Identification of Non-Transversal Motion Bifurcations of Linkages

The local analysis is an established approach to the study of singularities and mobility of linkages. The key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to distinguish different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

ON TRANSVERSAL VIBRATIONS OF AN AXIALLY MOVING BEAM UNDER INFLUENCE OF VISCOUS DAMPING

In this paper, a transversal vibration of an axially moving beam under the influence of viscous damping has been studied. The axial velocity of the beam is assumed to be positive, constant and small compared to wave-velocity. The beam is moving in a positive horizontal direction between the pair of pulleys and the length between the two pulleys is fixed. From a physical viewpoint, this model describes externally damped transversal motion for a conveyor belt system. The beam is assumed to be externally damped, where there is no restriction on the damping parameter which can be sufficiently large in contrast to much research material. The straightforward expansion method is applied to obtain approximated analytic solutions. It has been shown that the obtained solutions have not been broken out for any parametric values of the small parameter 𝜀. The constructed solutions are uniform and have been damped out. Even though there are several secular terms in the solutions, but they are small compared to damping.

Straightening of light in a one dimensional dilute photonic crystal

Light transport in a dilute photonic crystal is considered. The analytical expression for the transmission coefficient is derived. Straightening of light under certain conditions in a one-dimensional photonic crystal is predicted. Such behavior is caused by the formation of a localized state in transversal motion. The main contribution to the central diffracted wave transmission coefficient is due to states, that either close to the conductance band’s bottom or deeply localized in the forbidden gap. Both these states suppress mobility in the transverse direction and force light to be straightened. Straightening of light in the optical region along with small reflection make these systems very promising for use in solar cells.

The accuracy of estimating time to contact in transversal motion and head-on motion

The ability to estimate precisely the time to contact (TTC) of the objects is necessary for planning actions in dynamic environments. TTC estimation is involved in many everyday activities with different levels of difficulty. Although tracking a ball that moves at a constant speed and estimating the time it reaches a non-moving target can be fairly simple, tracking a fast moving car with inconsistent speeds and estimating the time it reaches another car is rather difficult. In this study, we asked participants to estimate TTC of an object in transversal and head-on motions. The object became invisible shortly after movement initiation. The results demonstrated that TTC estimation for transversal motion is more accurate than for head-on motion. We present a mathematical model to explain why humans are better in estimating TTC for transversal motion than for head-on motion.

Nonlinear Dynamics of a Slender Axially Graded Beam Embedded in a Viscoelastic Medium

In the present contribution the nonlinear dynamics of beams under axial time-dependent excitation is studied. The beams, which are embedded in a linear viscoelastic medium, are assumed as axially graded in terms of material properties. The transversal motion equation is derived under two main hypotheses, namely the beams satisfy the requirements of Euler-Bernoulli theory and undergo moderately large deflections.

Dynamics of Functionally Graded Beams on Viscoelastic Foundation

In the present contribution, the nonlinear dynamics of beams under axial time-dependent excitation is studied. The beams, which rest on a linear viscoelastic foundation, are assumed as axially graded both in terms of geometrical and material properties. The transversal motion equation is derived under two main hypotheses, namely the beams satisfy the requirements of Euler–Bernoulli theory and undergo moderately large deflections (MLDs).

Further Investigations on Vortex Self Induced Vibration (VSIV)

An experimental facility has been designed to study the transversal and response associated with vortex-induced vibration of a totally submerged horizontal cylinder hang on horizontally elastic support under the influence of vertical harmonic oscillating motion. The study aims to analyze the vortex self induced vibration (VSIV) phenomena, which occurs for instance with Steel Catenary Risers (SRCs) the deep offshore connected to floating platforms. These vibrations occur even in the absence of a current. The experiments were conducted in a tank at the LOC/COPPE/UFRJ (Laboratory of Waves and Current of COPPE, Federal University of Rio de Janeiro). The tests were carried out with Keulegan-Carpenter numbers equal to 10 and 20 and for several exciting frequencies. The vertical trajectories of the VSIV motion were then classified based on its different configurations such as oval-shape, eight-shape and etc. Different ranges of reduced velocities were also considered. The amplitude and frequency of transversal motion and also the forces calculated.