Micro/macro-slip damping in beams with frictional contact interface

Friction in contact interfaces of assembled structures is the prime source of nonlinearity and energy dissipation. Determination of the dissipated energy in an assembled structure requires accurate modeling of joint interfaces in stick, micro-slip and macro-slip states. The present paper proposes an analytical model to evaluate frictional energy loss in surface-to-surface contacts. The goal is to develop a continuous contact model capable of predicting the dynamics of friction interface and dissipation energy due to partial slips. To achieve this goal, the governing equations of a frictional contact interface are derived for two distinct contact states of stick and partial slip. A solution procedure to determine stick–slip transition under single-harmonic excitations is derived. The analytical model is verified using experimental vibration test responses performed on a free-frictionally supported beam under lateral loading. The theoretical and experimental responses are compared and the results show good agreements between the two sets of responses.     

Shear and compressional damping effects of constrained layered beams

A theory is formulated for combined shear and compressional damping effects of contrained layered beam structures with complicated cross section areas. The theory is applied to some selected theoretical examples. The calculation results indicate that the loss factor values of these beams are larger over a wider frequency range than could be expected from corresponding shear damping effect only or compressional damping treatment only.     

Optimum distribution of additive damping for vibrating beams

Cost and weight effectiveness of concentrated and distributed additive damping is studied for linear systems (discrete and continuous) under prescribed harmonic loads and/or displacements. Stiffness and mass changes due to additive damping are included. From a numerical example studied it can be concluded that optimal damping distributions can reduce resonant responses by about 40% as compared to uniformly distributed damping of the same cost or weight. The optimization technique as well as an exact displacement method for analysis of harmonically vibrating beams and frames are presented.     

Instability of parametric dynamic systems with non-uniform damping

A unified way of looking at parametric and combination resonances in systems with periodic coefficients and different amounts of damping in the various modes of vibration is presented. The stability boundaries of the coupled Mathieu equations are determined by the harmonic balance method, Fourier series with periods 2T and T being assumed. The basic characteristics of the solution are discussed and the method is applied to multiple-degree-of-freedom dynamic systems. The destabilizing effect on the combination resonances is obtained by the present method.     

Analytical approach for free vibration analysis of two-layer Timoshenko beams with interlayer slip

In this paper, an analytical procedure for free vibrations of shear-deformable two-layer beams with interlayer slip is developed. The effect of transverse shear flexibility of two layers is taken into account in a general way by assuming that each layer behaves as a Timoshenko beam element. Therefore, the layers have independent shear strains that depend indeed on their own shear modulus. This is the main improvement of the proposed model compared to existing models where the transverse shear flexibility is ignored or taken into account in a simplified way in which the shear strains of both layers are assumed to be equal whatever the shear modulus of the layers. In the proposed model, the two layers are connected continuously and the partial interaction is considered by assuming a continuous relationship between the interface shear flow and the corresponding slip. Based on these key assumptions, the governing differential equation of the problem is derived using Hamilton's principle and is analytically solved. The solutions for the eigenfrequencies and eigenmodes of four single span two-layer beams with classical Euler boundary conditions, i.e. pinned-pinned, clamped-clamped, clamped-pinned and clamped-free, are presented. Next, some numerical applications dealing with these four beams are carried out in order to compare the eigenfrequencies obtained with the proposed model against two existing models which consider different kinematic assumptions. Finally, a parametric study is conducted with the aim to investigate the influence of varying material and geometric parameters on the eigenfrequencies, such as shear stiffness of the connectors, span-to-depth ratios, flexural-to-shear moduli ratios and layer shear moduli ratios.     

Dynamic analysis of very flexible beams

The dynamic analysis of flexible beams with large deformations is difficult and few studies have been performed. In this paper, the vibration analysis of several very flexible beams with large deflections using the finite element approach is studied. The examples were a cantilever beam and rotating flexible robot arms. The results were compared with the results available in the published literature. Several successful checks on the finite element results were performed to ensure the accuracy of the solutions. Due to the geometrical nonlinearity, several static equilibrium shapes can exist for large deflections of a cantilever beam for a given load. Nonlinear dynamic finite element analysis was implemented to investigate the stability of these shapes.     

Gilbert damping in the layered antiferromagnet CrCl3

We theoretically and experimentally studied the Gilbert damping evolution of both acoustic and optical magnetic resonance modes in the layered flake Cr Cl;with an external magnetic field H applied in plane.Based on a Lagrangian equation and a Rayleigh dissipation function,we predicted that the resonance linewidth△H as a function of microwave frequencyωis nonlinear for both acoustic and optical modes in the Cr Cl;flake,which is significantly different from the linear relationship of△H-ωin ferromagnets.Measuring the microwave transmission through the Cr Cl;flake,we obtained theω–H dispersion and damping evolution△H–ωfor both acoustic and optical modes.Combining both our theoretical prediction and experimental observations,we concluded that the nonlinear damping evolution△H–ωis a consequence of the interlayer interaction during the antiferromagnetic resonance,and the interlayer Gilbert dissipation plays an important role in the nonlinear damping evolution because of the asymmetry of the non-collinear magnetizaiton between layers.     

