Dynamic Response of an Inhomogeneous Elastic Pile in a Multilayered Saturated Soil to Transient Torsional Load

In this paper, we solve the dynamic response of an inhomogeneous elastic pile embedded in a multilayered saturated soil and subjected to a transient torsional load via a semianalytical method. To portray the inhomogeneity of the pile and the stratification of surrounding soil, the pile-soil system is subdivided into Nth layers along the depth direction in view of the variation of shear modulus or cross-sectional dimension of the pile or differences in soil properties. Then, the vibration displacement solution with undermined constants for any saturated soil layer subjected to the time-harmonic torsional load is obtained by virtue of the separation of variables scheme. To establish the connection of adjacent longitudinal soil layers, the circumferential contact traction at the interface of the adjacent layers is treated as the distributed Winkler subgrade model independent of the radial distance. Then, by utilizing the continuity conditions of the pile-soil system and the method of recursion typically used in the transfer function technique, the torsional impedance of the pile top can be derived in the frequency domain. By virtue of inverse Fourier transform and convolution theorem, the velocity response of an inhomogeneous pile subjected to a transient half-sine exciting torque and embedded in a layered saturated soil is gained in the time domain. Finally, selected numerical results are gained to investigate the influence of typical defects in pile and soil layering on the velocity response of the pile top in the time domain.

On the speed and numerical stability of ice-dynamics approximations

<p>The Stokes solution to ice dynamics is computationally expensive, and in many cases unnecessary. Many approximations have been developed that reduce the complexity of the problem and thus reduce computational cost. Most approximations can generally be tuned to give reasonable solutions to ice-dynamics problems, depending on the domain and scale being simulated. However, the inherent numerical stability of time-stepping with different solvers has not been studied in detail. Here we investigate how different approximations lead to limits on the maximum timestep in mass conservation calculations for both idealized and realistic geometries. The ice-sheet models Yelmo and CISM are used to compare the following approximations: the shallow-ice approximation (SIA), the shallow-shelf approximation (SSA), the SIA+SSA approximation (Hybrid) and two variants of the L1L2 solver, namely one that reduces to SIA in the case of no-sliding (dubbed L1L2-SIA here) and the so-called depth-integrated viscosity approximation (DIVA). We find that these approaches vary significantly with respect to numerical stability. The extreme dependence on the local surface gradient of the SIA-based approximations (SIA, Hybrid, L1L2-SIA) leads to an amplified local velocity response and greater potential for instability, especially as grid resolution increases. In contrast, the SSA and DIVA approximations allow for longer time steps, because numerical oscillations in ice thickness are damped with increasing resolution. Given its high fidelity to the Stokes solution and its favorable stability properties, we demonstrate the strong case for using the DIVA approximation in many contexts.</p>

Dynamic Response Near Critical Build Heights in Ultrasonic Additive Manufacturing

Previous ultrasonic additive manufacturing (UAM) models ignore higher-order modes or do not simulate the entire weld cycle when studying the dynamics near critical height-to-width ratios. A multi-modal model was developed to study the dynamics near critical build heights. The cause for the critical height-to-width ratio is dynamic interaction between the substrate and sonotrode. As the build height approaches the critical height-width-ratio, the current model predicts a local maxima in the transverse velocity response directly under the moving load (simulated sonotrode excitation). This is validated by experimental observations from previous studies. However, the current model predicts that as the height is further increased, a maximum in the transverse velocity response occurs at a height-to-width ratio of 1.2 due to resonance of higher-order modes. This result indicates that a single mode-approximation is insufficient to describe the dynamics near critical build heights. In studying the time response for an entire weld cycle (1.5 s), the amplitude of the velocity response in the transverse direction varies greatly. This indicates that assuming a quasi-static or analyzing a short time period in a model excludes potential dynamics during an entire weld cycle (on the order of 1 s).

Experimental and Statistical Validation of Data on Mesh-Coupled Annular Distributor Design for Swirling Fluidized Beds

In this study, velocimetry and statistical analyses were conducted on a swirling fluidized bed. A bed of spherical particles (4 mm) was fluidized by using an annular distributor covered with mesh. The angles of rectangular blades in the distributor were set at 30°, 45°, 60°, 75° and 90°, and the cell size of the mesh cover was 2.5 × 2.5 mm2. The weight was varied from 500 to 1250 g and the effect of each variable on bed velocity response was quantified through velocimetry and statistical analysis. The statistical analysis was conducted using NCSS statistical software. The blade angle, bed weight and superficial velocity for 4 mm particles were statistically optimized at 750 g, 58.26° and 1.45 m/s, respectively. On the experimental side, these parameters have been optimized at 750 g, 60° and 1.41 m/s, respectively. A small difference of 1.74° was noticed in experimental and statistical predictions for the blade angle. The bed weights and superficial velocities were found to be same in both cases. The confidence interval (95%) for bed velocity was proposed in the range of 0.513 to 0.519 m/s. The experimentally optimized bed velocity remained within the proposed range. The well-agreeing results indicate good practical value of distributor design and high precision of the experimental measurements.