Vibration of a stiffened pipe filled with a bubbly liquid: analysis of resonance frequencies in function of bubble fraction

The characterization of the presence of bubbles in industrial fluid circuits may be extremely important for many safety issuses. It is well known that the acoustic properties of liquids can be drastically modified by a small amount of gaz content in the liquid. At sufficiently low frequencies, the speed of sound depends primarily on the gas volume fraction. The variation of the gas fraction may then induce some variations in the vibroacoustic behavior of the pipe transporting the liquid. Analysis of the pipe vibrations can then help in the monitoring of the bubble presence. In such a context, the aim of this study is to show how the the presence of bubbles in the liquid could affect the resonance frequencies of the pipe. A numerical vibroacoustical model has been developed to predict the vibroacoustical behavior of a stiffened cylindrical shell filled with a bubbly liquid exhibiting low frequency resonances. The model, experimentally verified with a well-characterized bubbly liquid, is then used to analyse the frequency shifts of the shell resonances in function of the bubble. Keywords : pipe, heavy fluid, numerical modelling, circumferential admittance approach, cylindrical shell, resonance frequency, void fraction

Study on the Axial Compression Postbuckling Similitude Model of the Stiffened Cylindrical Shell with Dimple Imperfections

The body of the new-type dry gas holder is a large stiffened cylindrical shell. Limited by the test site and economic conditions, the buckling characteristics of such holders are generally studied through scale model experiments. Taking the longitudinal-ring rectangular stiffened cylindrical shell as the research object, the generalized similitude condition and scaling principle formula of the structure are derived innovatively based on Donnell’s assumption and the energy method. By means of displacement loading and node coordinates updating, dimple imperfections are introduced into the ideal structure of the stiffened cylindrical shell, and then, the complete similitude and partial similitude analysis of axial compression nonlinear buckling for imperfect structures are carried out. The analysis results show that the complete similitude analysis of stiffened cylindrical shell axial-compression nonlinear buckling can be realized accurately; the partial similitude model for stiffened cylindrical shell axial-compression nonlinear buckling can better predict the buckling characteristics of its prototype structures, and the closer the Poisson’s ratio between the model and the prototype materials is, the more accurate the prediction results are. Meanwhile, the generalized similitude condition and scaling principle formula derived based on the energy method can provide useful reference for the model design and experimental verification of the axial compression buckling of the stiffened cylindrical shell with local geometric imperfections.

Nonlinear Traveling-Wave Vibration of a Ring-Stringer Stiffened Cylindrical Shell

The nonlinear traveling-wave vibration of a ring-stringer stiffened cylindrical shell is analyzed. Using Donnell’s nonlinear shell theory and Lagrange equations, the nonlinear dynamic model of the ring-stringer stiffened cylindrical shell is derived. Galerkin’s method based on multi-mode instead of single-mode approximation is used to discretize the shell’s displacements. Two types of orthogonal circumferential modes with same frequency are used and the interaction between them is considered in the analysis of the shell’s nonlinear traveling-wave vibration. The harmonic balance (HB) method, along with the pseudo-arc length continuation algorithm, is adopted to solve the forced vibration responses of the shell. The stability of the solution is determined by the Floquet theory. Through comparison with the results available in the literature, the correctness of the present nonlinear dynamic model and its solution process are validated first. Next, the mode selection rules are determined through a convergence study. Finally, the nonlinear traveling-wave vibration of the ring-stringer stiffened cylindrical shell is studied. Also, the paper investigates, in detail, the effects of stiffener parameters on the nonlinear dynamic characteristics of the stiffened shell.

Study on the Coupling Frequency of Double-Sided Submerged Ring-Stiffened Cylindrical Shells

Based on the Flügge theory and orthotropic theory, the acoustic vibration coupling model of ring-stiffened cylindrical shell is established by using the wave propagation method and virtual source method. And the effects of water immersion on both sides, free surface, and hydrostatic pressure on the cylindrical shell are considered in the coupling model. Muller three-point iterative method is used to solve the coupling frequency. The calculation results of degradation theory are compared with COMSOL’s calculation results and experimental results, respectively, which verifies the reliability of the theoretical method. Finally, the influence of fluid load, ring rib parameters, boundary conditions, hydrostatic pressure, and free surface on the coupled vibration of ring-stiffened cylindrical shell is analyzed by an example.