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Parameter and matrix solution techniques for analyzing forced vibrations response of damped multidegree of freedom systems
The Green's function method and the computer program SOUSSA (Steady Oscillatory and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed. The Green's function method is applied to the fully unsteady potential equation yielding an integro-differential-delay equation. This equation is approximated by a set of differential-delay equations in time using the finite element method. The Laplace transform is used to yield a matrix relating the velocity potential to the normal wash. The matrix of the generalized aerodynamic forces is obtained by premultiplying and postmultiplying the matrices relating generalized forces to the potential and the normal wash by the generalized coordinates. The program SOUSSA is compared with existing numerical results. Results indicate that the program is not only general, flexible, and easy to use, but also accurate and fast.
A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.
There exists a plethora of ice adhesion testing methods such as centrifuge-based methods, push/pull methods, and lap joint shear tests. However, these methods often cannot be done in-situ during an icing spray and require researcher handling/preparation prior to testing. Additionally, many of these methods test ice accretions that are not representative of the ice shapes that grow on airframes which can have unintended consequences such as edge or corner stress concentrations. In order to mitigate the issues present with other ice adhesion tests a novel, hands-free, in-situ test method imbedded into the leading edge of the airfoil has been developed and tested in the NASA Glenn Research Center Icing Research Tunnel. The mechanics of the new test method are discussed with finite element simulations being used to highlight the fundamental mechanics of this test method. The testing procedures used during the experimental test campaign are discussed along with the icing cloud test matrix. Analysis of the force-displacement results highlights the repeatability of the test method with regards to both sample behavior across several days of testing and different ice shapes. The results from first run of the day showed a significant discrepancy from subsequent runs and differential image analysis was used to determine differences in the interfacial bonding states between runs.
There exists a plethora of ice adhesion testing methods such as centrifuge-based methods, push/pull methods, and lap joint shear tests. However, these methods often cannot be done in-situ during an icing spray and require researcher handling/preparation prior to testing. Additionally, many of these methods test ice accretions that are not representative of the ice shapes that grow on airframes which can have unintended consequences such as edge or corner stress concentrations. In order to mitigate the issues present with other ice adhesion tests a novel, hands-free, in-situ test method imbedded into the leading edge of the airfoil has been developed and tested in the NASA Glenn Research Center Icing Research Tunnel. The mechanics of the new test method are discussed with finite element simulations being used to highlight the fundamental mechanics of this test method. The testing procedures used during the experimental test campaign are discussed along with the icing cloud test matrix. Analysis of the force-displacement results highlights the repeatability of the test method with regards to both sample behavior across several days of testing and different ice shapes. The results from first run of the day showed a significant discrepancy from subsequent runs and differential image analysis was used to determine differences in the interfacial bonding states between runs.
A report presents an algorithm that solves the following problem: Allocate the force and/or torque to be exerted by each thruster and reaction-wheel assembly on a spacecraft for best performance, defined as minimizing the error between (1) the total force and torque commanded by the spacecraft control system and (2) the total of forces and torques actually exerted by all the thrusters and reaction wheels. The algorithm incorporates the matrix vector relationship between (1) the total applied force and torque and (2) the individual actuator force and torque values. It takes account of such constraints as lower and upper limits on the force or torque that can be applied by a given actuator. The algorithm divides the aforementioned problem into two optimization problems that it solves sequentially. These problems are of a type, known in the art as semi-definite programming problems, that involve linear matrix inequalities. The algorithm incorporates, as sub-algorithms, prior algorithms that solve such optimization problems very efficiently. The algorithm affords the additional advantage that the solution requires the minimum rate of consumption of fuel for the given best performance.
Friction Stir Welding (FSW) is a new solid state process for joining metals by plasticizing and consolidating materials around the bond line using thermal energy producing from frictional forces. A feasibility study for FSW of Metal Matrix Composites (MMC) was investigated using aluminum 6092 alloy reinforced with 17% SiC particulates. FSW process consists of a special rotating pin tool that is positioned to plunge into the MMC surface at the bond line. As the tool rotates and move forward along the bond line, the material at the bond line is heated up and forced to flow around the rotating tip to consolidate on the tip's backside to form a solid state joint. FSW has the potential for producing sound welds with MMC because the processing temperature occurs well below the melting point of the metal matrix; thereby eliminating the reinforcement-to-matrix solidification defects, reducing the undesirable chemical reactions and porosity problems.
