Identification of Iwan distribution density function in frictional contacts

Mechanical contacts affect structural responses, causing localized nonlinear variations in the stiffness and damping. The physical behaviors of contact interfaces are quite complicated and almost impossible to model at the micro-scale. In order to establish a meaningful understanding of the friction effects and to predict the contact behavior, a robust parametric friction model is usually employed. This paper employs an Iwan-type model to predict the nonlinear effects of a frictional contact interface. The Iwan model is characterized by its distribution density function which is commonly identified by double differentiation of the experimentally obtained joint interface restoring force. Direct measurement of restoring forces at the contact interface is impractical and estimating it using an inverse approach introduces considerable uncertainties in identification of the density function. This paper develops a more reliable procedure in identification of the Iwan model by relating the density function to the joint interface dissipated energy. The energy dissipated in a contact interface is easily obtained from measurement and it is shown that the dissipation is uniquely defined using the density function and the vibration amplitude. In an experimental case study Iwan distribution density function in a frictional contact is obtained using measured dissipations at different vibration levels.     

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.     

A mode-based approach for the mid-frequency vibration analysis of coupled long- and short-wavelength structures

A mode-based approach is described for the mid-frequency vibration analysis of a complex structure built-up from a long-wavelength source and a short-wavelength receiver. The source and the receiver respectively have low and high modal densities and modal overlaps. Each substructure is described in terms of its uncoupled, free-interface natural modes. The interface forces and displacements are decomposed in terms of a set of interface basis functions. Enforcing equilibrium and continuity conditions along the interface hence yields an analytical solution for the vibration response of the built-up structure. Expressions for the frequency response of the source and the power transmitted to the receiver are found. The correlations between the modal properties of the source and the receiver along the interface are derived. These modify the dynamic stiffness matrix of the structure. The flexible receiver is seen to add effective mass and damping to the source. The modes of the short-wavelength receiver are then described statistically in terms of a simple standing wave model. This approximation avoids the need for a modal analysis of the receiver. The results are compared with those of other methods including fuzzy structure theory. Numerical and experimental examples for beam-stiffened plate models are presented.     

A model for the characterization of friction contacts in turbine blades

Stresses produced by the forced vibrations can lead to a significant reduction of the life of turbo engine blades. To predict the vibration amplitudes of this components an accurate dynamic analysis is necessary. The forced response calculation of these dynamic systems is strongly affected by the presence of the contact interfaces (i.e., underplatform dampers, shrouds, root joints). Different contact models are available in literature. These models make use of contact parameters, contact stiffness and friction coefficient to evaluate the damping and stiffness related to the contact interfaces. In this paper a model is proposed to characterize friction contact of non-spherical contact geometries obeying the Coulomb friction law with constant friction coefficient and constant normal load. The hysteresis curves of the oscillating tangential contact forces vs. relative tangential displacements and the dissipated energy at the contact are obtained for different contact geometries. The developed model is suitable to be implemented in numerical solvers for the calculation of the forced response of turbine blades with embedded friction contacts.     

Interface energy of semicoherent metal-ceramic interfaces

An ab initio based approach to determine energies and structures for semicoherent interfaces is developed and applied to the Fe(001)/VN(001) system. To account for elastic displacements resulting from the lattice misfit, we compare an atomistic approach using a model potential (embedded-atom method) with a continuum approach using the Peierls-Nabarro model. The total interface energy of the atomistic modeling is found to be well reproduced by the Peierls-Nabarro model, demonstrating that accurate interface energies of semicoherent interfaces can be obtained by combining first principles for the chemical part of the energy and a Peierls-Nabarro model to account for the elasticity of the media.     

Ellipsoidal particles at fluid interfaces

For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface-mediated interactions of capillary and fluctuation-induced type are analyzed. For contact angles different from 90( degrees ) , static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer-sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation-induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three-phase contact line, the asymptotic behavior of the fluctuation-induced force is determined analytically for both the close-distance and the long-distance regime and compared to numerical solutions.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.     

Dynamic analysis of slip damping in clamped layered beams with non-uniform pressure distribution at the interface

Slip damping is a mechanism exploited for dissipating noise and vibration energy in aerodynamic and machine structures. Such slip in layered structures can be simulated by applying pressure to hold the members together at the interface. However, while most analyses of the mechanism assume an environment of uniform pressure at the interface, experiments to date have confirmed that this is rarely the case. There have been recent attempts to relax the restriction of uniform interface pressure to allow for more realistic pressure profiles that are encountered in practice. However, such works have mostly been limited to static loading for which it has been established that the interfacial pressure gradient does play a dominant role in modulating the level of energy dissipation. This paper is an attempt to extend such analyses to account for cases of realistic dynamic loading that drive such structural vibration in the first instance. In particular, it is shown that under dynamic loads, frequency variation more than non-uniformity in the interface pressure can have significant effect on both the energy dissipation and the logarithmic damping decrement associated with the mechanism of slip damping in such layered structures.     

