An Efficient Reduced Order Modeling Technique for Nonlinear Vibration Analysis of Structures with Intermittent Contact

Bilinear modal representations for reduced-order modeling of localized piecewise-linear oscillators

Application of boundary-domain element method to the free vibration problem of plate structures

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The effects of small, random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of Component Mode Synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact interaction in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack, as well as vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared to those obtained with linear ROMs as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar those of mistuning, differences between the effects of mistuning and damage can be discerned by observing and comparing the response across different families of system modes.

Smart and e-textiles have nowadays an important increasing place in the garment industry. The rise of embedded telecommunications, especially smartphones in our pocket, enables us to provide a power source and a wireless link for smart textiles. The main issue is to develop garments able to receive power from smartphones and communicate with them without flexibility and comfort constraints bound to embedded solid-state electronic components. Consequently, this article aims to develop a fully textile NFC combiner to transfer data and power between a smartphone and sensors without any electronic components. It precisely describes textile NFC multiple combiners composed of textile NFC antennas linked by two-wire transmission lines. Also, theoretical analysis, simulations, and experiments have been conducted to adapt the resonant frequency of such structures to the NFC technology (13.56 MHz). Finally, our article generalizes textile NFC combiner resonant frequency equations for multiple combiners with any number of antennas.

The research aims at an experimental approval of the trapping mode effect theoretically predicted for an elastic plate-like structure with a horizontal crack. The effect is featured by a sharp capture of incident wave energy at certain resonance frequencies with its localization between the crack and plate surfaces in the form of energy vortices yielding long-enduring standing waves. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete frequency spectrum. To detect such resonance motion, a laser vibrometer based system has been employed for the acquisition and appropriate visualization of piezoelectrically actuated out-of-plane surface motion of a two-layer aluminum plate with an artificial strip-like delamination. The measurements at resonance and off-resonance frequencies have revealed a time-harmonic oscillation of good quality above the delamination in the resonance case. It lasts for a long time after the scattered waves have left that area. The measured frequency of the trapped standing-wave oscillation is in a good agreement with that predicted using the integral equation based mathematical model.

In 1986 Christian Soize and his co-workers at Office National d’Etudes et de Recherches Aérospatiales in Chatillon, France introduced the concepts of fuzzy structures to account for missing degrees of freedom in structural vibration problems. The elements of Soize’s methods have been recently outlined [J. Acoust. Soc. Am. 89, 1867 (1991)]. The present paper concerns the scattering of an incident plane wave from a fluid-loaded finite plate to which a discrete structural fuzzy has been attached. Analyses will be presented for cases where the frequency of the incident field is both above and below the cutoff frequency of the fuzzy attachment. Below the cutoff frequency the fuzzy adds an additional fluctuating mass term to the in-vacuo modal masses that contribute to the plate velocity solution. Above the cutoff frequency, one must account not only for the mass contribution of the attached fuzzy, but also for the fluctuating internal damping and modal density of the fuzzy. [Work supported by ONR.]

Very recent publications draw the attention to a possible revolution that nanotechnology can cause in aviation. The effervescence in the peak field of nanomaterials is remarkable, as evidenced by the number of Nobel prizes recently awarded. A class of nanomaterials, the nanosensors, whose object of study is the present work, represents a special interest in space applications. More specifically, this article proposes the synthesis of a nanosensor based on active control and manipulation of spin degrees of freedom in the graphene nanoribbons (GNR), the strongest known substance. Thus, the physical model, a GNR, is electrically connected to two electrodes. Different variations of Mn (Manganese) impurities in graphene, with the spins having preset configurations, are considered. When a magnetic field is detected, their spin change causing changes in the total energy and hence the variation of transmission function. Therefore, the concept of active control, which originated in the flight control and structural vibration problems, is naturally extended herein to the nanosensors synthesis. The used physico-mathematical model to determine the spin transport and the transmission function is based on density functional theory, Kohn-Sham equations and the SIESTA package. The differences between distinct GNR excited states were determined and it was established that the energy range overlaps the mid-infrared wavelengths. Therefore, structures of this kind may serve in spatial applications which exploit the infrared atmospheric window.

