Prototype Test and Numerical Analysis of a Shallow Cable with Novel Viscous Inertial Damper

As an essential component of offshore bridges, stay cables are prone to vibrations due to their low inherent damping characteristics. Various dampers have been used for cable vibration control; however, the experimental research and theoretical study of inertial dampers on real cables have not been conducted sufficiently. This study aims to investigate the damping performance of a novel viscous inertial damper (VID) and focuses on the frequency-dependent and displacement amplification phenomena of a cable-damper system. Tests were first conducted to verify the energy consumption capacity of a prototype damper. A shallow cable-VID system was established. Theoretically, complex-valued modes were analyzed to determine the influence of the inertial and viscous coefficients on the cable’s frequency and mode damping ratio. The test results and numerical analysis show that the VID has a good damping effect on the shallow cable. Considering multiple adjacent cable modes, the inertial and viscous coefficients can be optimized. After optimizing, the VID can simultaneously maximize both adjacent symmetric and antisymmetric modes’ damping ratios. The two frequencies are almost the same. The displacement amplification of the VID shows that a VID can overcome the shortcomings of displacement loss caused by traditional oil dampers. The implications of these findings of the VID on shallow cable are discussed, which will guide future research and applications of the VID or other inerter dampers.

In-Situ X-ray Photoelectron Spectroscopy and Raman Microscopy of Roselite Crystals, Ca2(Co2+,Mg)(AsO4)2 2H2O, from the Aghbar Mine, Morocco

Roselite from the Aghbar Mine, Morocco, [Ca2(Co2+,Mg)(AsO4)2 2H2O], was investigated by X-ray Photoelectron and Raman spectroscopy. X-ray Photoelectron Spectroscopy revealed a cobalt to magnesium ratio of 3:1. Magnesium, cobalt and calcium showed single bands associated with unique crystallographic positions. The oxygen 1s spectrum displayed two bands associated with the arsenate group and crystal water. Arsenic 3d exhibited bands with a ratio close to that of the cobalt to magnesium ratio, indicative of the local arsenic environment being sensitive to the substitution of magnesium for cobalt. The Raman arsenate symmetric and antisymmetric modes were all split with the antisymmetric modes observed around 865 and 818 cm−1, while the symmetric modes were found around 980 and 709 cm−1. An overlapping water-libration mode was observed at 709 cm−1. The region at 400–500 cm−1 showed splitting of the arsenate antisymmetric mode with bands at 499, 475, 450 and 425 cm−1. The 300–400 cm−1 region showed the corresponding symmetric bending modes at 377, 353, 336 and 304 cm−1. The bands below 300 cm−1 were assigned to lattice modes.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

The effect of an exterior electric field on the instability of dielectric plates

We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean dielectric plate, we show that a potential difference between the electrodes can induce a thinning of the plate and thus an increase of its planar area, similar to the scenarios encountered when there is no silicone oil. However, we also find that, depending on the material and geometric parameters, an increasing applied voltage can also lead to a thickening of the plate, and thus a shrinking of its area. In that scenario, Hessian instability and wrinkling bifurcation may then occur spontaneously once some critical voltages are reached.

Multiple zero group velocity Lamb modes in an anisotropic plate: propagation along different crystallographic axes

This paper studies the propagation of symmetric and antisymmetric Lamb waves along a 1 mm thick iodic acid plate (HIO3) in the 1–50 MHz frequency range. The Lamb mode propagation along three crystallographic planes was theoretically investigated, for two mutually orthogonal propagation directions. Several frequencies were found that correspond to Lamb modes with zero group velocity (ZGV) and non-null phase velocity values. The first symmetric Lamb mode, S1, was found to possess only one ZGV point, regardless of the propagation direction; higher order symmetric and antisymmetric modes with up to four ZGV points were found, depending on the propagation plane. The dependence of the ZGV frequencies on each elastic constant (c11, c13, c33, c55) of the HIO3 plate material was also investigated by changing the constant values by 5% and 10%. It was found that c33 and c55 affect the number of the ZGV points, while c11 and c13 affect the frequency of the ZGV points. The existence and frequencies of the ZGV points are strongly dependent on the proximity of standing longitudinal and transverse waves at nearby cutoff frequencies.

Cross-flow-type breakdown induced by distributed roughness in the boundary layer of a hypersonic capsule configuration

Direct numerical simulations are undertaken to investigate the nature of instability mechanisms induced by singular and distributed roughnesses on a blunt-capsule configuration. On the base of a capsule-like hemispherical forebody at wind-tunnel conditions ($M=5.9$), we analyse the development of unsteady disturbances behind a patch of two different roughness geometries. First, spanwise periodic roughness elements are considered and cross-validation with other methods of the stability analysis is achieved. Two main unstable modes are found in the roughness wake, corresponding to the symmetric and antisymmetric modes already known for single roughness elements. Second, the case of a patch of (pseudo-)randomly distributed roughness is presented. A new type of roughness-induced cross-flow-like instability is observed for the blunt-capsule configuration. The rapid growth of primary and secondary instabilities in the cross-flow-type vortex is analysed and quantified in both the linear and nonlinear stages up to the laminar–turbulent breakdown. Spatio-temporal Fourier analysis is performed to track the onset of secondary instabilities, whereas laminar–turbulent transition is identified by the steep increase of the wall heat flux.

Dispersion study of plane-strain vibrations in poroelastic solid bars with polygonal cross-section

This paper studies wave propagation in a poroelastic solid bar with polygonal cross-section under plane-strain conditions. The boundary conditions on the surface of the cylinder whose base curve is polygon are satisfied by means of the Fourier expansion collocation method. The frequency equations are discussed for both symmetric and antisymmetric modes in the framework of Biot’s theory of poroelastic solids. For illustration purposes, sandstone saturated materials and bony material are considered. The numerical results were computed as the basis of relevant material data . Phase velocity is computed against the wavenumber for various cross-sections and results are presented graphically.

Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

We introduce a system with one or two amplified nonlinear sites (‘hot spots’, HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied to selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable and unstable when the nonlinearity includes the cubic loss and gain, respectively. If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, whereas weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are also considered.

Dynamics Simulation of a Circular Membrane With an Eccentric Circular Areal Constraint

We investigate the dynamics of a circular membrane with an eccentric circular areal constraint under arbitrary initial conditions. The membrane is assumed to be fixed at its outer boundary and the constraint is assumed to impose zero displacement over a circular area of the membrane. The symmetric and antisymmetric modes of vibration of the membrane are derived and their orthogonality properties are established. Using the orthogonality conditions established in this paper, the complete solution to the constrained vibratory motion of the membrane is determined for arbitrary initial conditions. Two sets of numerical simulation results are presented.