Function Of Non-dimensional Frequency Research Articles

An improved time domain coupled model of Cross-Flow and In-Line Vortex-Induced Vibration for flexible risers

Vortex-induced vibration (VIV) is a complicated fluid-structure interaction problem. In this paper, an improved time domain coupled model to predict Cross-Flow (CF) and In-Line (IL) VIV of flexible risers is proposed, which can take the effect of added mass coefficient into account. The functions of non-dimensional amplitude and frequency based on the forced vibration experimental data are developed to obtain VIV hydrodynamic forces. The inertia force terms caused by added mass are simplified as functions of non-dimensional frequency. For CF VIV, the non-dimensional frequency with a range of [0.125, 0.20] is deemed to be the excitation region, while the lock-in and allocation criterion of IL VIV includes 2St and 3St two excitation regions. Coupling effect of CF and IL VIV is taken into consideration by integrating a magnification model for the IL excitation force associated with CF response amplitude. The excitation forces, added mass forces and damping forces are time-varied and would be updated in each step. To verify the developed model, two test models of flexible risers under uniform current are simulated. The envelopes of RMS displacement, time histories of strain, response frequency spectra and added mass coefficients show good agreement with the measured data.

Dynamic response of a layered half-space with interfacial cracks

The scattering of elastic waves by interfacial cracks in a layered medium is investigated in this paper. A hybrid numerical method is employed to obtain the solution. This method combines the finite element equations and the Green's function boundary integral representation. Numerical results are presented for the crack-opening displacements (CODs) and the Mode I and Mode II stress-intensity factors (SIFs) as functions of nondimensional frequency when normal and tangential time-harmonic line loads are applied to the free surface of the layered medium.

Lifting-Surface Theory of a Fully Submerged Hydrofoil

Lifting-surface theory of a fully submerged hydrofoil advanced at constant forward speed under the fixed submersion depth is developed, and then the properties of the lift and resistance are discussed in detail in relation with the effect of the Froude number. The disturbing velocity potential is, first of all, derived from the linearized condition on the free water surface. Then, from the boundary condition over the lifting surface, constructed on the Küchemann's conception, a basic integral equation is obtained for the distribution of circulation over the span, from which the lift-curve slope and the sum of the induced and wave-making resistance can be computed readily. This integral equation is solved by DeYoung and Harper's method. Comparisons of theoretical lift and resistance with the experimental data by NASA confirm the appropriateness of the construction of the present theory; and also the effects of the Froude number on the characteristics is definitely clarified. Damping and Inertia Coefficients for a Rolling or Swaying Vertical Strip 1Discussion by W. R. Porter2IN Table 2, of this paper, the author presents values of the damping constant for a vertical strip in horizontal (sway) oscillation for tabular values of nondimensional frequency. In the Addendum, he relates that another table, Table 3, was independently checked and found to vary only by 1 in the fourth decimal place. An unwary person may assume the same to be probably true for Table 2; and, therefore, the misprinted value at frequency 2.000 is hereby reported. The interval in the table at this frequency is sufficiently large that the irregular value may be otherwise undetected. Table 2 Table 3 In addition to correcting the misprint, the table as calculated by the writer at the Computation Center, MIT, presents confirmation that the original Table 2, except at 2.000, varies at most by 1 in the fourth decimal place. This new table provides entry at more closely spaced and more conventional frequencies with digit zero in the third decimal place. The new table also presents the wave-height ratio for convenience. The relation between wave-height ratio and damping constant is mentioned in the Addendum to the paper. To complete the presentation, a graph is shown here for the wave-height ratio for the vertical strip and also for the circular cylinder in horizontal (sway) oscillation as calculated by the writer. Fig. 01Wave-height ratio as a function of nondimensional frequency for vertical strip and circular cylinder in horizontal (sway) oscillation