Analogue-computer Simulation of an Autopilot Servo System Having Nonlinear Response Characteristics
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Jones, Arthur L↗
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Results for “nonlinear response”
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Stochastic Nonlinear Response of Woven CMCs
It is well known that failure of a material is a locally driven event. In the case of ceramic matrix composites (CMCs), significant variations in the microstructure of the composite exist and their significance on both deformation and life response need to be assessed. Examples of these variations include changes in the fiber tow shape, tow shifting/nesting and voids within and between tows. In the present work, the influence of scale specific architectural features of woven ceramic composite are examined stochastically at both the macroscale (woven repeating unit cell (RUC)) and structural scale (idealized using multiple RUCs). The recently developed MultiScale Generalized Method of Cells methodology is used to determine the overall deformation response, proportional elastic limit (first matrix cracking), and failure under tensile loading conditions and associated probability distribution functions. Prior results showed that the most critical architectural parameter to account for is weave void shape and content with other parameters being less in severity. Current results show that statistically only the post-elastic limit region (secondary hardening modulus and ultimate tensile strength) is impacted by local uncertainties both at the macro and structural level.
Kuang, C. Liu↗
A study of the nonlinear response of the upper atmosphere to episodic and stochastic acoustic‐gravity wave forcing
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Cissi Y. Lin↗
Energy conservation in the transient response of nonlinear beam vibration problems subjected to pulse loading - A numerical approach
The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.
Moyer, E. T., Jr.↗
The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.
Rizzi, Stephen A.↗
A theoretical and experimental investigation of the linear and nonlinear impulse responses from a magnetoplasma column
Linear and nonlinear responses of a magnetoplasma resulting from inhomogeneity in the background plasma density are studied. The plasma response to an impulse electric field was measured and the results are compared with the theory of an inhomogeneous cold plasma. Impulse responses were recorded for the different plasma densities, static magnetic fields, and neutral pressures and generally appeared as modulated, damped oscillations. The frequency spectra of the waveforms consisted of two separated resonance peaks. For weak excitation, the results correlate with the linear theory of a cold, inhomogeneous, cylindrical magnetoplasma. The damping mechanism is identified with that of phase mixing due to inhomogeneity in plasma density. With increasing excitation voltage, the nonlinear impulse responses display stronger damping and a small increase in the frequency of oscillation.
Grody, N. C.↗
The Effect of Basis Selection on Static and Random Acoustic Response Prediction Using a Nonlinear Modal Simulation
An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.
Rizzi, Stephen A.↗
Some studies on the nonlinear dynamic response of shell-type structures.
Nonlinear dynamic response of thin walled shells of revolution
VIBRATION EFFECT↗
An approximate method for determining response of nonlinear dynamic systems to random disturbances
Approximation method for determining response of nonlinear dynamic systems to random disturbances
DYNAMIC RESPONSE↗
Nonlinear Acoustic Response of an Aircraft Fuselage Sidewall Structure by a Reduced-Order Analysis
A reduced-order nonlinear analysis of a structurally complex aircraft fuselage sidewall panel is undertaken to explore issues associated with application of such analyses to practical structures. Of primary interest is the trade-off between computational efficiency and accuracy. An approach to modal basis selection is offered based upon the modal participation in the linear regime. The nonlinear static response to a uniform pressure loading and nonlinear random response to a uniformly distributed acoustic loading are computed. Comparisons of the static response with a nonlinear static solution in physical degrees-of-freedom demonstrate the efficacy of the approach taken for modal basis selection. Changes in the modal participation as a function of static and random loading levels suggest a means for improvement in the basis selection.
