John Dugundji

Theoretical considerations of panel flutter at high supersonic Mach numbers.

The general characteristics of panel flutter at high supersonic Mach numbers are examined theoretically. Linear plate theory and two-dimensional first-order aerodynamics are used. The paper attempts to clarify the important role of damping, the relationship between traveling and standing wave theories of panel flutter, and the effects of edge conditions. The solution procedures and general mathematical behavior may be of interest in other stability problems characterized by the appearance of complex eigenvalues.

Modeling and experimental verification of proof mass effects on vibration energy harvester performance

An electromechanically coupled model for a cantilevered piezoelectric energy harvester with a proof mass is presented. Proof masses are essential in microscale devices to move device resonances towards optimal frequency points for harvesting. Such devices with proof masses have not been rigorously modeled previously; instead, lumped mass or concentrated point masses at arbitrary points on the beam have been used. Thus, this work focuses on the exact vibration analysis of cantilevered energy harvester devices including a tip proof mass. The model is based not only on a detailed modal analysis, but also on a thorough investigation of damping ratios that can significantly affect device performance. A model with multiple degrees of freedom is developed and then reduced to a single-mode model, yielding convenient closed-form normalized predictions of device performance. In order to verify the analytical model, experimental tests are undertaken on a macroscale, symmetric, bimorph, piezoelectric energy harvester with proof masses of different geometries. The model accurately captures all aspects of the measured response, including the location of peak-power operating points at resonance and anti-resonance, and trends such as the dependence of the maximal power harvested on the frequency. It is observed that even a small change in proof mass geometry results in a substantial change of device performance due not only to the frequency shift, but also to the effect on the strain distribution along the device length. Future work will include the optimal design of devices for various applications, and quantification of the importance of nonlinearities (structural and piezoelectric coupling) for device performance.

Nonlinear Stall Flutter and Divergence Analysis of Cantilevered Graphite/Epoxy Wings

The nonlinear, stalled, aeroelastic behavior of rectangular, graphite/epoxy, cantilevered wings with varying amount of bending-torsi on stiffness coupling is investigated. A nonlinear aeroelastic analysis is developed using the nonlinear, stalled ONERA aerodynamic model initially presented by Tran and Petot. Nonlinear flutter calculations are carried out using Fourier analysis to extract the harmonics from the ONERA aerodynamics, then a harmonic balance method and a Newton-Raphson solver are applied to the resulting nonlinear, Rayleigh-Ritz aeroelastic formulation. Test wings were constructed and subjected to wind-tunnel tests for comparison against the developed analysis. Wind-tunnel tests show reasonable agreement between theory and experiment for static deflections, for linear flutter and divergence, and for nonlinear, torsional stall flutter and bending stall flutter limit cycles. The current nonlinear analysis shows a transition from divergence to bending stall flutter, which linear analyses are unable to predict.

Perturbation and harmonic balance methods for nonlinear panel flutter.

A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clampe d plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.

Postbuckling behavior of laminated plates using a direct energy-minimization technique

The postbuckling behavior of rectangular, flat, laminated, or sandwich plates is investigated using a model including the different anisotropic material coupling terms, the effect of transverse shear deformation, nonlinear strains, and initial out-of-plane imperfections. The Rayleigh-Ritz method is used to discretize the problem and, instead of solving a set of partial-diffe rential equations, a direct energy-minimization technique is used to solve the problem numerically. The solution procedure used is described in detail in the first part of this paper, and the results obtained for three example problems are presented in the second part. These results correlate well with corresponding experimental data that are also presented.

