Inertia

About: Inertia is a research topic. Over the lifetime, 12006 publications have been published within this topic receiving 164291 citations.

Axial instability of a free-surface front in a partially filled horizontal rotating cylinder

Abstract: We investigate the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis. A simplified model equation for the evolution of the free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity. This equation is solved numerically to determine the base state with no axial variation, and a numerical linear stability analysis is carried out to examine the onset of unstable axial modes. Various computational results are presented for the wavelength of the axial instability. Inertia is found to play an important role in the onset of the instability and the wavelength of the instability λ satisfies the power law λ∼γ1/3, where γ is surface tension. Finally some numerical simulations of the simplified evolution equation are presented to show that they can capture the steady shark-teeth patterns observed in recent experiments [R. E. Johnson, in Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu (Wo...

Seismic bearing capacity of foundation on cohesionless soil

Abstract: The seismic bearing capacity of a strip-surface foundation resting on a Mohr-Coulomb material is evaluated. The upper-bound theorem of the yield design theory is used to obtain an estimate of the ultimate load. The loading parameters consist of a normal and tangential force applied to the foundation and of inertia forces developed within the soil volume. The classical Prandtl-like mechanism is used to show that the reduction in the bearing capacity is mainly caused by the load inclination; the consideration of inertia forces within the soil is only responsible for a decrease in the bearing capacity that is at least an order of magnitude smaller than the one caused by the load inclination. It is therefore concluded that, from a practical engineering standpoint, the soil-inertia forces can be neglected.

The unsteady motion of solid bodies in creeping flows

Abstract: In treating unsteady particle motions in creeping flows, a quasi-steady approximation is often used, which assumes that the particle’s motion is so slow that it is composed of a series of steady states. In each of these states, the fluid is in a steady Stokes flow and the total force and torque on the particle are zero. This paper examines the validity of the quasi-steady method. For simple cases of sedimenting spheres, previous work has shown that neglecting the unsteady forces causes a cumulative error in the trajectory of the spheres. Here we will study the unsteady motion of solid bodies in several morecomplex flows: the rotation of an ellipsoid in a simple shear flow, the sedimentation of two elliptic cylinders and four circular cylinders in a quiescent fluid and the motion of an elliptic cylinder in a Poiseuille flow in a two-dimensional channel. The motion of the fluid is obtained by direct numerical simulation and the motion of the particles is determined by solving their equations of motion with solid inertia taken into account. Solutions with the unsteady inertia of the fluid included or neglected are compared with the quasi-steady solutions. For some flows, the effects of the solid inertia and the unsteady inertia of the fluid are important quantitatively but not qualitatively. In other cases, the character of the particles’ motion is changed. In particular, the unsteady effects tend to suppress the periodic oscillations generated by the quasi-steady approximation. Thus, the results of quasi-steady calculations are never uniformly valid and can be completely misleading. The conditions under which the unsteady effects at small Reynolds numbers are important are explored and the implications for modelling of suspension flows are addressed.

On the response of beams to an arbitrary number of concentrated moving masses

Abstract: A theory describing the response of a beam under an arbitrary number of moving masses is developed. The theory is based on the Fourier technique and shows that, for a simply supported beam, the resonance frequency is lower with no corresponding decrease in maximum amplitude when the inertia is considered.