Przekop, Adam↗
Nonlinear photorefractive response at high modulation depths
The response of photorefractive materials to sinusoidal intensity patterns of high modulation depths is considered. It is shown that the induced refractive-index response in this regime is highly nonlinear. Concise analytic expressions for the various nonlinear harmonics of the photorefractive response field are developed and compared with exact numerical solutions of the underlying charge-transport equations as well as with the results of previous theoretical models over a broad range of physical parameters. We show that the nonlinear response characteristics are strongly dependent on both the magnitude of applied electric fields and the relative concentrations of charge donor and acceptor sites in the material. For drift dominated recording, in particular, we determine analytically that in the limit of a minimal acceptor/donor ratio, the amplitudes of higher spatial harmonics of the response reach a maximum and eventually decay as functions of increasing applied field, whereas these amplitudes reach a nonzero limit in the case of a near-unity acceptor/donor ratio. Finally, we generalize our results to account for diffusion effects in an appended derivation.
Vachss, Frederick↗
Nonlinear transient responses of initially stressed composite plates
The nonlinear transient response of initially stressed composite plates is investigated using the finite element method. A nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions. In the time integration, the Newmark constant acceleration method in conjunction with an efficient and accurate iteration scheme is used. Numerical results for deflections and bending moments for isotropic and laminated plates are obtained.
Chen, J. K.↗
Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems
In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.
Gunter, E. J.↗
Triggering of longitudinal combustion instabilities in solid rocket motors: Nonlinear combustion response
Pulsed oscillations in solid rocket motors are investigated with emphasis on nonlinear combustion response. The study employs a wave equation governing the unsteady motions in a two-phase flow, and a solution technique based on spatial- and time-averaging. A wide class of combustion response functions is studied to second-order in fluctuation amplitude to determine if, when, and how triggered instabilities arise. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Based on the behavior of model dynamical systems, introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be the manner in which the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse.
Wicker, J. M.↗
Nonlinear random response prediction using MSC/NASTRAN
An equivalent linearization technique was incorporated into MSC/NASTRAN to predict the nonlinear random response of structures by means of Direct Matrix Abstract Programming (DMAP) modifications and inclusion of the nonlinear differential stiffness module inside the iteration loop. An iterative process was used to determine the rms displacements. Numerical results obtained for validation on simple plates and beams are in good agreement with existing solutions in both the linear and linearized regions. The versatility of the implementation will enable the analyst to determine the nonlinear random responses for complex structures under combined loads. The thermo-acoustic response of a hexagonal thermal protection system panel is used to highlight some of the features of the program.
Robinson, J. H.↗
The nonlinear viscoelastic response of resin matrix composite laminates
Possible treatments of the nonlinear viscoelastic behavior of materials are reviewed. A thermodynamic based approach, developed by Schapery, is discussed and used to interpret the nonlinear viscoelastic response of a graphite epoxy laminate, T300/934. Test data to verify the analysis for Fiberite 934 neat resin as well as transverse and shear properties of the unidirectional T300/934 composited are presented. Long time creep characteristics as a function of stress level and temperature are generated. Favorable comparisons between the traditional, graphical, and the current analytical approaches are shown. A free energy based rupture criterion is proposed as a way to estimate the life that remains in a structure at any time.
Hiel, C.↗
Nonlinear dynamic response of a uni-directional model for the tile/pad space shuttle thermal protection system
A unidirectional analysis of the nonlinear dynamic behavior of the space shuttle tile/pad thermal protection system is developed and examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. The analysis accounts for the highly nonlinear stiffening hysteresis and viscous behavior of the pad which joins the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude. Analytical studies indicate that with still higher amplitude the resonant frequency increases slowly. The nonlinear pad is also responsible for the analytically and experimentally observed distorted response wave shapes having high sharp peaks when the system is subject to sinusoidal loads. Furthermore, energy dissipation in the pad is studied analytically and it is found that the energy dissipated is sufficiently high to cause rapid decay of dynamic transients. Nevertheless, the sharp peaked nonlinear responses of the system lead to higher magnification factors than would be expected in such a highly damped linear system.
Housner, J. M.↗
Volterra Series Approach for Nonlinear Aeroelastic Response of 2-D Lifting Surfaces
The problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via Volterra series approach is addressed. The related aeroelastic governing equations are based upon the inclusion of structural nonlinearities, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of geometric nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.
Silva, Walter A.↗