Simulating the fluid forces and fluid-elastic instabilities of a clamped–clamped cylinder in turbulent axial flow

In this paper, the fluid forces and the dynamics of a flexible clamped–clamped cylinder in turbulent axial flow are computed numerically. In the presented numerical model, there is no need to tune parameters for each specific case or to obtain coefficients from experiments. The results are compared with the dynamics measured in experiments available in the literature. The specific case studied here consists of a silicone cylinder mounted in axial water flow. Computationally it is found that the cylinder loses stability first by buckling. The threshold for buckling is in quantitative agreement with experimental results and weakly nonlinear theory. At higher flow speed a fluttering motion is predicted, in agreement with experimental results. It is also shown that even a small misalignment between the flow and the structure can have a significant impact on the dynamical behavior. To provide insight in the results of these fluid–structure interaction simulations, forces are computed on rigid inclined and curved cylinders, showing the existence of two different flow regimes. Furthermore it is shown that the inlet turbulence state has a non-negligible effect on these forces and thus on the dynamics of the cylinder.     

Vibrations of Pinned–Pinned Heterogeneous Circular Beams Subjected to a Radial Force at the Crown Point

This article is concerned with the vibrations of heterogeneous circular beams under the assumption that the load of the beam is a dead one and is perpendicular to the centerline. It is assumed that (a) the radius of curvature is constant and (b) Young's modulus and the Poisson ratio depend on the cross-sectional coordinates. We have the following objectives: (1) to determine the Green function matrix for pinned–pinned beams provided that the beam is subjected to a radial load; (2) to develop such a numerical model which makes it possible to determine how the natural frequencies are related to a central concentrated load. We present some computational results in graphical format.     

Complex dynamics in physical pendulum equation with suspension axis vibrations

The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.     

Numerical Study of a Forced Pendulum with Friction

We first describe the model of a forced pendulum with viscousdamping and Coulomb friction. Then we show that a unique local solutionof the mathematically well-posed problem exists. An adapted numericalscheme is built. Attention is devoted to the study of the nonlinearbehaviour of a pendulum via a numerical scheme with small constant timesteps. We describe the global behaviour of the free and forcedoscillations of the pendulum due to friction. We show that chaoticbehaviour occurs when friction is not too large. Lyapunov exponents arecomputed and a Melnikov relation is obtained as a limit of regularisedCoulomb friction. For larger friction, asymptotic behaviour correspondsto equilibrium.     

Vibrations of polygonal plates with various boundary conditions

The bending vibrations of polygonal (L-shaped) plates with different shapes and boundary conditions are studied. The natural frequencies are calculated using the inverse-iteration and Kantorovich-Vlasov methods. To take the configuration of the domain into account, the fictitious domain method and an analog of the force method of structural mechanics are used. Different trends in the dependence of the lowest natural frequency of an L-shaped plate on its geometry are illustrated for different boundary conditions.Acorrelation between the extreme values of the bending frequency and some relations for the energy characteristics of the plate is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 63–72, May 2007.     

Interpretation of the Resonance Raman Spectra of Tetraphenylporphin Metal Complexes

Normal coordinate analyses have been carried out for D_4h models of tetraphenylporphin molecule and its deuterated analogs. The assignment of resonance Raman active modes of tetraphenylporphin metal complexes and their deuterated derivatives is given.     

Cartesian Dynamics of Simple Molecules III Non-Linear Triatomics (C2v Symmetry)

A simple spring model for the molecular vibrations of non-linear triatomic molecules with C_2v symmetry is described in terms of Cartesian co-ordinates. Analytical expressions for the stretching and bending mode frequencies are obtained and compared with previous derivations. Optimized values of force constants are calculated for models involving two or three adjustable parameters. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. The model provides a simple explanation of the near degeneracy of the symmetric and asymmetric stretching frequencies of H₂S and H₂Se.     

Cartesian Dynamics of Simple Molecules II Non-Centrosymmetric Linear Triatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to non-centrosymmetric linear triatomic molecules. Analytical expressions for the stretching and bending mode frequencies are obtained, which are equivalent to those derived by conventional methods. For most molecules, the effects of the interaction between the outside atoms are shown to be negligible, but for N₂O, complex solutions are obtained unless this is included. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. For N₂O, frequency shifts resulting from isotopic substitution are explained by reference to the calculated eigenvectors.