The stability and natural vibration of a standing tapered vertical column under its own weight are studied.Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for...The stability and natural vibration of a standing tapered vertical column under its own weight are studied.Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column.For vibrations we use an accurate,efficient initial value numerical method for the first three frequencies.Four kinds of columns with linear taper are considered.Both the taper and the cross section shape of the column have large influences on the vibration frequencies.It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency.Vibrations may occur in two different planes.展开更多
The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experie...The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experienced by the core fluid.It is found that Naviers condition does not hold for an unsteady core fluid.展开更多
The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow ...The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.展开更多
A heated triangular cylinder is suddenly cooled in a constant temperature bath.The transient heat conduction problem is transformed to the Helmholtz equation related to the vibration of membranes.Using the membrane an...A heated triangular cylinder is suddenly cooled in a constant temperature bath.The transient heat conduction problem is transformed to the Helmholtz equation related to the vibration of membranes.Using the membrane analogy,exact analytic solutions for the transient heat conduction problem for three triangular cross sections are found.展开更多
文摘The stability and natural vibration of a standing tapered vertical column under its own weight are studied.Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column.For vibrations we use an accurate,efficient initial value numerical method for the first three frequencies.Four kinds of columns with linear taper are considered.Both the taper and the cross section shape of the column have large influences on the vibration frequencies.It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency.Vibrations may occur in two different planes.
文摘The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experienced by the core fluid.It is found that Naviers condition does not hold for an unsteady core fluid.
文摘The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.
文摘A heated triangular cylinder is suddenly cooled in a constant temperature bath.The transient heat conduction problem is transformed to the Helmholtz equation related to the vibration of membranes.Using the membrane analogy,exact analytic solutions for the transient heat conduction problem for three triangular cross sections are found.
