Task-level control of the lateral leg spring model of cockroach locomotion

The Lateral Leg Spring model (LLS) was developed by Schmitt and Holmes to model the horizontal-plane dynamics of a running cockroach. The model captures several salient features of real insect locomotion, and demonstrates that horizontal plane locomotion can be passively stabilized by a well-tuned mechanical system, thus requiring minimal neural reflexes. We propose two enhancements to the LLS model. First, we derive the dynamical equations for a more flexible placement of the center of pressure (COP), which enables the model to capture the phase relationship between the body orientation and center-of-mass (COM) heading in a simpler manner than previously possible. Second, we propose a reduced LLS "plant model" and biologically inspired control law that enables the model to follow along a virtual wall, much like antenna-based wall following in cockroaches. © 2006 Springer.

The analysis of impact forces in randomly vibrating elastic systems

This work is concerned with the characteristics of the impact force produced when two randomly vibrating elastic bodies collide with each other, or when a single randomly vibrating elastic body collides with a stop. The impact condition includes a non-linear spring, which may represent, for example, a Hertzian contact, and in the case of a single body, closed form approximate expressions are derived for the duration and magnitude of the impact force and for the maximum deceleration at the impact point. For the case of two impacting bodies, a set of algebraic equations are derived which can be solved numerically to yield the quantities of interest. The approach is applied to a beam impacting a stop, a plate impacting a stop, and to two impacting beams, and in each case a comparison is made with detailed numerical simulations. Aspects of the statistics of impact velocity are also considered, including the probability that the impact velocity will exceed a specified value within a certain time. © 2012 Elsevier Ltd. All rights reserved.

The modes of a tethered, spherical balloon

Observations of a tethered meteorological balloon show that a strong vibration coupling exists between axial forcing of the tether and ovalling deformations of the balloon. Such coupling may lead to system instabilities and fatigue failure in a tethered-balloon system. This is particularly relevant in the case of a balloon launched from a moving vessel, as is proposed as part of the SPICE geoengineering project. This paper investigates the vibration characteristics of a tethered, spherical balloon using a simple analytical model: a tensioned, spherical membrane attached to a spring. The analytical solution for the natural frequencies and modeshapes of this system is compared to transfer functions obtained by laser vibrometry. These results are then used to determine the most suitable method of modelling the dynamic response of a tethered balloon.

The impact of sand slugs against beams and plates: Coupled discrete particle/finite element simulations

The impact of a slug of dry sand particles against a metallic sandwich beam or circular sandwich plate is analysed in order to aid the design of sandwich panels for shock mitigation. The sand particles interact via a combined linear-spring-and-dashpot law whereas the face sheets and compressible core of the sandwich beam and plate are treated as rate-sensitive, elastic-plastic solids. The majority of the calculations are performed in two dimensions and entail the transverse impact of end-clamped monolithic and sandwich beams, with plane strain conditions imposed. The sand slug is of rectangular shape and comprises a random loose packing of identical, circular cylindrical particles. These calculations reveal that loading due to the sand is primarily inertial in nature with negligible fluid-structure interaction: the momentum transmitted to the beam is approximately equal to that of the incoming sand slug. For a slug of given incoming momentum, the dynamic deflection of the beam increases with decreasing duration of sand-loading until the impulsive limit is attained. Sandwich beams with thick, strong cores significantly outperform monolithic beams of equal areal mass. This performance enhancement is traced to the "sandwich effect" whereby the sandwich beams have a higher bending strength than that of the monolithic beams. Three-dimensional (3D) calculations are also performed such that the sand slug has the shape of a circular cylindrical column of finite height, and contains spherical sand particles. The 3D slug impacts a circular monolithic plate or sandwich plate and we show that sandwich plates with thick strong cores again outperform monolithic plates of equal areal mass. Finally, we demonstrate that impact by sand particles is equivalent to impact by a crushable foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally, yet give predictions to within 5% of the full discrete particle calculations for the monolithic and sandwich beams and plates. These foam projectile calculations suggest that metallic foam projectiles can be used to simulate the loading by sand particles within a laboratory setting. © 2013 Elsevier Ltd.

A framework for the analysis of thermal losses in reciprocating compressors and expanders

This article presents a framework that describes formally the underlying unsteady and conjugate heat transfer processes that are undergone in thermodynamic systems, along with results from its application to the characterization of thermodynamic losses due to irreversible heat transfer during reciprocating compression and expansion processes in a gas spring. Specifically, a heat transfer model is proposed that solves the one-dimensional unsteady heat conduction equation in the solid simultaneously with the first law in the gas phase, with an imposed heat transfer coefficient taken from suitable experiments in gas springs. Even at low volumetric compression ratios (of 2.5), notable effects of unsteady heat transfer to the solid walls are revealed, with thermally induced thermodynamic cycle (work) losses of up to 14% (relative to the work input/output in equivalent adiabatic and reversible compression/expansion processes) at intermediate Péclet numbers (i.e., normalized frequencies) when unfavorable solid and gas materials are selected, and closer to 10-12% for more common material choices. The contribution of the solid toward these values, through the conjugate variations attributed to the thickness of the cylinder wall, is about 8% and 2% points, respectively, showing a maximum at intermediate thicknesses. At higher compression ratios (of 6) a 19% worst-case loss is reported for common materials. These results suggest strongly that in designing high-efficiency reciprocating machines the full conjugate and unsteady problem must be considered and that the role of the solid in determining performance cannot, in general, be neglected. © 2014 Richard Mathie, Christos N. Markides, and Alexander J. White. Published with License by Taylor & Francis.