Flexibility in flapping foil suppresses meandering of induced jet in absence of free stream

Thrust-generating flapping foils are known to produce jets inclined to the free stream at high Strouhal numbers St = fA/U-infinity, where f is the frequency and A is the amplitude of flapping and U-infinity is the free-stream velocity. Our experiments, in the limiting case of St —> infinity (zero free-stream speed), show that a purely oscillatory pitching motion of a chordwise flexible foil produces a coherent jet composed of a reverse Benard-Karman vortex street along the centreline, albeit over a specific range of effective flap stiffnesses. We obtain flexibility by attaching a thin flap to the trailing edge of a rigid NACA0015 foil; length of flap is 0.79 c where c is rigid foil chord length. It is the time-varying deflections of the flexible flap that suppress the meandering found in the jets produced by a pitching rigid foil for zero free-stream condition. Recent experiments (Marais et al., J. Fluid Mech., vol. 710, 2012, p. 659) have also shown that the flexibility increases the St at which non-deflected jets are obtained. Analysing the near-wake vortex dynamics from flow visualization and particle image velocimetry (PIV) measurements, we identify the mechanisms by which flexibility suppresses jet deflection and meandering. A convenient characterization of flap deformation, caused by fluid-flap interaction, is through a non-dimensional effective stiffness', EI* = 8 EI/(rho V-TEmax(2) s(f) c(f)(3)/2), representing the inverse of the flap deflection due to the fluid-dynamic loading; here, EI is the bending stiffness of flap, rho is fluid density, V-TEmax is the maximum velocity of rigid foil trailing edge, s(f) is span and c(f) is chord length of the flexible flap. By varying the amplitude and frequency of pitching, we obtain a variation in EI* over nearly two orders of magnitude and show that only moderate EI*. (0.1 less than or similar to EI * less than or similar to 1 generates a sustained, coherent, orderly jet. Relatively `stiff' flaps (EI* greater than or similar to 1), including the extreme case of no flap, produce meandering jets, whereas highly `flexible' flaps (EI* less than or similar to 0.1) produce spread-out jets. Obtained from the measured mean velocity fields, we present values of thrust coefficients for the cases for which orderly jets are observed.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

A non-resonant mass sensor to eliminate the ``missing mass'' effect during mass measurement of biological materials

Resonant sensors and crystal oscillators for mass detection need to be excited at very high natural frequencies (MHz). Use of such systems to measure mass of biological materials affects the accuracy of mass measurement due to their viscous and/or viscoelastic properties. The measurement limitation of such sensor system is the difficulty in accounting for the ``missing mass'' of the biological specimen in question. A sensor system has been developed in this work, to be operated in the stiffness controlled region at very low frequencies as compared to its fundamental natural frequency. The resulting reduction in the sensitivity due to non-resonant mode of operation of this sensor is compensated by the high resolution of the sensor. The mass of different aged drosophila melanogaster (fruit fly) is measured. The difference in its mass measurement during resonant mode of operation is also presented. That, viscosity effects do not affect the working of this non-resonant mass sensor is clearly established by direct comparison. (C) 2014 AIP Publishing LLC.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Orientation dependent mechanical properties of commercially pure (cp) titanium

The present investigation is an attempt at correlating the crystallographic orientation and mechanical properties of hexagonal commercially pure titanium (cp-titanium). Annealed cp-titanium sheets are subjected to tensile deformation along the rolling direction, along 45 degrees to the rolling direction and along 90 degrees to the rolling direction respectively. Crystallographic textures and mechanical properties of these cp-titanium samples are investigated in the present study. The hardness of different grains/orientations is estimated through nanoindentation, grain average misorientation, orientation estimated elastic stiffness and Taylor factor measurements. It is observed that the hardness of the grains close to basal orientation is higher compared to non-basal orientations. It is further observed that the estimated bulk mechanical properties of cp-titanium have a direct relationship with the volume fraction of basal grains/orientations. (C) 2014 Elsevier Inc All rights reserved.

Wave propagation analysis in adhesively bonded composite joints using the wavelet spectral finite element method

A wavelet spectral finite element (WSFE) model is developed for studying transient dynamics and wave propagation in adhesively bonded composite joints. The adherands are formulated as shear deformable beams using the first order shear deformation theory (FSDT) to obtain accurate results for high frequency wave propagation. Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle. The adhesive layer is modeled as a line of continuously distributed tension/compression and shear springs. Daubechies compactly supported wavelet scaling functions are used to transform the governing partial differential equations from time domain to frequency domain. The dynamic stiffness matrix is derived under the spectral finite element framework relating the nodal forces and displacements in the transformed frequency domain. Time domain results for wave propagation in a lap joint are validated with conventional finite element simulations using Abaqus. Frequency domain spectrum and dispersion relation results are presented and discussed. The developed WSFE model yields efficient and accurate analysis of wave propagation in adhesively-bonded composite joints. (C) 2014 Elsevier Ltd. All rights reserved.

