Piezoceramic Composite Actuators for Flow Control in Low Reynolds Number Airflow

The research presented here employs solid-state actuators for flow separation delay or for forced attachment of separated flow seen in airfoils at low Reynolds numbers. To reduce separation, periodic excitation to the flow around the leading edge of the airfoil is induced by Macro-Fiber Composite actuated clamped-free unimorph benders. An electromechanical model of the unimorph is briefly presented and parametric study is conducted to aid the design of a unimorph to output high deformation at a desired frequency. The optimum frequency and amplitude for lift improvement at post-stall angles are identified experimentally. Along with aerodynamic force and structural displacement measurements, helium bubble flow visualization is used to verify existing separated flow, and the attached flow induced by flow control. The lift enhancement induced by several flow control techniques is compared. A symmetric and non-uniform (3D) flow excitation results in the maximum lift enhancement at post-stall region at the lowest power consumption level. A maximum lift coefficient increase of 27.5% (in the post-stall region) is achieved at 125 Hz periodic excitation, with the 3D symmetric actuation mode at 5 m/s and the reduced frequency of 3.78. C(l,max) is increased 7.6% from the baseline.

Piezoaeroelastic Modeling and Analysis of a Generator Wing with Continuous and Segmented Electrodes

Unmanned air vehicles (UAVs) and micro air vehicles (MAVs) constitute unique application platforms for vibration-based energy harvesting. Generating usable electrical energy during their mission has the important practical value of providing an additional energy source to run small electronic components. Electrical energy can be harvested from aeroelastic vibrations of lifting surfaces of UAVs and MAVs as they tend to have relatively flexible wings compared to their larger counterparts. In this work, an electromechanically coupled finite element model is combined with an unsteady aerodynamic model to develop a piezoaeroelastic model for airflow excitation of cantilevered plates representing wing-like structures. The electrical power output and the displacement of the wing tip are investigated for several airflow speeds and two different electrode configurations (continuous and segmented). Cancelation of electrical output occurs for typical coupled bending-torsion aeroelastic modes of a cantilevered generator wing when continuous electrodes are used. Torsional motions of the coupled modes become relatively significant when segmented electrodes are used, improving the broadband performance and altering the flutter speed. Although the focus is placed on the electrical power that can be harvested for a given airflow speed, shunt damping effect of piezoelectric power generation is also investigated for both electrode configurations.

Power Factor Calculation by the Finite Element Method

The use of finite element analysis (FEA) to design electrical motors has increased significantly in the past few years due the increasingly better performance of modern computers. Even though the analytical software remains the most used tool, the FEA is widely used to refine the analysis and gives the final design to be prototyped. The power factor, a standard data of motor manufactures data sheet is important because it shows how much reactive power is consumed by the motor. This data becomes important when the motor is connected to network. However, the calculation of power factor is not an easy task. Due to the saturation phenomena the input motor current has a high level of harmonics that cannot be neglected. In this work the FEA is used to evaluate a proposed (not limitative) methodology to estimate the power factor or displacement factor of a small single-phase induction motor. Results of simulations and test are compared.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis. (c) 2008 Elsevier Ltd. All rights reserved.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

2D evaluation of crack openings using smeared and embedded crack models

This work deals with the determination of crack openings in 2D reinforced concrete structures using the Finite Element Method with a smeared rotating crack model or an embedded crack model In the smeared crack model, the strong discontinuity associated with the crack is spread throughout the finite element As is well known, the continuity of the displacement field assumed for these models is incompatible with the actual discontinuity However, this type of model has been used extensively due to the relative computational simplicity it provides by treating cracks in a continuum framework, as well as the reportedly good predictions of reinforced concrete members` structural behavior On the other hand, by enriching the displacement field within each finite element crossed by the crack path, the embedded crack model is able to describe the effects of actual discontinuities (cracks) This paper presents a comparative study of the abilities of these 2D models in predicting the mechanical behavior of reinforced concrete structures Structural responses are compared with experimental results from the literature, including crack patterns, crack openings and rebar stresses predicted by both models

Effects of elastic indenter deformation on spherical instrumented indentation tests: the reduced elastic modulus

