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

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

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

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

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

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

Fluid-structure interaction of three-dimensional magnetic artificial cilia

A numerical model is developed to analyse the interaction of artificial cilia with the surrounding fluid in a three-dimensional setting in the limit of vanishing fluid inertia forces. The cilia are modelled using finite shell elements and the fluid is modelled using a boundary element approach. The coupling between both models is performed by imposing no-slip boundary conditions on the surface of the cilia. The performance of the model is verified using various reference problems available in the literature. The model is used to simulate the fluid flow due to magnetically actuated artificial cilia. The results show that narrow and closely spaced cilia create the largest flow, that metachronal waves along the width of the cilia create a significant flow in the direction of the cilia width and that the recovery stroke in the case of the out-of-plane actuation of the cilia strongly depends on the cilia width

The Empirical Study of Relationship Marketing in Maritime Transportation Service

[[abstract]]Maritime transportation is one of the most important services in the international trade, especially for international cargo transportation. Literature reviews extract several components of trust and commitment for study. Theoretical foundations are drawn from the commitment-trust theory of relationship marketing to find out the key factor, the relationship result of cooperation. A conceptual model of business to business (B2B) is established to address new Key Mediating Variables (KMV) paradigm of the relationship marketing in maritime transportation service. Research findings reveal that (1) cognition-based and affect-based trusts are positively related to both normative and affective commitment respectively, but are negatively related to continuance commitment. The result infers that some moderated variables might exist; (2) perceived cognition-based and affect-based trusts are the fundamental factors of inter-organizational cooperative intention. Theoretical and managerial implications together with limitations and future suggestions for research are also discussed in the conclusion