Dielectric elastomers: Asymptotically-correct three-dimensional displacement field

Asymptotically-accurate dimensional reduction from three to two dimensions and recovery of 3-D displacement field of non-prestretched dielectric hyperelastic membranes are carried out using the Variational Asymptotic Method (VAM) with moderate strains and very small ratio of the membrane thickness to its shortest wavelength of the deformation along the plate reference surface chosen as the small parameters for asymptotic expansion. Present work incorporates large deformations (displacements and rotations), material nonlinearity (hyperelasticity), and electrical effects. It begins with 3-D nonlinear electroelastic energy and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a 2-D nonlinear plate analysis. Major contribution of this paper is a comprehensive nonlinear through-the-thickness analysis which provides a 2-D energy asymptotically equivalent of the 3-D energy, a 2-D constitutive relation between the 2-D generalized strain and stress tensors for the plate analysis and a set of recovery relations to express the 3-D displacement field. Analytical expressions are derived for warping functions and stiffness coefficients. This is the first attempt to integrate an analytical work on asymptotically-accurate nonlinear electro-elastic constitutive relation for compressible dielectric hyperelastic model with a generalized finite element analysis of plates to provide 3-D displacement fields using VAM. A unified software package `VAMNLM' (Variational Asymptotic Method applied to Non-Linear Material models) was developed to carry out 1-D non-linear analysis (analytical), 2-D non-linear finite element analysis and 3-D recovery analysis. The applicability of the current theory is demonstrated through an actuation test case, for which distribution of 3-D displacements are provided. (C) 2014 Elsevier Ltd. All rights reserved.

Modelling of soldier fly halteres for gyroscopic oscillations

Nature has evolved a beautiful design for small-scale vibratory rategyro in the form of dipteran halteres that detect body rotations via Coriolis acceleration. In most Diptera, including soldier fly, Hermetia illucens, halteres are a pair of special organs, located in the space between the thorax and the abdomen. The halteres along with their connecting joint with the fly's body constitute a mechanism that is used for muscle-actuated oscillations of the halteres along the actuation direction. These oscillations lead to bending vibrations in the sensing direction (out of the haltere's actuation plane) upon any impressed rotation due to the resulting Coriolis force. This induced vibration is sensed by the sensory organs at the base of the haltere in order to determine the rate of rotation. In this study, we evaluate the boundary conditions and the stiffness of the anesthetized halteres along the actuation and the sensing direction. We take several cross-sectional SEM (scanning electron microscope) images of the soldier fly haltere and construct its three dimensional model to get the mass properties. Based on these measurements, we estimate the natural frequency along both actuation and sensing directions, propose a finite element model of the haltere's joint mechanism, and discuss the significance of the haltere's asymmetric cross-section. The estimated natural frequency along the actuation direction is within the range of the haltere's flapping frequency. However, the natural frequency along the sensing direction is roughly double the haltere's flapping frequency that provides a large bandwidth for sensing the rate of rotation to the soldier flies.

Colored polydimethylsiloxane micropillar arrays for high throughput measurements of forces applied by genetic model organisms

Measuring forces applied by multi-cellular organisms is valuable in investigating biomechanics of their locomotion. Several technologies have been developed to measure such forces, for example, strain gauges, micro-machined sensors, and calibrated cantilevers. We introduce an innovative combination of techniques as a high throughput screening tool to assess forces applied by multiple genetic model organisms. First, we fabricated colored Polydimethylsiloxane (PDMS) micropillars where the color enhances contrast making it easier to detect and track pillar displacement driven by the organism. Second, we developed a semiautomated graphical user interface to analyze the images for pillar displacement, thus reducing the analysis time for each animal to minutes. The addition of color reduced the Young's modulus of PDMS. Therefore, the dye-PDMS composite was characterized using Yeoh's hyperelastic model and the pillars were calibrated using a silicon based force sensor. We used our device to measure forces exerted by wild type and mutant Caenorhabditis elegans moving on an agarose surface. Wild type C. elegans exert an average force of similar to 1 mu N on an individual pillar and a total average force of similar to 7.68 mu N. We show that the middle of C. elegans exerts more force than its extremities. We find that C. elegans mutants with defective body wall muscles apply significantly lower force on individual pillars, while mutants defective in sensing externally applied mechanical forces still apply the same average force per pillar compared to wild type animals. Average forces applied per pillar are independent of the length, diameter, or cuticle stiffness of the animal. We also used the device to measure, for the first time, forces applied by Drosophila melanogaster larvae. Peristaltic waves occurred at 0.4Hz applying an average force of similar to 1.58 mu N on a single pillar. Our colored microfluidic device along with its displacement tracking software allows us to measure forces applied by multiple model organisms that crawl or slither to travel through their environment. (C) 2015 AIP Publishing LLC.

