Journal of Aerospace Engineering

A mathematical model for the restoring force of the wire rope spring is presented. The model is semianalytical in nature and is fully defined by the dimensions and properties of the spring. Emphasis is placed on the tension-compression mode of deformation. An experimental investigation is described in which the force–displacement relationships, for a number of springs, were obtained. For modeling purposes, the restoring force is decomposed into an elastic force and a damping force. The elastic force is modeled by a geometric nonlinear finite beam element. The equivalent cross section is calculated assuming full slip among the individual wires and strands. The damping force is modeled by a constant and a displacement-dependent forces. Based on energy dissipation equivalence, an empirical expression for the damping force is developed.

On arbitrary plane quadrilaterals, difficulties in integrating energy densities prevented analysts from directly using shape function expressions in terms of the physical coordinate variables ( $x$ and $y$ ). With the availability of an exact integration procedure, shape functions are sought here as explicit expressions (in $x$ and $y$ ). Conventional isoparametric (indirect) representation, via canonical coordinate variables ( $\eta$ and $\xi$ ) on a unit square in the computational domain, do not reveal the presence of irrational algebraic expressions that were first elaborated on by Wachspress. Computer algebra systems demonstrate that the isoparametric shape functions are: for a general quadrilateral—linear and a square root of a quadratic (in $x$ and $y$ ); for a trapezoid—identical to the Wachspress rational polynomials; for a parallelogram—bilinear functions; and, moreover, even valid for a triangle with a side node. The failure of the isoparametric formulation for concave domains is traced to the negative argument of irrational parts. Shape functions in the physical domain ( $x$ and $y$ ) facilitate contour plotting of responses (e.g., temperature distributions) within quadrilateral elements. A subsequent paper details exact calculation of stiffness matrices where the presented shape functions (in $x$ and $y$ ) are indispensable.

The energy dissipation capacity of bolted joints operating in macroslip in a simple satellite model was investigated. A novel way of modeling the macroslip behavior was introduced and it was shown to work well. The method was established by setting the behavior of an elastoplastic element pair to match the experimental response of a bolted joint in macroslip. This pair consisted of two elastoplastic solid elements forming a unit, appropriately constrained by multipoint constraints. Experiments carried out on real satellite joint coupons were used to define the response of the joints for use in the modeling work. The energy dissipated by the joints was obtained by calculating the area under the force-displacement hysteresis loop in the elements through nonlinear transient analyses. It was found that if some of the joints operated in the macroslip region the energy dissipating capability of the joints could be increased significantly. The response of the satellite with these joints was investigated and it was found that vibration levels were reduced significantly.

A robotic excavator must be able to operate in all three states of manipulator motion: free space, contact, and exertion of a force against an environment. A position accommodation control scheme is ideally suited for this task. The position accommodation method described in this study uses a position controller to track a predefined trajectory in the absence of a force at the excavator bucket. If a force is detected, the measured force is used, through a compliance controller, to modify the commanded trajectory. This allows for better control of the complete excavation cycle. This paper describes a rheological method for modeling the soil–bucket interaction force and how that method must be modified to suit the unique case of excavation. Results for both a fixed and variable spring set-point are shown, illustrating the difference between a purely position controlled robot and one using a position accommodation/compliance controller, when used to dig a level trench.

In the last few decades, piezoceramic (PZT) transducers have been extensively used either as actuators or as sensors in the vibration and noise control of aero, civil, and mechanical (ACM) systems. Only in the last decade, PZT transducers have been used in the electromechanical impedance (EMI) models as both sensor and actuator for the structural health monitoring of ACM systems. In the EMI models, the PZT transducers are generally surface bonded to the host structure and are then subjected to one-dimensional (1D) voltage to interrogate the structure for the desired frequency range. The interrogation results in the prediction of electromechanical admittance signatures. These signatures serve as indicators of the health/integrity of the structure. However, the existing single PZT–structure interaction models consider the PZT transducer to be negligible in mass and thus ignored. Moreover, they impose restrictions on the PZT shape, size, and isotropy. This paper presents a novel semianalytical multiple three-dimensional PZT–structure interaction model which considers the “mass” of the PZT transducers, and the transducers are subjected to parallel (1D) sinusoidal voltage. Further, the model does not impose restriction on the shape (square or rectangular), size (thin or thick), and electrical properties (isotropic or anisotropic) of PZT. The derived model is also experimentally verified using lab-sized aluminum plate. As it is generic, the model is expected to be applicable for the nondestructive evaluation of most ACM systems.