Measurement of photocarrier injection efficiencies at the interface in double layered organic photoconductors

Photocarrier injection efficiencies from the carrier generation layer into the transport layer in double-layered photoconductors were measured by using a photoacoustic technique. Photoinjection efficiencies were derived by measuring the decrease in photoacoustic signal when an electric field was applied to the samples. A linear relationship was observed between the logarithm of the photoinjection efficiencies and the square root of the applied electric field. Photocarrier injection efficiencies are limited by a barrier between the carrier generation layer and the carrier transport layer.     

Plasmon beams interaction at interface between metal and dielectric with saturable Kerr nonlinearity

We present a novel theory of surface plasmon polariton interaction on the surface of dielectric with saturable Kerr nonlinearity. The effect of the total internal reflection of a weak signal plasmon beam from a high-power reference beam is discussed. Both ray and wave theories are used to describe signal propagation. The effect of the signal tunneling through the narrow inhomogeneity induced by the reference beam is considered.     

Green's functions of the forced vibration of Timoshenko beams with damping effect

This paper is concerned with the dynamic solutions for forced vibrations of Timoshenko beams in a systematical manner. Damping effects on the vibrations of the beam are taken into consideration by introducing two characteristic parameters. Laplace transform method is applied in the present study and corresponding Green's functions are presented explicitly for beams with various boundaries. The present solutions can be readily reduced to those for others classical beam models by setting corresponding parameters to zero or infinite. Numerical calculations are performed to validate the present solutions and the effects of various important physical parameters are investigated.     

Hydration and distribution of ions at the mica-water interface

Molecular-scale structures of mica surfaces in electrolyte solutions reveal how ion and interfacial hydration control cation adsorption. Key differences are obtained for Rb+and Sr2+ using resonant anomalous x-ray reflectivity: Rb+ adsorbs in a partially hydrated state and incompletely compensates the surface charge, but Sr2+ adsorbs in both fully and partially hydrated states while achieving full charge compensation. These differences are driven by balancing the energy cost of disrupting ion and interface hydration with the electrostatic attraction between the cation and charged surface.     

Complex power distribution analysis in plates covered with passive constrained layer damping patches

The vibration of a plate partially covered with a passive constrained layer damping (PCLD) patch is studied from an energetic point of view. The damped plate is excited by an acoustic plane wave. The study is done with a numerical two-dimensional multilayer plate model. Results of the present model are compared to those obtained with three-dimensional finite element models. It is shown that the present model gives accurate results, even for the layer's inner behavior. It is less expansive in terms of computational cost; hence, it can simulate efficiently the structure for higher frequencies. Mathematical formulas for complex mechanical power are presented, and the link with strain and kinetic energies and dissipated power is detailed. Both local and global complex power balance are established, and corresponding expressions for the discretized problem are formulated. Conservative and dissipative powers are studied for the PCLD damped plate. After a global balance analysis versus frequency, a local study has been carried out in order to quantify the relative contribution of the components of strain and stress tensors to the total strain energy and dissipated power; the individual layer's contributions is also investigated. The in-plane distributions of powers are mapped, showing the location where dissipative phenomenon occurs and where strain energy is stored. Finally, three criteria based on the previous power quantities are proposed in order to quantify the mechanical damping efficiency of the patch.     

Dynamic analysis of multilayered welded aluminum cantilever beams

Welded joints are often used to fabricate assembled structures in machine tools, automotive and many such industries requiring high damping. Vibration suppression in these applications can enhance the dynamic stability significantly. A little amount of work has been reported till date on the damping capacity of welded aluminum structures. The present work outlines the basic formulation for the slip damping mechanism in multilayered and tack welded aluminum beams, vibrating under dynamic conditions. It is observed that there are a number of vital parameters that govern the damping capacity of these structures. The developed damping model is found to be fairly in good agreement with experimental results.     

The damping of structural vibration by rotational slip in joints

Interfacial slip in joints is the major contributor to the inherent damping of most fabricated structures. By fastening joints tightly enough to prohibit translational slip, but not tightly enough to prohibit rotational slip (thereby making only a small sacrifice in static stiffness), it is shown, both experimentally and theoretically, that a useful increase in the inherent damping in a structure can be achieved, provided an optimum joint load is maintained. The analysis is simplified by using a general dynamic analysis computer program with a sub-program to model the friction joint.     

Observation of the lateral displacement of surface acoustic beams reflected at boundaries of layered substrates

The reflection of an acoustic surface wave incident on a velocity discontinuity is studied near the critical angle by using an optical-diffraction probe. The abrupt velocity change is implemented on fused quartz and on single crystal quartz substrates by plating the surface with a prism-shaped gold layer. A lateral displacement of the reflected beam, relative to the mirror-reflection path, is observed. For angles of incidence corresponding to total reflection, the phenomenon exhibits a behaviour which is similar to the Goos-Hänchen effect encountered at the total reflection of bounded electromagnetic waves. However, contrary to the electromagnetic case, it is found here that a significant lateral shift occurs also for angles well into the partial-reflection region and that the reflected beam profile is considerably distorted at the critical angle. These observations may be evidence of a leaky-wave mode along the boundary of the plated area, with the phase-matching condition satisfied at or near the critical angle.     

Excitation of surface wave beams at the interface between linear and nonlinear media

The spatial evolution of quasi-optical electromagnetic-wave beams propagating in the vicinity of an interface between linear and nonlinear media is studied. It is demonstrated that three-dimensional nonlinear surface beams can efficiently be excited by Gaussian beams of optimal shape, incident onto the nonlinear interface at angles exceeding the total internal reflection angle, and that giant nonlinear Goos-Hänchen effect can result from this process.