Effects of temperature and clay content on water absorption characteristics of modified MMT clay/cyclic olefin copolymer nanocomposite films: Permeability, dynamic mechanical properties and the encapsulated organic device performance

In the present study, amino-silane modified layered organosilicates were used to reinforce cyclic olefin copolymer to enhance the thermal, mechanical and moisture impermeable barrier properties. The optimum clay loading (4%) in the nanocomposite increases the thermal stability of the film while further loading decreases film stability. Water absorption behavior at 62 degrees C was carried out and compared with the behavior at room temperature and 48 degrees C. The stiffness of the matrix increases with clay content and the recorded strain to failure for the composite films was lower than the neat film. Dynamic mechanical analysis show higher storage modulus and low loss modulus for 2.5-4 wt% clay loading. Calcium degradation test and device encapsulation also show the evidence of optimum clay loading of 4 wt% for improved low water vapor transmission rates compared to other nanocomposite films. (C) 2014 Elsevier Ltd. All rights reserved.

Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Large Diameter Triaxial Tests on Geosynthetic-Reinforced Granular Subbases

The estimation of strength and stiffness of reinforced aggregates is very important for the design and construction of reinforced unpaved/paved road sections. This paper presents the experimental results from static and cyclic triaxial tests carried out on granular subbase samples reinforced with multiple layers of geogrid reinforcement. Aggregates of different size ranges were mixed in calculated proportions by weight to obtain the gradation specified for rural roads. Triaxial samples of 300 mm diameter and 600 mm height were prepared using this sampled aggregate. The strength and stiffness characteristics of this aggregate reinforced with geogrids at different elevations were determined from static and cyclic triaxial tests. Triaxial tests were also carried out on geocell encased aggregates, and the results are compared. From the experimental results it is observed that reinforced systems carried more stresses than unreinforced systems at the same strain level. The beneficial effect increased with increase in the quantity of reinforcement, whereas for geocell reinforcement, the advantage was evident only at higher strains. (C) 2014 American Society of Civil Engineers.

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ``energy-like measure'' in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate ``high-frequency'' dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

Tunable mechanical and thermal properties of ZnS/CdS core/shell nanowires

Using all-atom molecular dynamics (MD) simulations, we have studied the mechanical properties of ZnS/CdS core/shell nanowires. Our results show that the coating of a few-atomic-layer CdS shell on the ZnS nanowire leads to a significant change in the stiffness of the core/shell nanowires compared to the stiffness of pure ZnS nanowires. The binding energy between the core and shell region decreases due to the lattice mismatch at the core-shell interface. This reduction in binding energy plays an important role in determining the stiffness of a core/shell nanowire. We have also investigated the effects of the shell on the thermal conductivity and melting behavior of the nanowires.

Hybrid Elements for Modelling Squeeze Film Effects Coupled with Structural Interactions in Vibratory MEMS Devices

We present a hybrid finite element based methodology to solve the coupled fluid structure problem of squeeze film effects in vibratory MEMS devices, such as gyroscopes, RF switches, and 2D resonators. The aforementioned devices often have a thin plate like structure vibrating normally to a fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping. For accurate modelling of such devices the squeeze film effects must be incorporated. Extensive literature is available on squeeze film modelling, however only a few studies address the coupled fluid elasticity problem. The majority of the studies that account for the plate elasticity coupled with the fluid equation, either use approximate mode shapes for the plate or use iterative solution strategies. In an earlier work we presented a single step coupled methodology using only one type of displacement based element to solve the coupled problem. The displacement based finite element models suffer from locking issues when it comes to modelling very thin structures with the lateral dimensions much larger than the plate thickness as is typical in MEMS devices with squeeze film effects. In this work we present another coupled formulation where we have used hybrid elements to model the structural domain. The numerical results show a huge improvement in convergence and accuracy with coarse hybrid mesh as compared to displacement based formulations. We further compare our numerical results with experimental data from literature and find them to be in good accordance.