An analytical methodology to determine on-orbit dynamic member failure response of space structures

An analytical method is presented to investigate effects of dynamic member failure simultaneously on the orbital motion, attitude motion and axial deformation of a flexible multi-bay truss structure executing a co-planar motion around the earth in a general non-circular orbit. A set of coupled nonlinear equations of motion is derived using the Lagrangian principle for a special structural element-the dumbbell element-moving in an orbit. The equations of motion for the dumbbell shaped element includes damping using the Rayleigh dissipation function. The Central Difference method is used in conjunction with NewtonRaphson method and Jacobian iteration technique to solve the nonlinear coupled equations of motion and thereby obtaining the response in the time domain. The technique based on the finite element assemblage is followed to obtain the response of an orbital truss system, each member of which is represented by the dumbbell element. The sudden member failure is represented by the abrupt removal of the force carrying capacity of the member. The method is applied for a two-bay planar truss moving in a Low Earth Orbit (LEO) at an altitude of 200 km from the surface of the earth. Results from the study show that the effects of the sudden member failuire can be significant in the structure's response. The major significance of such detail analysis is especially pertinent for accurate vibration control, on-orbit damage detection and health monitoring and design to prevent progressive collapse of the orbital structure during its "service life." * Assistant Professor, Civil and Environmental Engineering, Member AIAA, ASCE, ASME t Graduate Research Assistants Givilaad Environments! Engineering, Student member AIAA copyright © American Institute of Aeronautics and Astronautics, Inc., 1996. All rights reserved. INTRODUCTION Because of their lightweight, high stiffness and ease of construction, truss-type structures are the preferred candidates for various large construction projects in space. Some of the applications of truss-type structures in space include space antennas, space mirror, support structures for satellites, solar panels, and for an optical mirror in a space telescope, antennas in various satellites, and large projects, such as, Microwave Radiometer and the International Space Station. These space systems are required to have a precise structural configuration and pointing accuracy. Therefore, it is extremely important to eliminate or minimize their vibration caused by space environmental disturbances, such as docking, deployment, maneuvers, meteoroid impact, and thermal changes. The areas dealing with control schemes, accurate structural modeling, in-flight response measurements, on-orbit health monitoring and damage detection, and system identification and verification of space structures have received a great deal of attention in recent years"*. Success in achieving any of the aforementioned functions greatly depends on knowing the response of the structure as accurately as possible. Moreover, the information of accurate structural response is extremely necessary for any attempt to design and construct structures in a particular orbital environment. Therefore, for these reasons and the reason to be discussed below, a refined and detail analysis technique should be used replacing the approximate techniques" as suggested and used by many investigators in the past. The major problem with the truss-type structures is their vulnerability to individual member failure. Member failure, which affects a small portion of the structure initially, has potential for propagating to other parts of the structure, the phenomena being known as progressive collapse. Sudden damage to an individual member or a portion of a structure in service environments can come Jrom a variety:of causes. suchjsjnateriaLdefect^ahricatioa errors, construction/connection flaws, impact accidents and abnormal loads. The member behavior under compression such as sudden buckling into post-buckling regime can also give rise to such an structural failure. The member failure problem can be particularly acute in harsh environments of space where structures also experience damage from impact and docking by orbiting objects, drastic temperature changes, and exposure to radiation and charged particles. Normally, structural engineers have dealt with the problem of member failure by introducing redundant members in the design of truss structures. This provision, although based on accepted engineering logic, has proved ineffective in a number of cases resulting in a catastrophic collapse as exemplified by several large lattice roof collapse on land". This approach is impractical for space structures where redundant members significantly increase launching payload. Ideally speaking a determinate truss structure will be most preferred for space application since this is highly economic due to the minimum numbers of members required but also provides greater ease in analysis and construction. It is not possible to send remedial measures to guard against progressive collapse in a lattice structure once it initiates, because the collapse usually lasts for a short duration. For space structures, effects of member failure are substantially increased because of the fact space structures are extremely light and large in dimensions. This increases the importance of understanding thoroughly the characteristics and response of the structure during member failure to achieve safe design. The member force redistribution during progressive failure in truss-like structure is recognized to be dynamic process-. It is, therefore important to introduce such dynamic effects, namely the rapid redistribution of member forces and the inertia forces caused by the member failure, in the evaluation of response of these structures under member failure scenario. Furthermore, the possible dynamic effects of member failure in a truss-like structure need to be considered for any accurate and precise methods of vibration control, damage detection using vibration measurements, and reserve strength determination of the structure. Several studies on the response of terrestrial truss structures considering the member failure as a static phenomenon (for example see Ref. 14), and some considering dynamic phenomenon,'" have been reported. However, this particular problem remains unexplored for truss structures moving in an orbit. This paper presents an analytical and numerical scheme to determine the undamped and damped response of a multi-bay truss structure moving in a general co-planar earth orbit subjected to the simultaneous action of dynamic member failure and external forces. The formulation for an axially flexible dumbbell structure executing coplanar motion in an orbit has been used as a building block representing individual members of the orbital truss system. Response of the structure studied includes orbital motion, pitch motion, and structural deformation. THEORETICAL DEVELOPMENT Fig. 1 shows a 'dumbbell model' of a 1dimensional axially flexible structure moving in a general earth orbit The generalized co-ordinates for the model are (a) the nondimensionalized radial distances (i.e. r,* and r2*) of end masses, m1 and nij, of the element from the center of the earth and (b) the angle of sweep (i.e. 6, and 62) of the radial lines corresponding to the end masses in the plane of motion. Kinetic Energy: The kinetic energy (Kg) of the structure with respect to the generalized co-ordinates is given by the following expression.