The damped mass-spring model is often employed for the dynamic modeling and vibration analysis of aerostatic bearing systems by taking the air film as equivalent springs. However, the stiffness and damping of the air film are frequency-dependent, making the commonly used approach of taking static stiffness or fixed value as the spring coefficient no longer applicable for a bearing subject to a complex external force containing different frequencies. To address this issue, this paper develops the damped mass-spring model for the aerostatic thrust bearing considering the frequency-varying stiffness and damping by means of the linear superposition method. It indicates that the air bearing is still a linear system despite the frequency-dependent character of dynamic coefficients because the bearing vibration satisfies the superposition principle. The improved dynamic modeling approach is able to accurately and efficiently predict the overall dynamic response of the thrust plate when the it is subjected to a multi-frequency vibration. In solving the overall dynamic response, the stiffness and damping associated with the responses of the transient part and steady part correspond to the natural vibration frequency and external disturbance frequencies, respectively. The feasibility and accuracy of the improved modeling approach are partly or completely verified by the direct trajectory calculation method, the CFD dynamic mesh simulation and a modal test. The proposed modeling method provides an effective way for the vibration analysis of air bearings, and in the meantime avoids the possible numerical errors caused by the traditional modeling approach.
The development of artillery in Europe at the end of the Middle Ages brought a necessary change in military architecture. This change was a radical rethinking of the entire geometry and architectural design of city walls which required an increase in thickness to resist repeated artillery strikes. The damage due to the impact loads on Middle Age fortification walls is analyzed herein with explicit dynamic analyses. This study was developed both with finite element models and an innovative rigid body-spring model with diagonal springs (RBSM), showing the different peculiarities of these two different approaches and how their results can be integrated. The numerical models clearly showed that the presence of an inner core of softer material tends to modify the impact effects by reducing the degree of damage at the expense of an extension of the damaged area.
Polymer solutions under shear flow are often observed in manufacturing processes. Classically, polymer behavior is represented by Kuhn’s bead-spring model, in which only the elongation of polymer chains is assumed. In recent years, the compression of polymer chains under shear flow has been reported. In this study, we investigated the behavior of polymer chains dissolved in various concentrations under shear flow. We measured the time variation of the fluorescence intensity emitted from a FRET (fluorescence resonance energy transfer) polymer, which enabled us to study the change in the distance between both ends of a polymer chain. The polymer chains appeared to stretch and compress depending on the concentration of the polymer solution. The results showed that the deformation of polymer chains was different from the classical theory. The FRET measurement is a promising diagnostic method for understanding the dynamics of polymer chains.
As a complementary way to traditional wave-equation-based forward modeling methods, lattice spring model (LSM) is introduced into seismology for wavefield modeling owing to its remarkable stability, high-calculation accuracy, and flexibility in choosing simulation meshes, and so forth. The LSM simulates seismic-wave propagation from a micromechanics perspective, thus enjoying comprehensive characterization of elastic dynamics in complex media. Incorporating an absorbing boundary condition (ABC) is necessary for wavefield modeling to avoid the artificial reflections caused by truncated boundaries. To the best of our knowledge, the perfectly matched layer (PML) method has been a routine ABC in the wave-equation-based numerical modeling of wave physics. However, it has not been used in the nonwave-equation-based LSM simulations. In this work, we want to apply PML to LSM to attenuate the boundary reflections. We divide the whole simulation region into PML region and inner region, PML region surrounds the inner region. To incorporate PML to LSM, we establish elastic-wave equations corresponding to LSM. The simulation in the PML region is conducted using the established wave equations and the simulation in the inner region is conducted using LSM. Three simulation examples show that the PML scheme is effective and outperforms Gaussian ABC.