Although the Hertz theory is not applicable in the analysis of the indentation of elastic-plastic materials, it is common practice to incorporate the concept of indenter/specimen combined modulus to consider indenter deformation. The appropriateness was assessed of the use of reduced modulus to incorporate the effect of indenter deformation in the analysis of the indentation with spherical indenters. The analysis based on finite element simulations considered four values of the ratio of the indented material elastic modulus to that of the diamond indenter, E/E(i) (0, 0.04, 0.19, 0.39), four values of the ratio of the elastic reduced modulus to the initial yield strength, E(r)/Y (0, 10, 20, 100), and two values of the ratio of the indenter radius to maximum total displacement, R/delta(max) (3, 10). Indenter deformation effects are better accounted for by the reduced modulus if the indented material behaves entirely elastically. In this case, identical load-displacement (P - delta) curves are obtained with rigid and elastic spherical indenters for the same elastic reduced modulus. Changes in the ratio E/E(i), from 0 to 0.39, resulted in variations lower than 5% for the load dimensionless functions, lower than 3% in the contact area, A(c), and lower than 5% in the ratio H/E(r). However, deformations of the elastic indenter made the actual radius of contact change, even in the indentation of elastic materials. Even though the load dimensionless functions showed only a little increase with the ratio E/E(i), the hardening coefficient and the yield strength could be slightly overestimated when algorithms based on rigid indenters are used. For the unloading curves, the ratio delta(e)/delta(max), where delta(e) is the point corresponding to zero load of a straight line with slope S from the point (P(max), delta(max)), varied less than 5% with the ratio E/E(i). Similarly, the relationship between reduced modulus and the unloading indentation curve, expressed by Sneddon`s equation, did not reveal the necessity of correction with the ratio E/E(i). The most affected parameter in the indentation curve, as a consequence of the indentation deformation, was the ratio between the residual indentation depth after complete unloading and the maximum indenter displacement, delta(r)/delta(max) (up to 26%), but this variation did not significantly decrease the capability to estimate hardness and elastic modulus based on the ratio of the residual indentation depth to maximum indentation depth, h(r)/h(max). In general, the results confirm the convenience of the use of the reduced modulus in the spherical instrumented indentation tests.

On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex-structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

Influence of hardness of the harder body on wear regime transition in a sliding pair of steels

In the unlubricated sliding wear of steels the mild-severe and severe-mild wear transitions have long been investigated. The effect of system inputs such as normal load, sliding speed, environment humidity and temperature, material properties, among others, on those transitions have also been studied. Although transitions seem to be caused by microstructural changes, surfaces oxidation and work-hardening, some questions remain regarding the way each aspect is involved. Since the early studies in sliding wear, it has usually been assumed that only the material properties of the softer body influence the wear behavior of contacting surfaces. For example, the Archard equation involves only the hardness of the softer body, without considering the hardness of the harder body. This work aims to discuss the importance of the harder body hardness in determining the wear regime operation. For this, pin-on-disk wear tests were carried out, in which the disk material was always harder than the pin material. Variations of the friction force and vertical displacement of the pin were registered during the tests. A material characterization before and after tests was conducted using stereoscopy and scanning electron microscopy (SEM) methods, in addition to mass loss, surface roughness and microhardness measurements. The wear results confirmed the occurrence of a mild-severe wear transition when the disk hardness was decreased. The disk hardness to pin hardness ratio (H(d)/H(p)) was used as a criterion to establish the nature of surface contact deformation and to determine the wear regime transition. A predominantly elastic or plastic contact, characterized by H(d)/H(p) values higher or lower than one, results in a mild or severe wear regime operation, respectively. (c) 2009 Elsevier B.V. All rights reserved.

Floquet stability analysis of the flow around an oscillating cylinder

This investigative work is concerned with the flow around a circular cylinder submitted to forced transverse oscillations. The goal is to investigate how the transition to turbulence is initiated in the wake for cases with different Reynolds numbers (Re) and displacement amplitudes (A). For each Re the motion frequency is kept constant, close to the Strouhal number of the flow around a fixed cylinder at the same Re. Stability analysis of two-dimensional periodic flows around a forced-oscillating cylinder is carried out with respect to three-dimensional infinitesimal perturbations. The procedure consists of performing a Floquet type analysis of time-periodic base flows, computed using the spectral/hp element method. With the results of the Floquet calculations, considerations regarding the stability of the system are drawn, and the form of the instability at its onset is obtained. The critical Reynolds number is observed to change with the amplitude of oscillation. With respect to instabilities, unstable modes with the same symmetry as mode A of a fixed cylinder are observed; however, they present different wavelengths. Also, the instabilities observed for the oscillating cylinder are distinctively stronger in the braid shear layers. Other unstable modes similar to mode B are found. Quasi-periodic modes are observed in the 2S wake, and subharmonic mode occurrences are reported in P + S wakes. (C) 2009 Elsevier Ltd. All rights reserved.

