Asymmetric and axisymmetric vibrations of finite transversely isotropic circular cylinders

This paper presents an approach for obtaining the exact frequency equations of axisymmetric and asymmetric free vibrations of transversely isotropic circular cylinders. The solution method is based on the three dimensional theory of linear elasticity and uses potential functions. Using this approach, the frequency spectra and vibration mode shapes are plotted for a number of transversely isotropic cylinders. The proposed approach introduces a number of merits compared to earlier approximate and exact solution methods. First, unlike numerically complicated series methods that provide approximate solutions, the proposed approach is exact. Second, combination of scalar functions employed for representing the displacement field is consistent with the physics of the problem. One scalar potential function has been considered for each component of the wave field inside the elastic cylinder. As a result, the solution is systematically divided into coupled and decoupled equations. In addition, by using this approach, there is no need to guess the final of the solution a priori. These merits make the proposed approach suitable for other vibration problems of anisotropic materials.     

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage. Supported by the National Natural Science Foundation of China (Grant No. 10532070), the Knowledge Innovation Program of Chinese Academy of Sciences (Grant No. KJCX2-YW-L07), and the LNM Initial Funding for Young Investigators     

A new single surface integral equation for light scattering by circular dielectric cylinders

A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the property of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown function for circular dielectric-coated cylinders. In addition, numerical simulations show that even applied to elliptic scatters our equation still gives reasonably good approximate solutions in the sub-wavelength limit.     

Elastic vibrations in thick hollow cylinders

The problem of vibrations in an infinite hollow cylinder deformed by pressures in the interior and exterior cylindrical surfaces, is solved by means of the integral transforms theory.     

Some new results for the multidimensional Landau-Lifshitz equations

In this Letter, we study the multidimensional Landau-Lifshitz equations for two cases of external magnetic fields depending on both time and position, and obtain some new interesting results. For the strong degenerate Landau-Lifshitz equation, we obtain a new blow up solution.     

Finite element analysis of the axisymmetric vibrations of cylinders

A finite element analysis is developed for finite and infinite solid or hollow cylinders in axisymmetric vibration. The elements themselves are solid or annular cylinders, and have 16 degrees of freedom. Results are given for the propagation constants of solid and hollow infinite cylinders, and excellent agreement is found with those from the exact Pochhammer theory and Mindlin and McNiven's three-mode theory. Frequency spectra are presented for the symmetric and antisymmetric modes of solid and hollow finite rods. Excellent agreement is found with experimental results, and this suggests that some of the results obtained from the three-mode theory by McNiven et al., and in particular the frequency of the end mode, are in error by more than 10%. Details of the finite element inertia and stiffness matrices appear in an appendix.     

In-plane vibrations of circular rings

Except in a few cases rings have been treated one-dimensionally as curved beams in analyses to determine their frequencies of vibration. Consequently, for thick rings there are large discrepancies between theoretical and experimental results. In this paper an analysis is carried out in which account is taken of the warping of the cross section. The displacement v in the circumferential direction is assumed to be of the form v₀ + v₁y + v₃y³ + v₅y⁵, where the v_i are functions of the angular co-ordinate θ. The frequencies of free vibration are determined by using the principle of minimum total potential energy. Numerical calculations are made for a ring of rectangular cross section. Results are in good agreement with experimental ones.     

Resonance frequencies of finite circular cylinders

Reference is made to a 1971 paper by Rumerman and Raynor in which the free vibration of finite circular cylinders was treated by expanding the displacement fields in terms of the pure axial and radial modes of the infinite cylinder.     

Free vibrations of circular cylindrical shells

The finite element method is used to predict the dynamic behaviour of circular cylindrical shells in free vibrations. A suitable shape function for the circumferential displacement distribution has been proposed. This reduces the three-dimensional character of the problem to a two-dimensional one. The simultaneous iteration method to determine the eigen-frequencies and eigenvectors is utilised for solving the eigenvalue problem. The accuracy of the method has been checked by verifying the results of known cases. Finally an experimental shell structure containing elastic rings welded at the ends has also been analysed and the experimental results compared with the theoretical ones.     

