Stephen A. Rizzi

Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures

A novel method for determining the nonlinear modal stiffness coefficients for an arbitrary finite element model is presented. The method is applicable to a wide class of problems exhibiting bending-membrane coupling and is suitable for use with commercial finite element codes having a geometrically nonlinear static capability. The equations of motion are written in modal coordinates with the nonlinear stiffness force components written as the product of second and third order modal displacements multiplied by unknown coefficients. Prescription of particular displacement fields renders a series of inverse linear and nonlinear static problems, which are solved to determine the unknown coefficients. Verification of stiffness coefficients found using this method and their use in equivalent linearization random vibration analysis are presented.

Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Modal bases having symmetric transverse displacements and modal bases having anti-symmetric transverse displacements may each be either transverse dominated or in-plane dominated. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of transverse dominated modes having a symmetric transverse displacement is important for all response regimes, it is found that the in-plane dominated modes having a symmetric transverse displacement become increasingly important in the nonlinear response regime. In the autoparametric response regime, the inclusion of both transverse and in-plane dominated modes, each with an anti-symmetric transverse displacement distribution, is found to be critical.

Dynamic Snap-Through of Thin-Walled Structures by a Reduced Order Method

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced order analysis, four categories of modal basis functions are identified including those having symmetric transverse (ST), anti-symmetric transverse (AT), symmetric in-plane (SI), and anti-symmetric in-plane (AI) displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the AT and SI modes must be included in the basis as they participate in the snap-through behavior.

Experimental snap-through boundaries for acoustically excited, thermally buckled plates

AbstractThis paper presents some recent experimental results on the dynamic snap-through behavior of a clamped, rectangular plate subject to thermal loading and intense acoustic excitation. The likelihood of snap-through oscillations is characterized in terms of boundaries separating regions of snap-through and no snap-through in the parameter space. Two scenarios are considered. First, using tonal inputs, the regions of snap-through are mapped in the sound pressure level—input frequency domain ((SPL, ω) plane). Second, random acoustic inputs are used, and the effect of varying the overall sound pressure level and frequency bandwidth are investigated ((SPL,

Piezoelectric Shunt Vibration Damping of F-15 Panel under High Acoustic Excitation

\omega _{center} + \bar \omega

Auralization of Hybrid Wing–Body Aircraft Flyover Noise from System Noise Predictions

) plane). Several nonlinear characteristics are evident and discussed.

Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions

*† A new capability has been developed for the creation of virtual environments for the study of aircraft community noise. It is applicable for use with both recorded and synthesized aircraft noise. When using synthesized noise, a three-stage process is adopted involving non-real-time prediction and synthesis stages followed by a real-time rendering stage. Included in the prediction-based source noise synthesis are temporal variations associated with changes in operational state, and low frequency fluctuations that are present under all operating conditions. Included in the rendering stage are the effects of spreading loss, absolute delay, atmospheric absorption, ground reflections, and binaural filtering. Results of prediction, synthesis and rendering stages are presented.

High‐temperature fiber‐optic lever microphone

At last years SPIE symposium, we reported results of an experiment on structural vibration damping of an F-15 underbelly panel using piezoelectric shunting with five bonded PZT transducers. The panel vibration was induced with an acoustic speaker at an overall sound pressure level (OASPL) of about 90 dB. Amplitude reductions of 13.45 and 10.72 dB were achieved for the first and second modes, respectively, using single- and multiple-mode shunting. It is the purpose of this investigation to extend the passive piezoelectric shunt- damping technique to control structural vibration induced at higher acoustic excitation levels, and to examine the controllability and survivability of the bonded PZT transducers at these high levels. The shunting experiments was performed with the Thermal Acoustic Fatigue Apparatus (TAFA) at the NASA Langley Research Center using the same F-15 underbelly panel. The TAFA is a progressive wave tube facility. The panel was mounted in one wall of the TAFA test section using a specially designed mounting fixture such that the panel was subjected to grazing-incidence acoustic excitation. Five PZT transducers were used with two shunt circuits designed to control the first and second modes of the structure between 200 and 400 Hz. We first determined the values of the shunt inductance and resistance at an OASPL of 130 dB. These values were maintained while we gradually increased the OASPL from 130 to 154 dB in 6-dB steps. During each increment, the frequency response function between accelerometers on the panel and the acoustic excitation measured by microphones, before and after shunting, were recorded. Good response reduction was observed up to the 148dB level. The experiment was stopped at 154 dB due to wire breakage from vibration at a transducer wire joint. The PZT transducers, however, were still bonded well on the panel and survived at this high dB level. We also observed shifting of the frequency peaks toward lower frequency when the OASPL was increased. Detailed experimental results will be presented.