Vibration modeling of structural fuzzy with continuous boundary

From experiments it is well known that the vibration response of a main structure with many attached substructures often shows more damping than structural losses in the components can account for. In practice, these substructures, which are not attached in an entirely rigid manner, behave like a multitude of different sprung masses each strongly resisting any motion of the main structure (master) at their base antiresonance. The "theory of structural fuzzy" is intended for modeling such high damping. In the present article the theory of fuzzy structures is briefly outlined and a method of modeling fuzzy substructures examined. This is done by new derivations and physical interpretations are provided. Further, the method is extended and simplified by introducing a simple deterministic approach to determine the boundary impedance of the structural fuzzy. By using this new approach, the damping effect of the fuzzy with spatial memory is demonstrated by numerical simulations of a main beam structure with fuzzy attachments. It is shown that the introduction of spatial memory reduces the damping effect of the fuzzy and in certain cases the damping effect may even be eliminated completely.     

Interface stress effect tuning and enhancing the energy dissipation of staggered nanocomposites

ABSTRACT

Natural biological composites and artificial biomimetic staggered composites with nanoscale internal structures can exhibit extraordinary energy dissipation, compared with conventional composites. It is believed that the interface stress effects of the interfaces between hard platelets and a viscous matrix play an important role in the extraordinary damping properties of such nanocomposites. In this study, a viscoelastic model is established to investigate the mechanism of the influence that the interface stress effect has on the damping properties, based on the Gurtin-Murdoch interface model and the tension-shear chain model. An explicit analytical solution of the effective dynamic moduli characterising the damping properties is obtained by using the correspondence principle, which is also validated by comparison with a finite element analysis. From the obtained analytical solution, an interface factor is abstracted to characterise the synergistic effect of the feature size and material parameters on the damping properties. Based on the model established, the optimal size of the platelets and the optimal loading frequency can be designed to achieve superior energy dissipation, when the staggered nanocomposites bear the dynamic load. Therefore, the findings of the present study not only reveal the damping mechanism of biological structures at nanoscale but also provide useful guidelines for the design of biomimetic nanocomposites from the nanoscale to the macroscopic scale.     

Longitudinal ultrasonic vibration assisted guillotining of stacked paper

Ultrasonic vibration assisted cutting is a complex process with high dynamics. The interaction between cutting tool and workpiece is of key interest to understand the entire process. Experimental investigations are limited by the dynamics of the measurement system, and thus appropriately modeling of the ultrasonic vibration assisted cutting process is essential. In this investigation, a dynamic model regarding the ultrasonic vibration assisted guillotining of stacked paper sheets is developed. A Kelvin–Voigt material model, representing the individual sheets, is chosen, with its stiffness and damping parameters being empirically determined. A novel measurement strategy for studying the contact time and interaction between cutting tool and workpiece is introduced. It allows the verification of the highly dynamic behavior of the developed model. With the dynamic model, the experimentally observed cutting forces can be calculated. It is found that the dynamic forces cause a quicker failure of the material, which leads to a lower compression of the stack prior to reaching the critical cutting force.     

Harmonic generation of an obliquely incident ultrasonic wave in solid-solid contact interfaces

The conventional acoustic nonlinear technique to evaluate the contact acoustic nonlinearity (CAN) at solid-solid contact interfaces (e.g., closed cracks), which uses the through-transmission of normally incident bulk waves, is limited in that access to both the inner and outer surfaces of structures for attaching pulsing and receiving transducers is difficult. The angle beam incidence and reflection technique, where both the pulsing and receiving transducers are located on the same side of the target, may allow the above problem to be overcome. However, in the angle incidence technique, mode-conversion at the contact interfaces as well as the normal and tangential interface stiffness should be taken into account. Based on the linear and nonlinear contact stiffness, we propose a theoretical model for the reflection of an ultrasonic wave angularly incident on contact interfaces. In addition, the magnitude of the CAN-induced second harmonic wave in the reflected ultrasonic wave is predicted. Experimental results obtained for the contact interfaces of A16061-T6 alloy specimens at various loading pressures showed good agreement with theoretical predictions. Such agreement proves the validity of the suggested oblique incidence model.     

An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries

We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains.     

Pole assignment of friction-induced vibration for stabilisation through state-feedback control

Friction-induced self-excited linear vibration is often governed by a second-order matrix differential equation of motion with an asymmetric stiffness matrix. The asymmetric terms are product of friction coefficient and the normal stiffness at the contact interface. When the friction coefficient becomes high enough, the resultant vibration becomes unstable as frequencies of two conjugate pairs of complex eigenvalues (poles) coalesce (when viscous damping is low).This short paper presents a receptance-based inverse method for assigning complex poles to second-order asymmetric systems through (active) state-feedback control of a combination of active stiffness, active damping and active mass, which is capable of assigning negative real parts to stabilise an unstable system.     

