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At least 73 records · Page 4

Development of impact resistant boron/aluminum composites for turbojet engine fan blades

Composite fabrication was performed by vacuum press diffusion bonding by both the foil-filament array and preconsolidated monotape methods. The effect of matrix material, fiber diameter, matrix enhancement, fiber volume reinforcement, test temperature, angle-plying, notch, impact orientation, processing variables and fabrication methods on tensile strength and Charpy impact resistance are evaluated. Root attachment concepts, were evaluated by room and elevated temperature tensile testing, as well as by pendulum-Izod and ballistic impact testing. Composite resistance to foreign object damage was also evaluated by ballistic impacting of panels using projectiles of gelatin, RTV rubber and steel at various velocities, and impingement angles. A significant improvement in the pendulum impact resistance of B-Al composites was achieved.

Melnyk, P.↗

Design considerations and experiences in the use of composite material for an aeroelastic research wing

Experiences in using composite skin material on an aeroelastic research wing used in flight flutter testing are described. Significant variations in skin shear modulus due to stress and temperature were encountered with the original fiberglass laminate skin designed to minimize wing torsional stiffness. These variations along with the sensitivity of wing torsional stiffness to the skin-to-frame attachment method complicated the structural model vibration mode predictions. A wing skin redesign with different fiber orientation and a reduction in the amount of skin-to-frame bonding resulted in more predictable modal characteristics without sacrificing design objectives. Design and modeling considerations for future applications are discussed.

Eckstrom, C. V.↗

Methods for the Organogenesis of Skeletal Muscle in Tissue Culture

Skeletal muscle structure is regulated by many factors, including nutrition, hormones, electrical activity, and tension. The muscle cells are subjected to both passive and active mechanical forces at all stages of development and these forces play important but poorly understood roles in regulating muscle organogenesis and growth. For example, during embryogenesis, the rapidly growing skeleton places large passive mechanical forces on the attached muscle tissue. These forces not only help to organize the proliferating mononucleated myoblasts into the oriented, multinucleated myofibers of a functional muscle but also tightly couple the growth rate of muscle to that of bone. Postnatally, the actively contracting, innervated muscle fibers are subjected to different patterns of active and passive tensions which regulate longitudinal and cross sectional myofiber growth. These mechanically-induced organogenic processes have been difficult to study under normal tissue culture conditions, resulting in the development of numerous methods and specialized equipment to simulate the in vivo mechanical environment.These techniques have led to the "engineering" of bioartificial muscles (organoids) which display many of the characteristics of in vivo muscle including parallel arrays of postmitotic fibers organized into fascicle-like structures with tendon-like ends. They are contractile, express adult isoforms of contractile proteins, perform directed work, and can be maintained in culture for long periods. The in vivo-like characteristics and durability of these muscle organoids make them useful for long term in vitro studies on mechanotransduction mechanisms and on muscle atrophy induced by decreased tension. In this report, we described a simple method for generating muscle organoids from either primary embrionic avain or neonatal rodent myoblasts.

Vandenburgh, Herman↗

Combination Space Station Handrail Clamp and Pointing Device

A device for attaching an experiment carrier to a space station handrail is provided. The device has two major components, a clamping mechanism for attachment to a space station handrail, and a pointing carrier on which an experiment package can be mounted and oriented. The handrail clamp uses an overcenter mechanism and the carrier mechanism uses an adjustable preload ball and socket for carrier positioning. The handrail clamp uses a stack of disk springs to provide a spring loaded button. This configuration provides consistent clamping force over a range of possible handrail thicknesses. Three load points are incorporated in the clamping mechanism thereby spreading the clamping load onto three separate points on the handrail. A four bar linkage is used to provide for a single actuation lever for all three load points. For additional safety, a secondary lock consisting of a capture plate and push lock keeps the clamp attached to the handrail in the event of main clamp failure. For the carrier positioning mechanism, a ball in a spring loaded socket uses friction to provide locking torque; however. the ball and socket are torque limited so that the ball ran slip under kick loads (125 pounds or greater). A lead screw attached to disk spring stacks is used to provide an adjustable spring force on the socket. A locking knob is attached to the lead screw to allow for hand manipulation of the lead screw.