Structured grid solvers such as NASA's OVERFLOW compressible Navier-Stokes flow solver can generate large data files that contain convergence histories for flow equation residuals, turbulence model equation residuals, component forces and moments, and component relative motion dynamics variables. Most of today's large-scale problems can extend to hundreds of grids, and over 100 million grid points. However, due to the lack of efficient tools, only a small fraction of information contained in these files is analyzed. OVERSMART (OVERFLOW Solution Monitoring And Reporting Tool) provides a comprehensive report of solution convergence of flow computations over large, complex grid systems. It produces a one-page executive summary of the behavior of flow equation residuals, turbulence model equation residuals, and component forces and moments. Under the automatic option, a matrix of commonly viewed plots such as residual histograms, composite residuals, sub-iteration bar graphs, and component forces and moments is automatically generated. Specific plots required by the user can also be prescribed via a command file or a graphical user interface. Output is directed to the user s computer screen and/or to an html file for archival purposes. The current implementation has been targeted for the OVERFLOW flow solver, which is used to obtain a flow solution on structured overset grids. The OVERSMART framework allows easy extension to other flow solvers.
A new method of control for telemanipulators called bilateral impedance control is investigated. This new method differs from previous approaches in that interaction forces are used as the communication signals between the master and slave robots. The new control architecture has several advantages: (1) It allows the master robot and the slave robot to be stabilized independently without becoming involved in the overall system dynamics; (2) It permits the system designers to arbitrarily specify desired performance characteristics such as the force and position ratios between the master and slave; (3) The impedance at both ends of the telerobotic system can be modulated to suit the requirements of the task. The main goals of the research are to characterize the performance and stability of the new control architecture. The dynamics of the telerobotic system are described by a bond graph model that illustrates how energy is transformed, stored, and dissipated. Performance can be completely described by a set of three independent parameters. These parameters are fundamentally related to the structure of the H matrix that regulates the communication of force signals within the system. Stability is analyzed with two mathematical techniques: the Small Gain Theorem and the Multivariable Nyquist Criterion. The theoretical predictions for performance and stability are experimentally verified by implementing the new control architecture on a multidegree of freedom telemanipulator.
This paper presents the theory and an evaluation of a spatial sine testing parameter estimation algorithm that uses directly the measured forced mode of vibration and the measured force vector. The parameter estimation algorithm uses an ARMA model and a recursive QR algorithm is applied for data reduction. In this first evaluation, the algorithm has been applied to a frequency response matrix (which is a particular set of forced mode of vibration) using a sliding frequency window. The objective of the sliding frequency window is to execute the analysis simultaneously with the data acquisition. Since the pole values and the modal density are obtained from this analysis during the acquisition, the analysis information can be used to help determine the forcing vectors during the experimental data acquisition.
Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.
A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.
Discrete element method for plastic analysis of complex built-up structures subjected to cyclic loading causing membrane stress and stress reversal
A variational method is used to obtain vibrational-rotational properties for ozone from an experimental quartic force field. Band positions, average structures, matrix elements for calculating infrared intensities, and effective rotational constants are reported for (O-16)3 and its O-18 isotopic species. Also, the degree to which the vibrational energies and properties are converged is investigated as a function of the basis set parameters and basis set size, and of the method of obtaining the Hamiltonian matrix elements. A convenient procedure for assigning the vibrational states is developed for variational vibrational wavefunction expansions.
A computational technique has been developed for performing preliminary design aeroelastic analyses of large aspect ratio lifting surfaces. This technique, applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. An integrating matrix is employed to solve these equations for divergence and flutter eigenvalues and steady aeroelastic deformation. Results are presented for simple examples which verify the technique and demonstrate how it can be applied to analyze lifting surfaces, including those constructed from composite materials.
A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques.
A system identification analysis was performed to determine reduced-order models of a computational fluid dynamics (CFD) solver for linear aeroelastic analysis and control design. The application was to the FUN3D code and the flexible half-span wind tunnel test article, in transonic flow conditions, used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. Multiple inputs (structural mode displacements and control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines and multiple outputs (generalized aerodynamic forces) were recorded, from which the matrix of frequency responses were computed using a single CFD run. A state-space model was then fit to the frequency response data using a maximum-likelihood estimator.
Computational aspects of (1) flutter optimization (minimization of structural mass subject to specified flutter requirements), (2) methods for solving the flutter equation, and (3) efficient methods for computing generalized aerodynamic force coefficients in the repetitive analysis environment of computer-aided structural design are discussed. Specific areas included: a two-dimensional Regula Falsi approach to solving the generalized flutter equation; method of incremented flutter analysis and its applications; the use of velocity potential influence coefficients in a five-matrix product formulation of the generalized aerodynamic force coefficients; options for computational operations required to generate generalized aerodynamic force coefficients; theoretical considerations related to optimization with one or more flutter constraints; and expressions for derivatives of flutter-related quantities with respect to design variables.