solution, the differential transformation method is nonetheless efficient and fairly easy to implement. The method is also shown to be very accurate when compared with a known analytical solution. The stability of heavy columns is further examined using approximate formulae currently available in the literature. In this case, the differential transformation method offers a reference for assessing the accuracy of the approximate buckling formulae.

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

The frequency of vibration of thick-walled toroidal shells is studied using a finite element formulation wherein the finite element is derived directly in toroidal coordinates. Hexagonal crystals of thallium and cadmium are used as representative transversely isotropic materials. The shell is assumed to be transversely isotropic with respect to the toroidal radial direction, and results based on that assumption are contrasted to a shell that is transversely isotropic with respect to the circumferential toroidal coordinate. It is established that an analysis based on a toroidal coordinate system is superior to an axisymmetric coordinate system and has some advantages over a commercial finite element code. Tables of results are presented that compare frequency of vibration for the above mentioned transversely isotropic materials and isotropic materials.

This paper supports quick and accurate prediction of the flutter onset speed of an F-16 Block 40/50 configured with external stores in the transonic flight regime. Current flutter prediction methods are reviewed and hypothesized mechanisms for limit cycle oscillation (LCO) are summarized. New efforts to correlate transonic small disturbance (TSD) theory methods with flight tests are outlined. Vibration analysis and structural optimization of an F-16 finite element model were used to match ground vibration testing results. Frequency tuning was found to be critical for accurate flutter speed predictions. Sensitivity to nonlinear aerodynamic effects and store modeling was examined.

The constrained viscoelastic layer damping treatment is an effective means for the passive vibration control of plate and beam-kind structures. In order to reduce the treatment cost, while minimizing structural modifications, particularly the increase in mass, constrained viscoelastic treatments can be successfully applied in a partial and localized manner. The effectiveness of these treatments depends on their extension and relative location with respect to the target mode shape, which is not usually expeditiously established. In order to minimize the cost of the numerical optimization of the partial treatments, an efficient numerical methodology based on the ratio between the modal strain energy of the treated area and that of the structure is hereby proposed. This method is used in the analysis of the location and extension effects of partial constrained viscoelastic treatments on the modal damping of thin plates. The numerical results are verified through an experimental study on specimens with partial constrained viscoelastic layer damping treatments.

The deflection, bending moment, shear force and acceleration-time histories of a two-span beam subjected to moving sprung vehicles are presented. The vehicle model is a 2DOF system with a constant velocity. The two-span beam with a rough surface is used as structure model. The beam is defined in modal domain by natural frequencies, mode shapes and modal damping values. The rough surface is modeled by filtered white noise. The equations of motion for the coupled vehicle-structure system are formulated, for non-dimensionalized variables in the system equation. The first-order linear stochastic differential equations are solved, and the effects of the span passage rate and other important parameters are studied.

This technical note aims to clarify the influence of numerical time integration schemes (such as the Newmark method) on the eigenfrequency of the system. With a straightforward analysis of three consecutive time instants it is shown that the eigenfrequency of the time-discretized system is different from the eigenfrequency of the original (continuous) system, and that this frequency shift depends on the magnitude of the applied time step. As such, it affects both free and forced vibrations. In particular, for the analysis of forced vibrations at resonance the excitation frequency must be matched with the eigenfrequency of the time-discretized system rather than the eigenfrequency of the system prior to time discretization.