Hughes, Stephen J.↗

Simulation Development and Analysis of Crew Vehicle Ascent Abort

NASA's Commercial Crew Program is an integral step in its journey to Mars as it would expedite development of space technologies and open up partnership with U.S. commercial companies. NASA reviews and independent assessment of Commercial Crew Program is fundamental to its success, and being able to model a commercial crew vehicle in a simulation rather than conduct a live test would be a safer, faster, and less expensive way to assess and certify the capabilities of the vehicle. To this end, my project was to determine the feasibility of using a simulation tool named SOMBAT version 2.0 to model a multiple parachute system for Commercial Crew Program simulation. The main tasks assigned to me were to debug and test the main parachute system model, (capable of simulating one to four main parachute bodies), and to utilize a graphical program to animate the simulation results. To begin tackling the first task, I learned how to use SOMBAT by familiarizing myself with its mechanics and by understanding the methods used to tweak its various parameters and outputs. I then used this new knowledge to set up, run, and analyze many different situations within SOMBAT in order to explore the limitations of the parachute model. Some examples of parameters that I varied include the initial velocity and orientation of the falling capsule, the number of main parachutes, and the location where the parachutes were attached to the capsule. Each parameter changed would give a different output, and in some cases, would expose a bug or limitation in the model. A major bug that I discovered was the inability of the model to handle any number of parachutes other than three. I spent quite some time trying to debug the code logically, but was unable to figure it out until my mentor taught me that digital simulation limitations can occur when some approximations are mistakenly assumed for certain in a physical system. This led me to the realization that unlike in all of the programming classes I have taken thus far that focus on pure logic, simulation code focuses on mimicking the physical world with some approximation and can have inaccuracies or numerical instabilities. Learning from my mistake, I adopted new methods to analyze these different simulations. One method the student used was to numerically plot various physical parameters using MATLAB to confirm the mechanical behavior of the system in addition to comparing the data to the output from a separate simulation tool called FAST. By having full control over what was being outputted from the simulation, I could choose which parameters to change and to plot as well as how to plot them, allowing for an in depth analysis of the data. Another method of analysis was to convert the output data into a graphical animation. Unlike the numerical plots, where all of the physical components were displayed separately, this graphical display allows for a combined look at the simulation output that makes it much easier for one to see the physical behavior of the model. The process for converting SOMBAT output for EDGE graphical display had to be developed. With some guidance from other EDGE users, I developed a process and created a script that would easily allow one to display simulations graphically. Another limitation with the SOMBAT model was the inability for the capsule to have the main parachutes instantly deployed with a large angle between the air speed vector and the chutes drag vector. To explore this problem, I had to learn about different coordinate frames used in Guidance, Navigation & Control (J2000, ECEF, ENU, etc.) to describe the motion of a vehicle and about Euler angles (e.g. Roll, Pitch, Yaw) to describe the orientation of the vehicle. With a thorough explanation from my mentor about the description of each coordinate frame, as well as how to use a directional cosine matrix to transform one frame to another, I investigated the problem by simulating different capsule orientations. In the end, I was able to show that this limitation could be avoided if the capsule is initially oriented antiparallel to its velocity vector.

Wong, Chi S.↗

The use of moments of momentum to account for crystal habits

A three-step theory of crystal growth is proposed which involves first an association of molecules or ions in solution to form an impinging growth unit, then second the orientation of this unit prior to its impact on the surface of a crystal, and finally the attachment of this unit to the crystal face. From this theory the habit of a crystal is dependent upon the moments of momentum of the impinging growth unit. The results of sample calculations are presented or sodium chloride, succinic acid, sucrose, and chromium boride. The faces predicted by this proposed theory are compared with those predicted by other, energy-based calculations and with those experimentally observed. The proposed theory suggests alternative strategies for crystallization and habit modification which may be of technological importance. Listings of the two computer programs that were used are provided.

