scholarly journals Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2162
Author(s):  
Rui Nie ◽  
Tianyun Li ◽  
Xiang Zhu ◽  
Cheng Zhang
Keyword(s):  
Free Surface ◽  
Free Vibration ◽  
Natural Frequency ◽  
Liquid Surface ◽  
Energy Functional ◽  
Calculation Model ◽  
Vibration Characteristics ◽  
Free Liquid Surface ◽  
Immersion Depth ◽  
Infinite Domain

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.

scholarly journals Bulging Modes of Circular Bottom Plates in Rigid Cylindrical Containers Filled with a Liquid

1997 ◽  
Vol 4 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Marco Amabili
Keyword(s):  
Free Surface ◽  
Liquid Surface ◽  
Dynamic Pressure ◽  
Ritz Method ◽  
Free Vibrations ◽  
Free Liquid Surface ◽  
Mode Shapes ◽  
Bottom Plate ◽  
Free Surface Waves ◽  
Theoretical Approaches

In this article the free vibrations of the bottom plate of an otherwise rigid circular cylindrical tank filled with liquid are studied, considering only the bulging modes (when the amplitude of the plate displacement is predominant with respect to that of the free surface). The tank axis is vertical, thus the free liquid surface is orthogonal to the tank axis. The liquid is assumed to be inviscid, and the contribution of the free surface waves to the dynamic pressure on the free liquid surface is neglected. Wet and dry mode shapes of the plate are assumed to be the same, so that the natural frequencies are obtained by using the nondimensionalized added virtual mass incremental (NA VMI) factors and the modal properties of dry plates. This simplifies computations compared to other existing theoretical approaches. NAVMI factors express the nondimensionalized ratio between the reference kinetic energy of the liquid and that of the plate and have the advantage that, due to their nondimensional form, they can be computed once and for all. Numerical results for simply supported and clamped bottom plates, as well as for supported plates with an elastic moment edge constraint are given. For more accurate results, and to exceed the limits of the assumed modes approach, the Rayleigh-Ritz method is applied and results are compared to those obtained by using the NAVMI factors and other existing methods in the literature.

Free Vibration of Initially Stressed Circular Disks

1965 ◽  
Vol 87 (2) ◽  
pp. 258-264 ◽  
Author(s):  
C. D. Mote
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Variable Thickness ◽  
Transverse Vibration ◽  
Fundamental Mode ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Vibration Characteristics ◽  
Initial Stresses ◽  
Circular Disks

The approximate free vibration characteristics of centrally clamped, variable thickness disks are analyzed by the Rayleigh-Ritz technique. Natural frequencies of transverse vibration are computed, taking into consideration rotational and thermal in-plane stresses as well as purposely induced initial stresses. Initial stresses can significantly raise the minimum disk natural frequency throughout a prescribed rotational and thermal environment. The fundamental mode of disk vibration is one of zero nodal circles and either zero, one, or two nodal diameters, depending upon the disk geometry and the rotational-thermal environment.

scholarly journals Analysis of turbulence on cylinder with additional fairing with free surface

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Siqin Chen ◽  
Xiaomin Li
Keyword(s):  
Free Surface ◽  
Drag Coefficient ◽  
Liquid Surface ◽  
Lift Coefficient ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Free Liquid Surface ◽  
Uniform Grid ◽  
Different Depths ◽  
High Reynolds

In this study, two dimensional unsteady flow of cylinder and cylinder with additional fairing close to a free surface was numerically investigated. The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations(SIMPLE). The Volume of Fluid(VOF) method applied to simulate a free surface. Non- uniform grid structures were used in the simulation with denser grids near the cylinder. Under the conditions of Reynolds number 150624, 210874, 210874 and 331373, the cylinders were simulated with different depths of invasion. It was shown that the flow characteristics were influenced by submergence depth and Reynolds numbers. When the cylinder close to the free surface, the drag coefficient, lift coefficient and Strouhal numbers will increase due to the effect of free liquid surface on vortex shedding. With additional fairing, can effectively reduce the influence of the free surface on the drag coefficient. Fairing will reduce lift coefficient at high Reynolds numbers, but increase lift coefficient when Reynolds numbers is small. Fairing can effectively reduce Strouhal numbers, thus can well suppress the vortex induced vibration.

scholarly journals Construction of basic functions for problems of fluid oscillations in a tank

2019 ◽  
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Liquid Surface ◽  
Singular Integral Equations ◽  
Spherical Shape ◽  
Free Liquid Surface ◽  
Surface Shape ◽  
Slight Rise ◽  
Oscillation Frequencies ◽  
The Impact

Considerable number of studies and publications is devoted to issues of dynamic behavior of liquids, the impact on the surface tension of a liquid in partially filled tanks in particular. The study of liquid vibrations in partially fluid-filled cylindrical containers with the presence of a free surface is an important technical task. The influence of the free surface curvature of the tank filler on the oscillation frequency is taken into account. It is assumed that the liquid is incompressible and inviscid, and its motion is irrotational. The method to solve a boundary value problem for determining fluid oscillations in a reservoir has been developed, and an integral presentation of an unknown velocity potential is proposed. The geometrical characteristics of the free liquid surface have been determined. It is taken into account that the free liquid surface deviates from the equilibrium position and assumes a spherical shape. A system of singular integral equations has been obtained for unknown values of the potential and flow. The method of boundary elements with constant approximation of an unknown density on the elements has been used to solve the system numerically. The oscillation frequencies for the zero harmonic are determined in accordance with the level of the free-surface elevation. It has been determined that the deviation of the free surface shape from the flat and even a slight rise in the free surface level leads to noticeable changes in the vibration frequencies. The vibrational modes obtained in the study mostly coincide with the modes for a flat free surface and can serve as the basic system of functions in the studies of free and forced fluid vibrations in tanks, as well as, in the study of the intrinsic and forced sloshing in the reservoirs provided surface tension is taken into account.

scholarly journals Numerical Investigation of the Free Vibration of Partially Clamped Rectangular Plates

2018 ◽  
Vol 23 (2) ◽  
pp. 385-400
Author(s):  
M.A. Gharaibeh ◽  
A.M. Obeidat ◽  
M.H. Obaidat
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Parametric Design ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
The Finite Element Method ◽  
Comprehensive Investigation ◽  
Plate Size

Abstract This paper studies the free vibration characteristics of rectangular plates with partially clamped edges around the corners using the finite element method. ANSYS Parametric Design Language (APDL) was utilized to produce the finite element (FE) models and to run the analysis. The FE models were used to obtain the plate first natural frequency and mode shape. A comprehensive investigation of the effect of the plate geometric parameters and different boundary condition properties on the natural frequency and mode shapes is presented. The results showed that the vibration characteristics of the structure are greatly dependent on the plate size and the constraint properties.

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