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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Dynamic Response of a Semiactive Suspension System with Hysteretic Nonlinear Energy Sink Based on Random Excitation by means of Computer Simulation

This paper aims to investigate the property and behavior of the hysteretic nonlinear energy sink (HNES) coupled to a half vehicle system which is a nine-degree-of-freedom, nonlinear, and semiactive suspension system in order to improve the ride comfort and increase the stability in shock mitigation by using the computer simulation method. The HNES model is a semiactive suspension device, which comprises the famous Bouc–Wen (B-W) model employed to describe the force produced by both the purely hysteretic spring and linear elastic spring of potentially negative stiffness connected in parallel, for the half vehicle system. Nine nonlinear motion equations of the half vehicle system are derived in terms of the seven displacements and the two dimensionless hysteretic variables, which are integrated numerically by employing the direct time integration method for studying both the variables of vertical displacements, velocities, accelerations, chassis pitch angle, and the ride comfort and driver safety, respectively, based on the bump and random road inputs of the pseudoexcitation method as excitation signal. Simulation results show that, compared with the HNES model and the magnetorheological (MR) model coupled to the half vehicle system, the ride comfort and stability have been evidently improved. A successful validation process has been performed, which indicated that both the ride comfort and driver safety properties of the HNES model coupled to half vehicle significantly improved.

Chen, Hui↗
NASA NTRS1979

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.

Bainum, P. M.↗
NASA NTRS1986

A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1986

A combined integrating- and differentiating-matrix formulation for boundary-value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1988

Problems in fluid dynamics

A scheme was developed for the parametric differentiation and integration of gas dynamics equations. A numerical integration of the gas dynamics equations is necessarily performed for a specific set of parameter values. The linear variational equations are obtained by differentiating the exact equations with respect to each of the relevant parameters. The resulting matrix of flow quantities is referred to as the Jacobi matrix. The subsequent procedure is then straightforward. The method was tested for two dimensional supersonic flow past an airfoil, with airfoil thickness, camber, and angle of attack varied. This approach has great potential value for rapidly assessing the effect of design changes. The other focus of the work was on problems in fluid stability, bifurcations, and turbulence.

Sirovich, Lawrence↗
NASA NTRS1991

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility being the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements. Recent efforts have focused on reducing run time, improving accuracy and adding more boundary condition choices.

Klang, Eric C.↗
NASA NTRS1990

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility is the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements.

Owen, Vicki L.↗
NASA NTRS1995

High-speed correction factor to the O(+)-O resonance charge exchange collision frequency

The high-speed correction factor to the O(+)-O collision frequency, resulting from drift velocities between ions and neutrals, is calculated by solving the integral expression in this factor both numerically and analytically. Although the analytic solution is valid for either small or large drift velocities between ions and neutrals, for temperatures of interest and all drift velocities considered, agreement is found between analytic and detailed numerical integration results within less than 1% error. Let T(sub r) designate the average of the ion and neutral temperatures in K, and u = nu(sub d)/alpha, where nu(sub d) is the relative drift velocity in cm/s, and alpha = 4.56 x 10(exp 3) square root of T(sub r) cm/s is the thermal velocity of the O(+)-O system. Then, as u ranges from 0 to 2, the correction factor multiplying the collision frequency increases monotonically from 1 to about 1.5. An interesting result emerging from this calculation is that the correction factor for temperatures of aeronomical interest is to a good approximation independent of the temperature, depending only on the scaled velocity u.

Omidvar, K.↗
NASA NTRS1984

A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.

Radhakrishnan, K.↗
DOE OSTI2022

m-CUBES An efficient and portable implementation of multi-dimensional integration for gpus

The task of multi-dimensional numerical integration is frequently encountered in physics and other scientific fields, e.g., in modeling the effects of systematic uncertainties in physical systems and in Bayesian parameter estimation. Multi-dimensional integration is often time-prohibitive on CPUs. Efficient implementation on many-core architectures is challenging as the workload across the integration space cannot be predicted a priori. We propose m-Cubes, a novel implementation of the well-known Vegas algorithm for execution on GPUs. Vegas transforms integration variables followed by calculation of a Monte Carlo integral estimate using adaptive partitioning of the resulting space. m-Cubes improves performance on GPUs by maintaining relatively uniform workload across the processors. As a result, our optimized Cuda implementation for Nvidia GPUs outperforms parallelization approaches proposed in past literature. We further demonstrate the efficiency of m-Cubes by evaluating a six-dimensional integral from a cosmology application, achieving significant speedup and greater precision than the CUBA library's CPU implementation of VEGAS. We also evaluate m-Cubes on a standard integrand test suite. m-Cubes outperforms the serial implementations of the Cuba and GSL libraries by orders of magnitude speedup while maintaining comparable accuracy. Our approach yields a speedup of at least 10 when compared against publicly available Monte Carlo based GPU implementations. In summary, m-Cubes can solve integrals that are prohibitively expensive using standard libraries and custom implementations. A modern C++ interface header-only implementation makes m-Cubes portable, allowing its utilization in complicated pipelines with easy to define stateful integrals. Compatibility with non-Nvidia GPUs is achieved with our initial implementation of m-Cubes using the Kokkos framework.

Sakiotis, Ioannis↗
NASA NTRS1984

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Radhakrishnan, K.↗
NASA NTRS1973

The Lyapunov stabilization of satellite equations of motion using integrals

A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.

Nacozy, P. E.↗
NASA NTRS1991

Biological production models as elements of coupled, atmosphere-ocean models for climate research

Process models of phytoplankton production are discussed with respect to their suitability for incorporation into global-scale numerical ocean circulation models. Exact solutions are given for integrals over the mixed layer and the day of analytic, wavelength-independent models of primary production. Within this class of model, the bias incurred by using a triangular approximation (rather than a sinusoidal one) to the variation of surface irradiance through the day is computed. Efficient computation algorithms are given for the nonspectral models. More exact calculations require a spectrally sensitive treatment. Such models exist but must be integrated numerically over depth and time. For these integrations, resolution in wavelength, depth, and time are considered and recommendations made for efficient computation. The extrapolation of the one-(spatial)-dimension treatment to large horizontal scale is discussed.

Platt, Trevor↗