Barber, P. G.↗

Jet-diffuser Ejector - Attached Nozzle Design

Attached primary nozzles were developed to replace the detached nozzles of jet-diffuser ejectors. Slotted primary nozzles located at the inlet lip and injecting fluid normal to the thrust axis, and rotating the fluid into the thrust direction using the Coanda Effect were investigated. Experiments indicated excessive skin friction or momentum cancellation due to impingement of opposing jets resulted in performance degradation. This indicated a desirability for location and orientation of the injection point at positions removed from the immediate vicinity of the inlet surface, and at an acute angle with respect to the thrust axis. Various nozzle designs were tested over a range of positions and orientations. The problems of aircraft integration of the ejector, and internal and external nozzle losses were also considered and a geometry for the attached nozzles was selected. The effect of leaks, protrusions, and asymmetries in the ejector surfaces was examined. The results indicated a relative insensitivity to all surface irregularities, except for large protrusions at the throat of the ejector.

Alperin, M.↗

Strength capabilities and load requirements while performing torquing tasks in zero gravity

A generic examination of the loads produced by individuals performing maximal efforts with a torquing tool in zero gravity, to determine operator strength when performing torquing tasks; quantify the loads placed on foot restraints while performing these tasks; and examine effects of orientation and direction of tool rotation on strength effectiveness was conducted. The experiment was conducted aboard NASA's KC-135 reduced-gravity aircraft, using two force plates attached to a test stand, one with a foot restraint. Subjects used a wrench to apply maximum torques to various fittings, in different positions, in clockwise and counterclockwise directions. It was seen that these subjects could produce approximately 400 to 750 N of force, depending on the orientation of the tool and the direction of effort. The most force could be produced when pushing the tool upwards. A force effectiveness ratio (FER) defined as an indication of how much of the subjects' total effort actually went into performing the desired task. Values of FER ranged from 0.55 to 0.90, with the greatest FER occurring with UP and DOWN efforts, and the lowest with AWAY and LEFT efforts. Designers can use these results to set specifications for craft structures; tools can be developed based on the known strength of the tool users; and tasks can be developed to not exceed the crewmembers' capabilities.

Poliner, Jeffrey↗

Influence of Nucleation Mechanisms on the Radiative Properties of Deep Convective Clouds and Subvisible Cirrus in CRYSTAL/FACE

