176 research outputs found
Parametric Design of Minimal Mass Tensegrity Bridges Under Yielding and Buckling Constraints
This paper investigates the use of the most fundamental elements; cables for
tension and bars for compression, in the search for the most efficient bridges.
Stable arrangements of these elements are called tensegrity structures. We show
herein the minimal mass arrangement of these basic elements to satisfy both
yielding and buckling constraints. We show that the minimal mass solution for a
simply-supported bridge subject to buckling constraints matches Michell's 1904
paper which treats the case of only yield constraints, even though our boundary
conditions differ. The necessary and sufficient condition is given for the
minimal mass bridge to lie totally above (or below) deck. Furthermore this
condition depends only on material properties. If one ignores joint mass, and
considers only bridges above deck level, the optimal complexity (number of
elements in the bridge) tends toward infinity (producing a material continuum).
If joint mass is considered then the optimal complexity is finite. The optimal
(minimal mass) bridge below deck has the smallest possible complexity (and
therefore cheaper to build), and under reasonable material choices, yields the
smallest mass bridge.Comment: 56 pages, 25 figures, 13 tables. Internal Report 2014-1: University
of California, San Diego, 201
Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection
Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist
Placing dynamic sensors and actuators on flexible space structures
Input/Output Cost Analysis involves decompositions of the quadratic cost function into contributions from each stochastic input and each weighted output. In the past, these suboptimal cost decomposition methods of sensor and actuator selection (SAS) have been used to locate perfect (infinite bandwidth) sensor and actuators on large scale systems. This paper extends these ideas to the more practical case of imperfect actuators and sensors with dynamics of their own. NASA's SCOLE examples demonstrate that sensor and actuator dynamics affect the optimal selection and placement of sensors and actuators
Sensitivity, optimal scaling and minimum roundoff errors in flexible structure models
Traditional modeling notions presume the existence of a truth model that relates the input to the output, without advanced knowledge of the input. This has led to the evolution of education and research approaches (including the available control and robustness theories) that treat the modeling and control design as separate problems. The paper explores the subtleties of this presumption that the modeling and control problems are separable. A detailed study of the nature of modeling errors is useful to gain insight into the limitations of traditional control and identification points of view. Modeling errors need not be small but simply appropriate for control design. Furthermore, the modeling and control design processes are inevitably iterative in nature
Experimental investigation of the softening-stiffening response of tensegrity prisms under compressive loading
The present paper is concerned with the formulation of new assembly methods
of bi-material tensegrity prisms, and the experimental characterization of the
compressive response of such structures. The presented assembly techniques are
easy to implement, including a string-first approach in the case of ordinary
tensegrity prisms, and a base-first approach in the case of systems equipped
with rigid bases. The experimental section shows that the compressive response
of tensegrity prisms switches from stiffening to softening under large
displacements, in dependence on the current values of suitable geometric and
prestress variables. Future research lines regarding the mechanical modeling of
tensegrity prisms and their use as building blocks of nonlinear periodic
lattices and acoustic metamaterials are discussed
An extended ordinary state-based peridynamics for non-spherical horizons
This work presents an extended ordinary state-based peridynamics (XOSBPD)
model for the non-spherical horizons. Based on the OSBPD, we derive the XOSBPD
by introducing the Lagrange multipliers to guarantee the non-local dilatation
and non-local strain energy density (SED) are equal to local dilatation and
local SED, respectively. In this formulation, the XOSBPD removes the limitation
of spherical horizons and is suitable for arbitrary horizon shapes. In
addition, the presented XOSBPD does not need volume and surface correction and
allows non-uniform discretization implementation with various horizon sizes.
Three classic examples demonstrate the accuracy and capability for complex
dynamical fracture analysis. The proposed method provides an efficient tool and
in-depth insight into the failure mechanism of structure components and solid
materials.Comment: 19 pages, 9 figure
Multiscale tunability of solitary wave dynamics in tensegrity metamaterials
A new class of strongly nonlinear metamaterials based on tensegrity concepts
is proposed and the solitary wave dynamics under impact loading is
investigated. Such systems can be tuned into elastic hardening or elastic
softening regimes by adjusting local and global prestress. In the softening
regime these metamaterials are able to transform initially compression pulse
into a solitary rarefaction wave followed by oscillatory tail with
progressively decreasing amplitude. Interaction of a compression solitary pulse
with an interface between elastically hardening and softening materials having
correspondingly low-high acoustic impedances demonstrates anomalous behavior: a
train of reflected compression solitary waves in the low impedance material;
and a transmitted solitary rarefaction wave with oscillatory tail in high
impedance material. The interaction of a rarefaction solitary wave with an
interface between elastically softening and elastically hardening materials
with high-low impedances also demonstrates anomalous behavior: a reflected
solitary rarefaction wave with oscillatory tail in the high impedance branch;
and a delayed train of transmitted compression solitary pulses in the low
impedance branch. These anomalous impact transformation properties may allow
for the design of ultimate impact mitigation devices without relying on energy
dissipation.Comment: 4 pages, 4 figure
Minimum output variance control for FSN models: Continuous-time case
In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as opposed to the infinite signal-to-noise ratio assumed in LQG theory. Computational errors in the controller implementation are treated similarly. The objective is to design a state feedback control law such that the closed loop system is mean square asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite control gains – as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optimality are derived. An optimal control law which involves the positive definite solution of a Riccati-like equation is derived. An algorithm for solving the Riccati-like equation is given and its convergence is guaranteed if a solution exists
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