Vibration suppression of a cantilever beam using magnetically tuned-mass-damper

Eddy currents are induced by the movement of a conductor through a stationary magnetic field or a time varying magnetic field through a stationary conductor. These currents circulate in the conductive material and are dissipated, causing a repulsive force between the magnet and the conductor. These electromagnetic forces can be used to suppress the vibrations of a flexible structure. A tuned mass damper is a device mounted in structures to reduce the amplitude of mechanical vibrations and is one of the effective vibration suppression methods. In the present study, an improved concept of this tuned mass damper for the vibration suppression of structures is introduced. This concept consists of the classical tuned mass damper and an eddy current damping. The important advantages of this magnetically tuned mass damper are that it is relatively simple to apply, it does not require any electronic devices and external power, and it is effective on the vibration suppression. The proposed concept is designed for a cantilever beam and the analytical studies on the eddy current damping and its effects on the vibration suppression. To show the effectiveness of the proposed concept and verify the eddy current damping model, experiments on a cantilever beam are performed. It is found that the proposed concept could significantly increase the damping effect of the tuned mass damper even if not adequately tuned.     

接触缺陷的振动调制超声导波检测技术研究

针对常规线性超声检测方法无法实现板结构接触类缺陷(如微裂纹、脱粘等)检测问题,将超声导波技术与振动声调制技术相结合,利用稀疏分布传感器发展了一种板结构中接触缺陷非线性超声检测方法。通过低频振动改变缺陷的接触状况,使得通过接触面的高频导波信号的相位和幅值受到调制。对受低频振动调制的超声导波二维时间序列进行时频分析,由于接触类缺陷的存在,在振动调制超声导波序列的时频分布上出现明显的低频振动频率分量。利用提取出的低频振动频率下的超声导波信号,进行了结构接触缺陷成像处理。检测试验表明,基于振动声调制的超声导波缺陷成像方法可以实现结构中的接触类缺陷检测。      

Importance of tread inertia and damping on the tyre/road contact stiffness

Predicting tyre/road interaction processes like roughness excitation, stick-slip, stick-snap, wear and traction requires detailed information about the road surface, the tyre dynamics and the local deformation of the tread at the interface. Aspects of inertia and damping when the tread is locally deformed are often neglected in many existing tyre/road interaction models. The objective of this paper is to study how the dynamic features of the tread affect contact forces and contact stiffness during local deformation. This is done by simulating the detailed contact between an elastic layer and a rough road surface using a previously developed numerical time domain contact model. Road roughness on length scales smaller than the discretisation scale is included by the addition of nonlinear contact springs between each pair of contact elements. The dynamic case, with an elastic layer impulse response extending in time, is compared with the case where the corresponding quasi-static response is used. Results highlight the difficulty of estimating a constant contact stiffness as it increases during the indentation process between the elastic layer and the rough road surface. The stiffness–indentation relation additionally depends on how rapidly the contact develops; a faster process gives a stiffer contact. Material properties like loss factor and density also alter the contact development. This work implies that dynamic properties of the local tread deformation may be of importance when simulating contact details during normal tyre/road interaction conditions. There are however indications that the significant effect of damping could approximately be included as an increased stiffness in a quasi-static tread model.     

Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces

We present a new method for computing two-dimensional Stokes flow with moving interfaces that respond elastically to stretching. The interface is moved by semi-Lagrangian contouring: a distance function is introduced on a tree of cells near the interface, transported by a semi-Lagrangian time step and then used to contour the new interface. The velocity field in a periodic box is calculated as a potential integral resulting from interfacial and body forces, using a technique based on Ewald summation with analytically derived local corrections. The interfacial stretching is found from a surprisingly natural formula. A test problem with an exact solution is constructed and used to verify the speed, accuracy and robustness of the approach.     

Damping uncertainty due to noise and exponential windowing

Estimation of damping levels in structures is required in many applications and the theoretical damping predictions in many cases are either difficult or not very reliable. Therefore, determination of damping levels based on experimental data is employed quite often. However, in some cases, experimental approach may not be able to provide definite answers either in the sense that the identified damping level may exhibit high level of uncertainty. In experimental approach, the most widely used methods for damping determination require vibration spectrums or the Frequency Response Function(s) which are obtained by Fourier transformation of the time-domain data. During this process, it is often necessary, especially for lightly damped structures, to modify the time-domain data by using exponential windowing so as to minimise the leakage effect in the spectrum. The so-called numerical damping artificially added by this process can be subtracted later in order to obtain the correct damping level. However, for lightly damped structures, the artificially introduced numerical damping can be significantly greater than the actual damping level. This inevitably brings the accuracy and the reliability issues, especially when the data are contaminated by noise. This paper addresses damping uncertainty in frequency-domain estimation when (i) the data are contaminated by noise and (ii) numerical damping via exponential windowing is introduced during the signal processing phase of the spectrum estimation. Some numerical simulations are performed first in order to assess the adverse effects of noise on damping estimations and resulting damping uncertainty is examined as a function of noise level in the data. Then, damping uncertainty due to the use of exponential windowing is investigated using experimental data. A relationship between damping uncertainty and the level of added numerical damping is presented when the so-called Line-Fit method is used for damping estimation from measured Frequency Response Functions.