During the past few years we have conducted work on several different topics, as reflected by our publications. As one of the Co-Project scientists for The Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida Area Cirrus Experiment (CRYSTAL FACE) we worked to help design the mission and then conduct it in the field. Another major activity during the past two years has been to pull together various groups to formulate plans for follow on missions to CRYSTAL FACE. We organized a workshop at the University of Colorado during the summer of 2003 to assess the best locations for future missions. Working with a group of about 10 scientists from around the country we prepared a science-planning document (Tropical Composition, Cloud and Climate Coupling Experiment (TC(sup 4)) that outlined the rationale, locations, strategy to accomplish the goals, and possible payloads for a set of three tropical missions. We also prepared background materials for various NRAs being prepared at NASA Headquarters for missions in Costa Rica, Darwin and Guam. In conjunction with the group at NASA Ames we have helped build a new numerical model for deep convection and have applied that model to simulate the CRYSTAL data. Our goal in particular has been to better understand how convection distributes water vapor isotopes. CRYSTAL observations of water isotopes are very different from those suggested by previous workers who assumed the isotopes would obey Rayleigh fractionation. The water isotope study has several implications. First it is a check on the realism of the deep convection model. Second, the isotopes are a measure of the precipitation removal in the atmosphere. Hence they provide a constraint on a parameter that is difficult to otherwise measure. Finally it has been suggested that isotopes may be the key to unraveling the water transport into the stratosphere and upper troposphere. Such transport is critical both for the radiation balance and for stratospheric chemistry. Ours is the first model that is able to treat this transport. Our initial results have just been submitted to Geophys. Res. Lett (Smith et al., 2005). Essentially we are able to explain the vertical profiles of isotopes in the tropical tropopause transition layer. We are also able to account for stratospheric humidity and isotope abundances with this model. We have also been heavily involved in trying to improve our understanding of nitric acid condensation on ice. Gao et al (2004) have shown that water supersaturations above ice occur when the atmosphere is supersaturated with respect to nitric acid trihydrate. As one of the co-authors of that work, we suggested the mechanism that may explain why this is occurring. Essentially, ice does not like to grow near unit supersaturation, but does so because the water molecules can find sites on the ice surface to attach themselves to before they fly off the ice surface. This phenomena was well known in the 1960s when it was a source of debate about whether condensation and evaporation coefficients for ice would be the same. Evaporation does not require any molecular orientation, while condensation does, so it was possible that the coefficients would differ. They don't differ because the water molecules rapidly move across the surface and find places to attach. Nitric acid may be occupying these preferred sites and therefore the water molecules can't find a desirable place to attach. We anticipate that this research will be the subject of laboratory work during the coming few years. Another possibility that has been suggested is that cubic ice is forming in clouds. We have measured the vapor pressure of cubic ice, and plan to publish that result in the next few months. We have also been working on additional aspects of the condensation of nitric acid on ice. With Y. Kondo we studied the condensation of NOy on ice using the SOLVE data. Gamblin et al. have continued this work. The CRYSTAL NOy and HNO, groups have shown th their data can be fit using standard Langmuir isotherms as suggested in some, but not all, laboratory studies. We have found in the SOLVE data set that this is not the case. Moreover some laboratory studies show there are important kinetic effects that may be occurring in the atmosphere limiting the transfer of nitric acid to the ice. The SOLVE data seem consistent with these studies. We are currently re-analyzing the CRYSTAL data to look for these kinetic effects. There are a number of implications of these studies. One of the more interesting is that the nitric acid coating on ice can be used as a cloud clock to determine how long the cloud parcel has been in existence. We have also been involved with several laboratory studies. We have worked to improve the database on ice optical constants, which are critical for remote sensing. We have also studied the ways in which ice nucleates on clays. We suspect now that the standard theories used for depositional ice nucleation are completely incorrect. Further work will be needed to develop a new theory.

Toon, Owen B.↗

Accurate GPS measurement of the location and orientation of a floating platform

This article describes the design and initial tests of the GPS portion of a system for making seafloor geodesy measurements. In the planned system, GPS antennas on a floating platform will be used to measure the location of an acoustic transducer, attached below the platform, which interrogates an array of transponders on the seafloor. Since the GPS antennas are necessarily some distance above the transducer, a short-baseline GPS interferometer consisting of three antennas is used to measure the platform's orientation. A preliminary test of several crucial elements of the system was performed. The test involved a fixed antenna on the pier and a second antenna floating on a buoy about 80 m away. GPS measurements of the vertical component of this baseline, analyzed independently by two groups using different software, agree with each other and with an independent measurement within a centimeter. The first test of an integrated GPS/acoustic system took place in the Santa Cruz Basin off the coast of southern California in May 1990. In this test a much larger buoy, designed and built at SIO, was equipped with three GPS antennas and an acoustic transducer that interrogated a transponder on the ocean floor. Preliminary analysis indicates that the horizontal position of the transponder can be determined with a precision of about a centimeter.