Joint damping and nonlinearity in dynamics of space structures

Analysis of the effect of linear joint characteristics on the vibration of a free-free, three-joint beam model shows that increasing joint damping increases resonant frequencies and modal damping, but only to the point at which the joint gets «locked up» by damping. The maximum amount of passive modal damping obtainable from the joints is greater for low-stiffness joints and for modal vibrations where large numbers of joints are actively participating. A joint participation factor is defined to study this phenomenon. Analysis of the nonlinear three-joint model, with cubic spring at the joints, shows classical single-degree-of-freedom nonlinear response behavior at each resonance of the multiple-degree-of-freedom

Buckling and Failure of Sandwich Plates with Graphite-Epoxy Faces and Various Cores

A study of the compressive failure of sandwich plates was conducted. Twenty-one panels (250 X 250 mm) were manufactured with [ + 457 - 45/0 ]s graphite-epoxy face sheets and three types of cores- Nomex honeycomb, Rohacell foam, and aluminum honeycomb-in three different thicknesses - 3.2, 6.4, and 9.6 mm. These panels were tested under uniaxial compression with clamped loaded edges and simply supported sides, and overall buckling was the only type of instability that was observed here. The effects of these different cores were investigated, and three types of failure modes were observed - core failure, disbond, and face fracture. Initial out-of-plane imperfections were found to have an important effect on the final failure load for thick panels but only a small influence for thin panels. Using the stresses predicted by a nonlinear analysis and appropriate failure criteria, namely maximum transverse shear stress for the core or bond failure and stress interaction for the face fracture, failure load predictions that are in good agreement with the experimental data can be made.

Size effect of flexible proof mass on the mechanical behavior of micron-scale cantilevers for energy harvesting applications

Mechanical behavior of micron-scale cantilevers with a distributed, flexible proof mass is investigated to understand proof mass size effects on the performance of microelectromechanical system energy harvesters. Single-crystal silicon beams with proof masses of various lengths were fabricated using focused ion beam milling and tested using atomic force microscopy. Comparison of three different modeling results with measured data reveals that a “two-beam” method has the most accurate predictive capability in terms of both resonant frequency and strain. Accurate strain prediction is essential because energy harvested scales with strain squared and maximum strain will be a design limit in fatigue.

Efficiency of piezoelectric mechanical vibration energy harvesting

Harvesting efficiency of a piezoelectric vibration energy harvesting system is investigated to provide design guidelines for harvesting devices with optimal performance. Harvesting power efficiency (η), defined as the ratio of device output power (Pout) to mechanical input power (Pin), is an essential but unexplored metric for comparison of harvesters operating in different power-input environments. Power extracted from piezoelectric harvesters has been of primary interest and proper accounting of mechanical input power and efficiency metrics has not been considered. Here, we present a closed form solution for harvesting efficiency that allows device comparison and furthermore, efficiency-optimized versus power-optimized electrical loading conditions are compared along with a case study. A key finding is that optimal design parameters for efficiency are quite different than optima for output power (e.g., a single optimum versus dual optima at different frequencies), requiring multi-objective design. These new findings provide guidelines on system parameters that can be manipulated for optimized performance in different ambient source conditions.

Analytical extraction of residual stresses and gradients in MEMS structures with application to CMOS-layered materials

Accurate thin-film characterization is a key requirement in the MEMS industry. Residual stresses determine both the final shape and the functionality of released micromachined structures, and should therefore be accurately assessed. To date, a number of techniques to characterize thin-film materials have been developed, from substrate curvature measurement to methods that exploit the post-release deformation of test structures. These techniques have some major drawbacks, from high implementation costs to accuracy limitations due to improper boundary condition modeling. Here, we present a new technique for the characterization of multilayered, composite MEMS structures that uses easily accessible experimental information on the post-release deformation of microbridges only, with no need for multiple beam lengths. The method is based on an analytical solution of the (post-)buckling problem of microbridges, including the effect of residual stresses (both mean and gradient) and non-ideal clamping (boundary flexibility). The method allows simultaneous characterization of both the mean and the gradient residual stress components, as well as the effective boundary condition associated with the fabrication process, yielding approximately one order of magnitude improvement in resolution compared to extant methods using the same type and number of test structures. The higher resolution is largely attributable to proper accounting for boundary flexibility by our method, with the boundary condition for the structures in this work being ~90% as stiff in bending relative to the commonly assumed perfectly clamped condition. Additional enhancement can be achieved with post-release deformation measurements of simple cantilevers in addition to the microbridges. The method is useful as it ensures very low stress extraction uncertainty using a limited number of microbridge test structures, and it is transferrable to package-stress characterization. The analytical approach can also be extended to device design, quantifying the effect of residual stresses and boundary flexibility on a structures post-release state.