James F. Wilson

Elastica of cantilevered beams with variable cross sections

Abstract Numerical and experimental methods are developed for solving the elastica of cantilevered beams of variable cross sections subjected to combined loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula — Falsi methods, respectively, are used to solve the governing differential equations and to compute the beams horizontal deflection at the free end. Extensive numerical results, including deflected shapes and free-end rotations, are presented in non-dimensional form for elastic beams whose area moment of inertia (bending stiffness) varies linearly with beam length. In these studies, such beams are subjected to combinations of tip vertical loads, tip bending moments, and vertical distributed loads that vary linearly with beam length. Experimental studies are presented that complement the theoretical results.

Flexible Robot Manipulators and Grippers: Relatives of Elephant Trunks and Squid Tentacles

Elephants and squids have continuously flexible appendages that are well adapted for manipulating and gripping. In this paper we briefly review the overall structural forms and motions of elephant trunks and squid tentacles. We then discuss how we incorporated some of their biological characteristics in the design of a flexible arm manipulator with open loop control (Part 1) and in the design of a flexible, two-fingered gripper with closed loop control (Part 2).

The dynamics of loosely jointed structures

Abstract Loosely jointed structures have joint connections that exhibit non-linear lateral force–displacement behavior in bending. Examples include scaffolds, bleachers and other temporary frames. Formulated herein is a lumped parameter, dynamic sway model of a multi-bay, n-story scaffold with bilinear elastic joint connections. Responses are evaluated numerically for an approximate model: a two degree of freedom scaffold in plane sway motion caused by harmonic base excitation. Chaotic, quasi-periodic, and periodic responses are investigated over a practical range of non-dimensional system parameters. The results show that the type of response is especially sensitive to the magnitude of joint damping.

Design optimization of prestressed concrete spans for high speed ground transportation

Abstract The problem of designing stiff, lightweight, and least expensive elevated spans to support ground vehicles is investigated. A computer program using the direct search method was developed to calculate optimum geometric configurations of prestressed concrete girders with nonlinear constraint conditions involving stresses and deflections; with specified inputs on loading, unit costs and overall size; and with checks on buckling, shear and ultimate section strength. Parameters allow-for choices between stiff, expensive configurations or flexible, less expensive designs. Several numerical results for simple spans are included.

Lightning-induced fracture of masonry and rock

As a lightning channel on its way to ground meets a standing masonry or rock structure, radiant energy from the channel can induce a thermal shock of sufficient intensity to cause the structure to fracture and collapse. Mathematical models for two such structural failure mechanisms are proposed: one describing violent surface separations or spalling, and the other characterizing internal cracking from sudden increased pore pressure in the solid. Experimental data and case studies are used to complement these theories of lightning-induced failure.

Parametric spin resonance for a spinner with an orbiting pivot

Abstract Dynamics are investigated for a rigid spinner with a hole, concentric with its mass center, into which a pivot is loosely fitted. As the spinner is excited by the motion of the contacting pivot, the spinner may sustain a quasi-steady spin angular velocity θ in the pivots orbiting plane. This spin motion, defined as parametric spin resonance (PSR), is investigated for the case of prescribed, bi-directional, harmonic pivot motion of frequency ω. The ranges of the systems non-dimensional parameters needed to achieve PSR are determined. Experimental data both explain the spinners direction of rotation and complement the predicted existence of quasi-steady values of θ. The analysis explains the characteristic motions of such toys as the Hula-Hoop and the Indian Windmill (the Gee-Haw Whimmy Diddle), and in general may explain certain unwanted vibrations in machinery with worn or loosely-fitting bearings.

Static Design of Cable Mooring Arrays for Offshore Guyed Towers

Abstract The key consideration in controlling the dynamic response of an offshore guyed tower subjected to environmental loading is the selection of the stiffness characteristics of the cable mooring array. In the present study, each cable in the array consists of three segments: a leading segment attached to the tower, a short heavy middle segment, and a seabed trailing segment attached at the extremity to an anchor pile. A nonlinear static model is presented in algorithmic form that defines the stiffness characteristics of the cable array. The model involves the inelastic static catenary equations coupled with conditions of geometric compatibility, formulated in terms of seven nondimensional system parameters. The effects of varying each of the system parameters on the stiffness characteristics of example cable arrays are presented and the implications for cable design are discussed.

Robotic Mechanics and Animal Morphology

The wealth of information on animal structure and motion could well assist the engineer in robotic design. Books and journal articles going back to the early 1800’s document systematic observations by experimental scientists, mostly biologists and zoologists. Although this literature is steeped in the jargon of specialists and sometimes presents conflicting theories for the same observed phenomenon, the engineer with some patience may glean much from articles about the essential mechanisms by which animals move their appendages for locomotion and in gathering food.

Similitude experiments on projectile-induced fracture of monolithic glass

Abstract Experiments were used to identify the II-groups that best scaled the fracture of monolithic plate glass under central impact by a projectile mass. Threshold impact velocities for glass fracture were measured for three groups of geometrically similar, laboratory-scale, rectangular specimens, for two types of edge constraints: (i) all edges clamped, and (ii) short edges clamped and long edges free. Different sets of Π-groups were needed for the two types of edge constraints, if the threshold impact velocities measured for the smallest specimens are to be used to predict those for the larger ones. Furthermore, edge flaws on the specimen face, caused by the diamond cutter used to size the specimens, and the orientation of the cut face to the oncoming projectile, affected the threshold impact velocities significantly. Extensive drop tests showed that, for other parameters remaining constant, the threshold projectile impact velocity is higher for a window glass whose previously cut surface faces toward, rather than away from, the oncoming projectile, regardless of the edge constraints.

Reconstruction of tractor semitrailer accidents using Gauss's principle of least constraint

Abstract Tractor semitrailer accidents are often caused by impact loading to some part of the vehicle and this leads to a loss of steering control and jackknifing. Impact loading may come from contact with another vehicle, or may occur on an isolated tractor semitrailer from maneuvers such as braking with subsequent brake lock-up, from suddenly steering into a turn where the cornering may lead to lateral wheel skidding, or from some combination of these factors. Without regard to the location, magnitude, or cause of impact loading, the accident reconstruction analyses herein rely on a knowledge of the tractor semitrailers pre- and post-jackknife trajectories leading to a rest state. The tractor semitrailer is modeled as two rigid bodies hinged together and in-plane motion, to which is applied a system energy balance and Gausss principle of least constraints. Explicit results are derived for the pre- and post-impact vehicle speeds as a function of the system parameters. Results of a case study for a tractor semitrailer initially in straight line motion show the sensitivity of the velocities to a range of trajectory surface-tyre friction conditions. Further, for constant friction conditions, the maximum post-impact linear velocities are from 1–2% less than the velocities just prior to impact; and for impending jackknife, the angular velocities of the tractor are about three times that of the trailer.