Free vibrations of an elastic cylinder in a cross flow and their effects on the near wake

Fluid-structure interactions resulting from the free vibrations of a two-dimensional elastic cylinder in a cross flow are not well understood. Experimental data pertaining to the interaction behavior is rather scarce, especially that related to the phenomenon of synchronization where the vortex shedding frequency is approximately equal to the natural frequency of the fluid-structure system. The present investigation attempts to examine this problem experimentally using a laser vibrometer to assess the bending displacements and a laser Doppler anemometer to measure the velocities in the wake. Experiments were carried out over a range of reduced velocities. The reduced velocity was first varied by using cylinders of different materials and then by changing the free stream velocity, while maintaining the cylinder diameter constant. A proper choice of materials and reduced velocity allowed the synchronization phenomenon to be investigated. For the range of reduced velocity investigated, the vibration amplitude of the cylinder is finite, even at synchronization, and increases with reduced velocity. The results further show that more than one mode of vibration is excited away from synchronization; however, only the first mode is evident at synchronization. In addition, the near-wake flow behind the elastic cylinder, at three different Reynolds numbers in the sub-critical range, was measured in detail and the data was used to analyse the vibration effects on the mean and turbulence field compared to those measured behind a relatively rigid cylinder at the same Reynolds numbers. It is found that cylinder vibrations have little or no effect on the mean drag and the normalized mean field. However, cylinder vibrations enhance turbulent mixing, thus resulting in a substantial increase in the turbulent intensities. This implies that the large-scale vortical motion is also affected. Nevertheless, turbulence structure in the inertial sub-range is not affected by cylinder vibrations. The slopes of the velocity spectra in this range is still measured to be −5/3 for the freely vibrating cylinders investigated. Received: 20 December 1998/Accepted: 20 September 1999     

Finite elastic torsional instability of incompressible thermo-hyperelastic cylinder

Torsional instability of an incompressible thermo-hyperelastic cylindrical rod, subjected to axial stretching and large torsions, is examined within the framework of finite elasticity. When the cylinder is stretched and twisted by a sufficiently large degree, a knot may form suddenly at one point. This inherent elastic instability is analyzed with the minimum potential energy principle and the critical values of torsion are obtained. The distribution of stresses as well as the tensile force and the torque are studied. Effect of temperature change is specifically discussed. The project supported by the National Natural Science Foundation of China (10402018, 10272069) and Shanghai Key Project Program (Y0103) The English text was polished by Keren Wang.     

Forced vibrations of laminated materials with a stochastic structure

S. P. Timoshenko Institute of Mechanics of the Ukrainian Academy of Sciences, Kiev. "Energiya" Scientific-Industrial Association, Moscow. Translated from Prikladnaya Mekhanika, Vol. 30, No. 5, pp. 24–31, May, 1994.     

Non-linear free periodic vibrations of variable stiffness composite laminated plates

Steady-state free vibrations, with large amplitude displacements, of variable stiffness composite laminated plates (VSCL) are analysed. The intentions of this research are: (1)?to find out how the natural frequencies and (mode) shapes evolve with the displacement amplitude in this new type of laminated composite material; (2)?to describe modal interactions in VSCL due to energy interchanges under the coupling induced by non-linearity; (3)?to compare the VSCL with traditional, constant stiffness, laminated plates. The VSCL of interest here have curvilinear fibres and the numerical analysis carried out is based on a recently developed p-version finite element with hierarchic basis functions. The element follows first-order shear deformation theory and considers Von Kármán??s non-linear terms. The time domain equations of motion are first reduced using the linear modes of vibration and then transformed to the frequency domain via the harmonic balance method. These frequency domain equations are solved by an arc-length continuation method.     

Free vibrations of square elastic tubes with a free end

The localized vibrations of a thin-walled square tube with a free end are studied. By means of asymptotic methods, an expression for the natural frequency is found. The asymptotic results agree well with the numerical results obtained using the Finite Element Method. The dependence of the natural frequency on the tube length is analyzed.     

Asymmetric vibrations of an elastic sphere

Historically, the vector Navier equation governing the dynamic response of an elastic, homogeneous, isotropic sphere has been solved using the Helmholtz decomposition of the displacement vector. Further, many of the problems in the literature have been restricted to ones involving axisymmetric geometry. In this presentation, the time-dependent Navier equation is solved using a set of vector spherical harmonics which, previously, has been used primarily in quantum mechanics studies but which seems particularly useful in solving asymmetric problems with nonconservative body forces. Expressions for the displacements, strains, and stresses and a discussion of the vibrations of an elastic sphere are given.Part of the material presented here was developed while the author was on a Developmental Leave at the University of Texas at Austin.