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Nonequilibrium system representation by statistical mechanical ensemble expressing time correlation function for linear/nonlinear transport coefficients
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.
Measurement of Volterra kernels of finite order nonlinear system
Accelerating convergence of discretization algorithms of approximate solution of nonlinear operator equations
Bounded topologies are considered for functional differential equations of the neutral type in which present dynamics of the system are influenced by its past behavior. A special bounded topology is generated on a collection of absolutely continuous functions with essentially bounded derivatives, and an application to a class of nonlinear neutral functional differential equations due to Driver (1965) is presented.
Describing-function analysis of launch vehicle stability with nonlinear thrust vectoring
Empirical orthogonal function modeling is explained and applied to identify compact discrete-time nonlinear unsteady aerodynamic models from data generated by an unsteady three-dimensional compressible Navier-Stokes flow solver for an airfoil undergoing various pitching motions. Model structures, model parameter estimates, and model parameter uncertainty estimates for nondimensional lift, drag, and pitching moment coefficient models were determined autonomously and directly from the data. Prediction tests using data that were not used in the modeling process showed that the identified models exhibited excellent prediction capability, which is a strong indicator of an accurate model.
Optimum state variable selection to determine constraints for nonlinear system stability, using Liapunov second method
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
We have developed a Matlab toolbox for wavefront control of optical systems. We have applied this toolbox to the optical models of James Webb Space Telescope (JWST) in general and to the JWST Testbed Telescope (TBT) in particular, implementing both unconstrained and constrained wavefront optimization to correct for possible misalignments present on the segmented primary mirror or the monolithic secondary mirror. The optical models implemented in Zemax optical design program and information is exchanged between Matlab and Zemax via the Dynamic Data Exchange (DDE) interface. The model configuration is managed using the XML protocol. The optimization algorithm uses influence functions for each adjustable degree of freedom of the optical mode. The iterative and non-iterative algorithms have been developed to converge to a local minimum of the root-mean-square (rms) of wavefront error using singular value decomposition technique of the control matrix of influence functions. The toolkit is highly modular and allows the user to choose control strategies for the degrees of freedom to be adjusted on a given iteration and wavefront convergence criterion. As the influence functions are nonlinear over the control parameter space, the toolkit also allows for trade-offs between frequency of updating the local influence functions and execution speed. The functionality of the toolbox and the validity of the underlying algorithms have been verified through extensive simulations.
A method for improving the efficiency of nonlinear structural analysis by the use of global displacement functions is presented. The computer programs include options to define the global functions as input or let the program automatically select and update these functions. The program was applied to a number of structures: (1) 'pear-shaped cylinder' in compression, (2) bending of a long cylinder, (3) spherical shell subjected to point force, (4) panel with initial imperfections, (5) cylinder with cutouts. The sample cases indicate the usefulness of the procedure in the solution of nonlinear structural shell problems by the finite element method. It is concluded that the use of global functions for extrapolation will lead to savings in computer time.
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.
Asymptotic rate of convergence of Gauss-Seidel type iterative processes for nonlinear difference equations
A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.
Controlling time variable nonlinear multivariable systems using Lipunous direct method