Active Vibration Suppression of One-dimensional Nonlinear Structures Using Optimal Dynamic Inversion

A flexible robot arm can be modeled as an Euler-Bernoulli beam which are infinite degrees of freedom (DOF) system. Proper control is needed to track the desired motion of a robotic arm. The infinite number of DOF of beams are reduced to finite number for controller implementation, which brings in error (due to their distributed nature). Therefore, to represent reality better distributed parameter systems (DPS) should be controlled using the systems partial differential equation (PDE) directly. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a controller to suppress nonlinear vibration of a beam. The method used in this paper determines control forces directly from the PDE model of the system. The formulation has better practical significance, because it leads to a closed form solution of the controller (hence avoids computational issues).

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

High-temperature deformation processing maps for a NiTiCu shape memory alloy

The properties of widely used Ni-Ti-based shape memory alloys (SMAs) are highly sensitive to the underlying microstructure. Hence, controlling the evolution of microstructure during high-temperature deformation becomes important. In this article, the ``processing maps'' approach is utilized to identify the combination of temperature and strain rate for thermomechanical processing of a Ni(42)Ti(50)Cu(8) SMA. Uniaxial compression experiments were conducted in the temperature range of 800-1050 degrees C and at strain rate range of 10(-3) and 10(2) s(-1). Two-dimensional power dissipation efficiency and instability maps have been generated and various deformation mechanisms, which operate in different temperature and strain rate regimes, were identified with the aid of the maps and complementary microstructural analysis of the deformed specimens. Results show that the safe window for industrial processing of this alloy is in the range of 800-850 degrees C and at 0.1 s(-1), which leads to grain refinement and strain-free grains. Regions of the instability were identified, which result in strained microstructure, which in turn can affect the performance of the SMA.

Stability of domain structures in multi-domain proteins

Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR.

Spectral Finite Element Modeling of Complex Structures for Applications in Real-time Structural Health Monitoring

In this paper we discuss the recent progresses in spectral finite element modeling of complex structures and its application in real-time structural health monitoring system based on sensor-actuator network and near real-time computation of Damage Force Indicator (DFI) vector. A waveguide network formalism is developed by mapping the original variational problem into the variational problem involving product spaces of 1D waveguides. Numerical convergence is studied using a h()-refinement scheme, where is the wavelength of interest. Computational issues towards successful implementation of this method with SHM system are discussed.

Simultaneous Geometry Optimization and Material Selection for Truss Structures

In this work, we explore simultaneous design and material selection by posing it as an optimization problem. The underlying principles for our approach are Ashby's material selection procedure and structural optimization. For the simplicity and ease of initial implementation of the general procedure, truss structures under static load are considered in this work in view of maximum stiffness, minimum weight/cost and safety against failure. Along the lines of Ashby's material indices, a new design index is derived for trusses. This helps in choosing the most suitable material for any design of a truss. Using this, both the design space and material database are searched simultaneously using optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous even though the material selection is an inherently discrete problem.