Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

On four-group ML decodable distributed space time codes for cooperative communication

A construction of a new family of distributed space time codes (DSTCs) having full diversity and low Maximum Likelihood (ML) decoding complexity is provided for the two phase based cooperative diversity protocols of Jing-Hassibi and the recently proposed Generalized Non-orthogonal Amplify and Forward (GNAF) protocol of Rajan et al. The salient feature of the proposed DSTCs is that they satisfy the extra constraints imposed by the protocols and are also four-group ML decodable which leads to significant reduction in ML decoding complexity compared to all existing DSTC constructions. Moreover these codes have uniform distribution of power among the relays as well as in time. Also, simulations results indicate that these codes perform better in comparison with the only known DSTC with the same rate and decoding complexity, namely the Coordinate Interleaved Orthogonal Design (CIOD). Furthermore, they perform very close to DSTCs from field extensions which have same rate but higher decoding complexity.

Geoarchaeological Evidence of a Chola-Period Tsunami from an Ancient Port at Kaveripattinam on the Southeastern Coast of India

Literature of the ancient Chola Dynasty (A.D. 9th-11th centuries) of South India and recent archaeological excavations allude to a sea flood that crippled the ancient port at Kaveripattinam, a trading hub for Southeast Asia, and probably affected the entire South Indian coast, analogous to the 2004 Indian Ocean tsunami impact. We present sedimentary evidence from an archaeological site to validate the textual references to this early medieval event. A sandy layer showing bed forms representing high-energy conditions, possibly generated by a seaborne wave, was identified at the Kaveripattinam coast of Tamil Nadu, South India. Its sedimentary characteristics include hummocky cross-stratification, convolute lamination with heavy minerals, rip-up clasts, an erosional contact with the underlying mud bed, and a landward thinning geometry. Admixed with 1000-year-old Chola period artifacts, it provided an optically stimulated luminescence age of 1091 perpendicular to 66 yr and a thermoluminescence age of 993 perpendicular to 73 yr for the embedded pottery sherds. The dates of these proxies converge around 1000 yr B. P., correlative of an ancient tsunami reported from elsewhere along the Indian Ocean coasts. (C) 2011 Wiley Periodicals, Inc.

Static balancing of a four-bar linkage and its cognates

Motivated by the need to statically balance the inherent elastic forces in linkages, this paper presents three techniques to statically balance a four-bar linkage loaded by a zero-free-length spring attached between its coupler point and an anchor point on the ground. The number of auxiliary links and balancing springs required for the three techniques is less than or equal to that of the only technique currently in the literature. One of the three techniques does not require auxiliary links. In these techniques, the set of values for the spring constants and the ground-anchor point of the balancing springs can vary over a one-parameter family. Thrice as many balancing choices are available when the cognates are considered. The ensuing numerous options enable a user to choose the most practical solution. To facilitate the evaluation of the balancing choices for all the cognates, Roberts-Chebyshev cognate theorem is extended to statically balanced four-bar linkages. (C) 2011 Elsevier Ltd. All rights reserved.

Experimental and Theoretical Studies of Unusual Four-Membered Metallacycles from Reactions of Group 4 Metallocene Bis(trimethylsilyl)-acetylene Complexes with the Sulfurdiimide Me3SiN=S=NSiMe3

The use of the sulfurdiimide RN=S=NR' (R = R' = SiMe3, 3) in reactions with group 4 metallocene bis(trimethylsilyl)-acetylene complexes of the type [Cp2M(L (eta(2)-Me3Si-C2SiMe3)] (1: M = Ti, no L; 2: M = Zr, L = pyridine) has led to the formation of four-membered metallacycles 4M containing the group 4 metal, nitrogen and sulfur. DFT calculations performed on compound 4Ti indicate that this complex is best described as a sigma-complex with cyclic delocalisation of the ring electrons. Moreover, pseudo-Jahn-Teller distortion plays a significant role in stabilising this complex.

Geometrically non-linear dynamics of composite four-bar mechanisms

This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.

Adam-Gibbs Relation for Glass-Forming Liquids in Two, Three, and Four Dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in two, three, and four spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in three and four dimensions. But in two dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.

Spray characterization of gasoline-ethanol blends from a multi-hole port fuel injector

This work reports the measured spray structure and droplet size distributions of ethanol-gasoline blends for a low-pressure, multi-hole, port fuel injector (PFI). This study presents previously unavailable data for this class of injectors which are widely used in automotive applications. Specifically, gasoline, ethanol, and gasoline-ethanol blends containing 10%, 20% and 50% ethanol were studied using laser backlight imaging, and particle/droplet image analysis (PDIA) techniques. The fuel mass injected, spray structure and tip penetrations, droplet size distributions, and Sauter mean diameter were determined for the blends, at two different injection pressures. Results indicate that the gasoline and ethanol sprays have similar characteristics in terms of spray progression and droplet sizes in spite of the large difference in viscosity. It appears that the complex mode of atomization utilized in these injectors involving interaction of multiple fuel jets is fairly insensitive to the fuel viscosity over a range of values. This result has interesting ramifications for existing gasoline fuel systems which need to handle blends and even pure ethanol, which is one of the renewable fuels of the future. (C) 2012 Elsevier Ltd. All rights reserved.

Integrated magnetics based multi-port bidirectional DC-DC converter topology for discontinuous-mode operation

A new type of multi-port isolated bidirectional DC-DC converter is proposed in this study. In the proposed converter, transfer of power takes place through addition of magnetomotive forces generated by multiple windings on a common transformer core. This eliminates the need for a centralised storage capacitor to interface all the ports. Hence, the requirement of an additional power transfer stage from the centralised capacitor can also be eliminated. The converter can be used for a multi-input, multi-output (MIMO) system. A pulse width modulation (PWM) strategy for controlling simultaneous power flow in the MIMO converter is also proposed. The proposed PWM scheme works in the discontinuous conduction mode. The leakage inductance can be chosen to aid power transfer. By using the proposed converter topology and PWM scheme, the need to compute power flow equations to determine the magnitude and direction of power flow between ports is alleviated. Instead, a simple controller structure based on average current control can be used to control the power flow. This study discusses the operating phases of the proposed multi-port converter along with its PWM scheme, the design process for each of the ports and finally experimental waveforms that validate the multi-port scheme.