Purcell, G. H., Jr.↗

Precision attitude control for tethered satellites

Tethered spacecraft are particularly well suited to serve as isolation platforms for space-borne observatories. It has previously been shown that, due to the relatively large tether force, conventional means of performing attitude control for tethered satellites are inefficient for any mission with pointing requirements more stringent than about 1 deg. A particularly effective method of implementing attitude control for tethered satellites is to use the tether tension force to generate control moments by moving the tether attach point relative to the subsatellite center of mass. This paper presents the development of a precision pointing control algorithm for tethered satellites and the simulation of the control system with laboratory hardware. The control algorithm consists of a linear quadratic regulator feedback law and a Kalman filter. The control algorithm has been shown to regulate the vehicle orientation to within 0.60 arcsec rms. This level of precision was achieved only after including a mass center estimator and accurately modeling the effects of the nonlinear attach point motion actuator.

Kline-Schoder, Robert J.↗

End effector with astronaut foot restraint

The combination of a foot restraint platform designed primarily for use by an astronaut being rigidly and permanently attached to an end effector which is suitable for attachment to the manipulator arm of a remote manipulating system is described. The foot restraint platform is attached by a brace to the end effector at a location away from the grappling interface of the end effector. The platform comprises a support plate provided with a pair of stirrups for receiving the toe portion of an astronaut's boots when standing on the platform and a pair of heel retainers in the form of raised members which are fixed to the surface of the platform and located to provide abutment surfaces for abutting engagement with the heels of the astronaut's boots when his toes are in the stirrups. The heel retainers preclude a backward sliding movement of the feet on the platform and instead require a lifting of the heels in order to extract the feet. The brace for attaching the foot restraint platform to the end effector may include a pivot or swivel joint to permit various orientations of the platform with respect to the end effector.

Monford, Leo G., Jr.↗

The dynamics of large flexible earth pointing structures with a hybrid control system

The dynamics and control of large flexible structures nominally oriented along the local horizontal are analyzed. Orientation and shape control is assumed to be provided by a hybrid system consisting of a passive spring loaded gimballed dumbbell damper in addition to active point thrusters. In addition to the passive damping capability, the dumbbell, through attachment at the center of mass of the main structure, also provides a favorable composite moment of inertia ratio required for gravitational stabilization. The hybrid system is seen to generally result in improved transient responses to initial perturbations in orientation and modal shape functions, while requiring less force impulse than that for the active system operating alone.

Bainum, P. M.↗

s-wave threshold in electron attachment - Results in 2-C4F6 and CFCl3 at ultra-low electron energies

Electron attachment lineshapes and cross sections are reported for the processes 2-C4F6(-)/2-C4F6 and Cl(-)/CFCl3 at electron energies of 0-120 and 0-140 meV, and at resolutions of 6 and 7 meV (FWHM), respectively. As in previous measurements in CCl4 and SF6, the results show resolution-limited narrow structure in the cross section at electron energies below 15 meV. This structure arises from the divergence of the s-wave cross section in the limit of zero electron energy. Comparisons are given with swarm-measured results, and with collisional ionization (high-Rydberg attachment) data in this energy range.

