Dynamic method

Abstract: The probability density evolution method (PDEM) for dynamic responses analysis of non-linear stochastic structures is proposed. In the method, the dynamic response of non-linear stochastic structures is firstly expressed in a formal solution, which is a function of the random parameters. In this sense, the dynamic responses are mutually uncoupled. A state equation is then constructed in the augmented state space. Based on the principle of preservation of probability, a one-dimensional partial differential equation in terms of the joint probability density function is set up. The numerical solving algorithm, where the Newmark-Beta time-integration algorithm and the finite difference method with Lax–Wendroff difference scheme are brought together, is studied. In the numerical examples, free vibration of a single-degree-of-freedom non-linear conservative system and dynamic responses of an 8-storey shear structure with bilinear hysteretic restoring forces, subjected to harmonic excitation and seismic excitation, respectively, are investigated. The investigations indicate that the probability density functions of dynamic responses of non-linear stochastic structures are usually irregular and far from the well-known distribution types. They exhibit obvious evolution characteristics. The comparisons with the analytical solution and Monte Carlo simulation method demonstrate that the proposed PDEM is of fair accuracy and efficiency. Copyright © 2005 John Wiley & Sons, Ltd.

Abstract: A universal dynamic model of fixed joints is built through considering the relative motion between the sub-structures of the fixed joints and the coupling among various degrees of freedom. The dynamic model may accurately reflect the dynamic characteristics of the joints. Based on the inverse relationship between the frequency response function matrix and the dynamic stiffness matrix of a Multi-Degree-Of-Freedom system, a high-accuracy parameter identification method is proposed to recognize the dynamic model parameters of the joints using the dynamic test data of the whole structure including the joints. The error between the theoretical and experimental results of the model is less than 10%, while the error of the Yoshimura model is three times bigger than that of the model. The effectiveness and accuracy of the dynamic model and its parameter identification have been validated. The establishment of the model will provide a theoretical foundation for the precisely dynamic modeling of the CNC Machine Tool.

Abstract: Determination of the static characteristics of air bearings constitutes the necessary first phase in a design problem, which determines general feasibility. In order to realize a successful application, a good knowledge and assessment of the dynamic behaviour is needed to complement the previous step. In a conventional, passive bearing application, dynamically stable behaviour should be ensured by overcoming the occurrence of self-excited vibrations; the so-called “pneumatic hammering”. In active bearing applications, on the other hand, the dynamic bearing force, induced by actuation of the gap geometry or supply pressure, provides for a means of enhancing bearing static and dynamic performance, when integrated in a mechatronics system context. This paper presents on the one hand an overview of the methods used to model the dynamic characteristics of aerostatic films, deducing that the method of harmonic perturbation is often sufficient in providing a good estimate of the dynamic stiffness. This is confirmed by comparing theoretical results with dynamic response experiments. On the other hand, the general problem of active dynamic compensation is outlined and an application example is provided to show the high levels of performance achievable by employing this method.