Water entry of stripe-coated hydrophobic circular cylinders

Abstract  

This paper visually demonstrates water entry of horizontal hydrophobic circular cylinders, 12 mm in diameter and 300 mm long, by three types of coating of a water-repellent material; (a) perfectly coated, (b) right half surface coated, and (c) stripe coated. After the entry of the cylinder into water, the hydrophobic surface of the cylinder forms an air cavity behind it, whereas the hydrophilic surface is perfectly wetted. As a result, the resulting cavities are found to independently grow and break off from the cylinder even for the Type (c).     

Natural frequencies of free finite-length circular cylinders

Sets of tables are given for the natural frequencies of the first five symmetric and first five antisymmetric modes of a hollow or solid cylinder for circumferential wave numbers n = 0, 1, 2. Contour graphs are given for the lowest frequencies as functions of (length)/(mean radius) and (thickness)/(mean radius).     

Polarizability of two parallel conducting circular cylinders

We give exact results for the polarizabilities, longitudinal and transverse, of two parallel cylinders of the same radius. The expressions are infinite sums, which converge rapidly if the cylinders are separated by a radius or more. In close approach the sums converge slowly, but are replaced by equivalent integral expressions, which give simple analytical results in this limit. The contact values of the longitudinal and transverse polarizabilities are π²/6 and π²/12 times the large-separation values. The longitudinal contact value is approached infinitely rapidly as the separation tends to zero, while the approach of the transverse polarizability to its contact value is regular.     

Errors in shell finite element models for the vibration of circular cylinders

Four commonly used shell theories, membrane, thin, thick and proportional theories, are compared with an accurate triangular torus cubic finite element method in their ability to predict the natural frequencies and mode shapes of infinite and free-free finite length solid and hollow circular cylinders. In the computation each shell theory is replaced by a finite element approximation which satisfies the same basic assumptions as the shell theory. Error curves are given for the first two axial-shear, torsional-shear and radial-stretch modes of infinite cylinders. Error contours are given for the first symmetric and first antisymmetric mode of cylinders for circumferential wave numbers n = 0, 1, 2.     

Guided waves in a circular duct containing an assembly of circular cylinders

This paper provides an analytical scheme to calculate the admissible acoustic propagation modes of fluid in a circular duct containing an assembly of circular cylinders, as might occur in gas-cooled fast breeder reactors and advanced gas-cooled reactors. The duct wall and cylinders are assumed to be stationary, and their axes are assumed to be parallel to each other. The solution to the acoustic wave equation is expressed in a sum of the partial fluid velocity potentials associated with each rod co-ordinate and duct co-ordinate. The technique of transformation of cylindrical wave functions is then used to solve the boundary value problem. Two kinds of acoustic boundary conditions are considered, acoustically hard and acoustically soft, respectively.     

Free vibrations of elastic circular toroidal shells

In this paper, the free vibrations of elastic in vacuo circular toroidal shells under different boundary conditions are studied using the linear Sanders thin shell theory. Beam functions are used to describe the motion along the meridional direction whilst trigonometric functions are used to represent the deformation of the cross section. It is shown that both the natural frequencies and the mode shapes can be accurately predicted as long as the employed beam functions satisfy the boundary conditions at the ends of the shells. The dependence of the free vibration characteristics of an elastic toroidal shell upon boundary conditions and toroidal to cross-sectional radius ratio is also illustrated and explained in this paper.     

Free vibration of circular cylinders of variable thickness

Flexural vibrations of finite length circular cylinders with shear diaphragm ends and symmetric circumferential wall thickness variations are described by using the Rayleigh-Ritz method. Both symmetric and asymmetric solutions are presented. Only circumferential variations in the wall radial dimension are considered; the method is amenable, however, to consideration of longitudinal variations in wall thickness as well. The cylinder wall thickness variation is described as a Fourier series and the vibration is described as a series of modes of a uniform cylinder with the same mean radius. The theory has been applied to a cylinder whose inner bore is circular but is non-concentric with the circular outer surface. The mode shapes have been investigated experimentally by using time-averaged holograms of the vibrating cylinder and the results compare well with the predictions of the theory. The frequencies of the modes agree with the theoretical predictions to within 2%.