Chutjian, A.↗

Clearance Analysis of Node 3 Aft CBM to the Stowed FGB Solar Array

In early 2011, the ISS Vehicle Configuration Office began considering the relocation of the Permanent Multipurpose Module (PMM) to the aft facing Common Berthing Mechanism (CBM) on Node 3 to open a berthing location for visiting vehicles on the Node 1 nadir CBM. In this position, computer-aided design (CAD) models indicated that the aft end of the PMM would be only a few inches from the stowed Functional Cargo Block (FGB) port solar array. To validate the CAD model clearance analysis, in the late summer of 2011 the Image Science and Analysis Group (ISAG) was asked to determine the true geometric relationship between the on-orbit aft facing Node 3 CBM and the FGB port solar array. The desired measurements could be computed easily by photogrammetric analysis if current imagery of the ISS hardware were obtained. Beginning in the fall of 2011, ISAG used the Dynamic Onboard Ubiquitous Graphics (DOUG) program to design a way to acquire imagery of the aft face of Node 3, the aft end-cone of Node 1, the port side of pressurized mating adapter 1 (PMA1), and the port side of the FGB out to the tip of the port solar array using cameras on the Space Station Remote Manipulator System (SSRMS). This was complicated by the need to thread the SSRMS under the truss, past Node 3 and the Cupola, and into the space between the aft side of Node 3 and the FGB solar array to acquire more than 100 images from multiple positions. To minimize the number of SSRMS movements, the Special Purpose Dexterous Manipulator (SPDM) would be attached to the SSRMS. This would make it possible to park the SPDM in one position and acquire multiple images by changing the viewing orientation of the SPDM body cameras using the pan/tilt units on which the cameras are mounted. Using this implementation concept, ISAG identified four SSRMS/SPDM positions from which all of the needed imagery could be acquired. Based on a photogrammetric simulation, it was estimated that the location of the FGB solar array could be measured within an accuracy of about 1 in. in each axis relative to the ISS Analysis Coordinate System (ISSACS). In October 2011, a proposed image-acquisition plan was drafted by ISAG and released for review. The ISS Robotics flight control team (ROBO) proposed minor changes to SPDM positions 1 and 4 to meet ISS proximity requirements. The updated image acquisition plan and draft chit were presented to and approved by the Systems Working Group (SWG) November 18 and were sent to the Vehicle Configuration Board (VCB) in early December 2011. Working with ROBO on 3 successive days (February 21, 22, and 23), ISAG collected 161 images of the ISS. Approximately 40 images were collected from each of the four different SSRMS/SPDM positions, with each set mapping the region from the Node 3 end cone, across Node 1, along the forward port side portion of the FGB, and out the port side FGB solar arrays. From this imagery, the best 80 images were selected for use in the analysis. The images were radiometrically enhanced to improve color and contrast and loaded into the FotoG analysis software along with the camera parameters and control data, which consisted of the coordinates for 54 handrail attachment bolts on the aft face of Node 3, in the ISSACS coordinate system. The results of this analysis produced the measured coordinates of 116 points distributed across the face of the FGB solar array panels (see figure 3) along with propagated uncertainty estimates in each coordinate axis. These results were sent to the ISS Vehicle Configuration Office, which sent them to the Configuration Analysis Modeling and Mass Properties (CAMMP) team for comparison with the Russian-provided CAD model for the retracted FGB solar arrays. The CAMMP analysis unexpectedly showed that the measured location of the port FGB solar array was up to 41-in. further outboard than the design and was slightly twisted about its rotational axis. The unexpected comparison results produced some initial concern regarding the accuracy of the photogrammetric measurements. To verify the measured results, ISAG personnel conducted a second analysis using just the imagery of the solar arrays in an arbitrary coordinate system defined by the three corner points of the inboard-most panel, with the design distance between points A1 and A10 as the only scale. The new measurements agreed with the original results to within less than 1 in. RMS in each axis, confirming the original solar array measurements. ISAG produced a final report for the ISS Vehicle Configuration Office documenting an apparent anomaly in the retracted configuration of the port FGB solar arrays. A copy of the measurement report was translated and sent to the Russian Space Agency. During a Vehicle Integrated Performance and Resources (VIPeR) teleconference September 24, 2012, the Russians acknowledged receipt of a translated copy of the ISAG report. The Russian representative stated that the head of the solar array design team claimed that the measured configuration was impossible unless the structure was physically broken. The Russians acknowledged that they had no expertise in photogrammetry, so the analysis technique employed was a "black box" to them, and they did not know how to use the ISAG results. They asked for a single image in which the overextension of the port solar array could be obviously seen. On November 10, 2012, during a face-to-face meeting with their Russian counterparts at JSC, ISAG presented nadir-view imagery of the FGB acquired during Space Shuttle rendezvous. Using the known width of the pressurized portion of the FGB as a scale, this analysis clearly showed that the port FGB solar array was extended outboard further than the Russian design for the retracted solar array.

Liddle, Donn↗

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.

Bainum, P. M.↗

On the dynamics of large orbiting flexible beams and platforms oriented along the local horizontal

The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.

Bainum, P. M.↗

Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

Chuang, Ching H.↗