Design of compliant mechanisms considering thermal effect compensation and topology optimization

Compliant mechanisms can achieve a specified motion as a mechanism without relying on the use of joints and pins. They have broad application in precision mechanical devices and Micro-Electro Mechanical Systems (MEMS) but may lose accuracy and produce undesirable displacements when subjected to temperature changes. These undesirable effects can be reduced by using sensors in combination with control techniques and/or by applying special design techniques to reduce such undesirable effects at the design stage, a process generally termed ""design for precision"". This paper describes a design for precision method based on a topology optimization method (TOM) for compliant mechanisms that includes thermal compensation features. The optimization problem emphasizes actuator accuracy and it is formulated to yield optimal compliant mechanism configurations that maximize the desired output displacement when a force is applied, while minimizing undesirable thermal effects. To demonstrate the effectiveness of the method, two-dimensional compliant mechanisms are designed considering thermal compensation, and their performance is compared with compliant mechanisms designs that do not consider thermal compensation. (C) 2010 Elsevier B.V. All rights reserved.

Finite Element Analysis and Optimization of a Single-Axis Acoustic Levitator

A finite element analysis and a parametric optimization of single-axis acoustic levitators are presented. The finite element method is used to simulate a levitator consisting of a Langevin ultrasonic transducer with a plane radiating surface and a plane reflector. The transducer electrical impedance, the transducer face displacement, and the acoustic radiation potential that acts on small spheres are determined by the finite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a fiber-optic vibration sensor. The numerical acoustic radiation potential is verified experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reflector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reflector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W.

Embrittlement of electrical steel laminations by nitrogen pick-up during heat treatment

Heat treated electrical steel laminations have shown evidence of low ductility behavior, characterized by a small number of bends till fracture, on repeated bending tests. The laminations were produced using a new grade of electrical steel with much lower aluminum content than usual. The problem happens when the oxygen potential (measured by the dew point of the atmosphere) of the heat treatment atmosphere is abnormally high. Furthermore, ductility can be restored by a low-oxygen potential heat treatment. Although the heat treatment resulted in a loss of ductility, the magnetic properties were not deteriorated. The low ductility samples always show intergranular fracture, whereas the un-treated laminations fracture by cleavage. The low ductility is associated with the formation of silicon manganese nitride precipitates formed at grain boundaries, although they are not the cause of the low ductility. Ductility could be restored by a low dew point heat treatment but the inclusions remained in the grain boundaries. The low ductility and its recovery must be ascribed to the presence of nitrogen atoms segregated to the grain boundaries when the heat treatment atmosphere has a high oxygen potential. The lack of aluminum in the composition of the steel hinders the scavenging effect of this element on nitrogen atoms in solution in the steel. (C) 2009 Elsevier Ltd. All rights reserved.

Thermodynamic self-consistency issues related to the Cluster Variation Method: The case of the BCC Cr-Fe (Chromium-Iron) system

The Cluster Variation Method (CVM), introduced over 50 years ago by Prof. Dr. Ryoichi Kikuchi, is applied to the thermodynamic modeling of the BCC Cr-Fe system in the irregular tetrahedron approximation, using experimental thermochemical data as initial input for accessing the model parameters. The results are checked against independent data on the low-temperature miscibility gap, using increasingly accurate thermodynamic models, first by the inclusion of the magnetic degrees of freedom of iron and then also by the inclusion of the magnetic degrees of freedom of chromium. It is shown that a reasonably accurate description of the phase diagram at the iron-rich side (i.e. the miscibility gap borders and the Curie line) is obtained, but only at expense of the agreement with the above mentioned thermochemical data. Reasons for these inconsistencies are discussed, especially with regard to the need of introducing vibrational degrees of freedom in the CVM model. (C) 2008 Elsevier Ltd. All rights reserved.