Galerkin-Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures

This work deals with the modeling of nonsmooth vibro-impact motion of a continuous structure against a rigid distributed obstacle. Galerkin's approach is used to approximate the solutions of the governing partial differential equations of the structure, which results in a system of ordinary differential equations (ODEs). When these ODEs are subjected to unilateral constraints and velocity jump conditions, one must use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a computationally demanding task. Ivanov proposed a nonsmooth transformation for a vibro-impacting multi-degree-of-freedom system subjected to a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions; however, he did not explore its application for simulating distributed collisions in spatially continuous structures. We adopt Ivanov's transformation to deal with multiple unilateral constraints in spatially continuous structures. Also, imposing the velocity jump conditions exactly in the modal coordinates is nontrivial and challenging. Therefore, in this work we use a modal-physical transformation to convert the system from modal to physical coordinates on a spatially discretized grid. We then apply Ivanov's transformation on the physical system to simulate the vibro-impact motion of the structure. The developed method is demonstrated by modeling the distributed collision of a nonlinear string against a rigid distributed surface. For validation, we compare our results with the well-known penalty approach

Fluid flow due to collective non-reciprocal motion of symmetrically-beating artificial cilia

Using a magneto-mechanical solid-fluid numerical model for permanently magnetic artificial cilia, we show that the metachronal motion of symmetrically beating cilia establishes a net pressure gradient in the direction of the metachronal wave, which creates a unidirectional flow. The flow generated is characterised as a function of the cilia spacing, the length of the metachronal wave, and a dimensionless parameter that characterises the relative importance of the viscous forces over the elastic forces in the cilia

Surface instabilities in shock loaded granular media

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The initiation and growth of instabilities in granular materials loaded by air shock waves are investigated via shock-tube experiments and numerical calculations. Three types of granular media, dry sand, water-saturated sand and a granular solid comprising PTFE spheres were experimentally investigated by air shock loading slugs of these materials in a transparent shock tube. Under all shock pressures considered here, the free-standing dry sand slugs remained stable while the shock loaded surface of the water-saturated sand slug became unstable resulting in mixing of the shocked air and the granular material. By contrast, the PTFE slugs were stable at low pressures but displayed instabilities similar to the water-saturated sand slugs at higher shock pressures. The distal surfaces of the slugs remained stable under all conditions considered here. Eulerian fluid/solid interaction calculations, with the granular material modelled as a Drucker–Prager solid, reproduced the onset of the instabilities as seen in the experiments to a high level of accuracy. These calculations showed that the shock pressures to initiate instabilities increased with increasing material friction and decreasing yield strain. Moreover, the high Atwood number for this problem implied that fluid/solid interaction effects were small, and the initiation of the instability is adequately captured by directly applying a pressure on the slug surface. Lagrangian calculations with the directly applied pressures demonstrated that the instability was caused by spatial pressure gradients created by initial surface perturbations. Surface instabilities are also shown to exist in shock loaded rear-supported granular slugs: these experiments and calculations are used to infer the velocity that free-standing slugs need to acquire to initiate instabilities on their front surfaces. The results presented here, while in an idealised one-dimensional setting, provide physical understanding of the conditions required to initiate instabilities in a range of situations involving the explosive dispersion of particles

Analytical approach for entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium

The transportation of biological and industrial nanofluids by natural propulsion like cilia movement and self-generated contraction-relaxation of flexible walls has significant applications in numerous emerging technologies. Inspired by multi-disciplinary progress and innovation in this direction, a thermo-fluid mechanical model is proposed to study the entropy generation and convective heat transfer of nanofluids fabricated by the dispersion of single-wall carbon nanotubes (SWCNT) nanoparticles in water as the base fluid. The regime studied comprises heat transfer and steady, viscous, incompressible flow, induced by metachronal wave propulsion due to beating cilia, through a cylindrical tube containing a sparse (i.e. high permeability) homogenous porous medium. The flow is of the creeping type and is restricted under the low Reynolds number and long wavelength approximations. Slip effects at the wall are incorporated and the generalized Darcy drag-force model is utilized to mimic porous media effects. Cilia boundary conditions for velocity components are employed to determine analytical solutions to the resulting non-dimensionalized boundary value problem. The influence of pertinent physical parameters on temperature, axial velocity, pressure rise and pressure gradient, entropy generation function, Bejan number and stream-line distributions are computed numerically. A comparative study between SWCNT nanofluids and pure water is also computed. The computations demonstrate that axial flow is accelerated with increasing slip parameter and Darcy number and is greater for SWCNT- nanofluids than for pure water. Furthermore the size of the bolus for SWCNT-nanofluids is larger than that of the pure water. The study is applicable in designing and fabricating nanoscale and microfluidics devices, artificial cilia and biomimetic micro-pump

Physical hydrodynamic propulsion model study for creeping viscous flow through a ciliated porous tube

The present investigation focuses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed i.e. inertial forces are small compared with viscous forces and therefore very low Reynolds number (Re<<1) is taken into account. The wavelength of metachronal wave is also considered as very large for cilia movement. The physical problem is linearized and exact solutions are developed for the differential equation problem. Mathematica software is used to compute and illustrate numerical results. The influence of slip parameter and Darcy number on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. It is found that with increasing magnitude of slip parameter the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micro-machines in drug delivery

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.Comment: 12 pages, 6 figures, to appear in EPJ

Mechanical properties of Ti-6Al-4V selectively laser melted parts with body-centred-cubic lattices of varying cell size

Significant weight savings in parts can be made through the use of additive manufacture (AM), a process which enables the construction of more complex geometries, such as functionally graded lattices, than can be achieved conventionally. The existing framework describing the mechanical properties of lattices places strong emphasis on one property, the relative density of the repeating cells, but there are other properties to consider if lattices are to be used effectively. In this work, we explore the effects of cell size and number of cells, attempting to construct more complete models for the mechanical performance of lattices. This was achieved by examining the modulus and ultimate tensile strength of latticed tensile specimens with a range of unit cell sizes and fixed relative density. Understanding how these mechanical properties depend upon the lattice design variables is crucial for the development of design tools, such as finite element methods, that deliver the best performance from AM latticed parts. We observed significant reductions in modulus and strength with increasing cell size, and these reductions cannot be explained by increasing strut porosity as has previously been suggested. We obtained power law relationships for the mechanical properties of the latticed specimens as a function of cell size, which are similar in form to the existing laws for the relative density dependence. These can be used to predict the properties of latticed column structures comprised of body-centred-cubic (BCC) cells, and may also be adapted for other part geometries. In addition, we propose a novel way to analyse the tensile modulus data, which considers a relative lattice cell size rather than an absolute size. This may lead to more general models for the mechanical properties of lattice structures, applicable to parts of varying size

Numerical modelling of fluid-structure interaction using fictitious domain method: application towards compressible fluid flow

The interactions between a deformable solid and surrounding fluid are non-linear multiphysics prob- lem that are crucial for the design of many engineering systems. The fictitious domain method is one of the numerical methods to solve FSI problems and has been successfully implemented for FSI problems involving incompressible flows. The objective of the present work is to adopt the fictitious domain method to study fluid-structure interaction problems involving compressible fluids. For this method we are employing Eulerian and Lagrangian finite element formulation for the fluid and solid, respectively, and both bodies are coupled using a Lagrange multiplier. This multiplier allows the solid not to be integral part of the fluid mesh, thus avoiding the need of mesh updating as in case of other numerical methods for FSI problems