AN IMPROVED ROTOR MODEL WITH EQUIVALENT DYNAMIC EFFECTS OF THE SUPPORT STRUCTURE

This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending two standard Gauss-type quadrature rules. These blending rules approximate the inner products and increase the convergence rate by two extra orders when compared to those with fully-integrated inner products. To quantify the approximation errors, we generalize the Pythagorean eigenvalue error theorem of Strang and Fix. To reduce the computational cost, we further propose a two-point rule for C1 quadratic isogeometric elements which produces equivalent inner products on uniform meshes and yet requires fewer quadrature points than the optimally-blended rules.

Some effects of threshold singularities on a dynamical system with intermittent contact and breakage

A globally convergent method to accelerate topology optimization using on-the-fly model reduction

In this paper, we first present an efficient physical level simulation method for the dynamic analysis of electrostatic micro-electromechanical systems (MEMS). This method is then used to analyze MEMS dynamics. Stiffness hardening or softening of MEM structures has been shown to depend both on the applied voltage and the geometry. The existence of multiple resonant peaks in the frequency response diagram has been presented. We have shown that a DC bias along with an appropriate AC bias can give fast switching at a considerably less peak power requirement. Finally, a reduced order model has been developed based on Karhunen-Loeve decomposition for the dynamic simulation of MEMS. Reduced order models are cheap in terms of memory and computational time and are needed to perform fast and efficient system-level composite circuit and micro-mechanical simulations.

Successful application of fracture mechanics methodology to component fatigue life prediction requires knowledge of flight cycle loading, local stress and material conditions, da/dN characterization for the material, and the stress intensity factor(s) for the appropriate crack geometry(ies). It is generally assumed that all of the aforementioned conditions are well within current state-of-the-art design procedures for through-thickness cracks. It is further assumed that the part-through, surface crack stress intensity factor distribution is now sufficiently easily characterized that accurate fatigue life predictions can be made for this class of crack geometries. Major unresolved issues for surface cracks exist for small surface cracks, which are initiated within surface layers of machining stress and flight cycle-induced plastic zones near structural notches. The issues include definition of the material properties within the surface layer, unknown surface “values” of the stress intensity factor distribution, crack growth through highly varying stress/material property fields at the surface, and the applicability of macrocrack growth models to small cracks. Further experimental and analytical effort is required in order to achieve accurate fatigue life prediction design methodologies for small surface crack problems in real structures.

The reduction of the large order models of complex systems into a sufficiently low dimensional order in such a way that important dynamic characteristics of the real system are preserved, is a nontrivial task. The motivations for such a model order reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. In the present article, major techniques in model order reduction are briefly discussed. The characteristic similarities and differences are highlighted, their advantages and disadvantages are underlined, and further research requirements and trends are commented upon. Introduction and Perspective One of the central issues in the active control of complex systems such as large flexible space structures (LFSS) is the derivation of a correct mathematical model for both the controlled and the uncontrolled dynamical systems. Theoretically, there are infinitely many elastic modes or degrees of freedom (DOF) in the distributed parameter (DP) models of LFSS, usually with very low natural damping. Moreover, the flexible modes contribute to the actual deformation of the structure.' The truly infinite dimensional character of LFSS models has to be approximated by some fidelity finite (but usually very large) dimensional model. The normal approach taken by engineers to achieve this end is via modal models with a large number of modes that provide a reasonable representation of the spacecraft dynamic characteristics. However, a difficult problem still remains to be the development of a model of lowenough dimensional order that it can be utilized by the onboard controller, yet high enough dimensional order that it preserves the dynamic characteristics of the real system represented and controlled. The motivations for such a reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. Discretization procedures will not be discussed herein and it will be assumed that a large finite dimensional model has been generated somehow and for implementation and other practical considerations, the model needs to be further reduced. *This work was-supported, in part, by the Air Force Wright Aeronautical, Air Force Systems Command, Flight Dynamics Lab, Structures and Dynamics Division, while the author was employed with HR-Textron, Valencia, California. There are various approaches to model order reduction; some are or pseudo-optimal and others are ad-hoc methods based on practical considerations and engineering experience and judgment. These techniques are known by different names such as reduction, condensation, economization, aggregation, optimal projection, and other combinations thereof. It has often been pointed out that such techniques generally constitute application of Rayleigh-Ritz/Galerkin optimization, and matrix transformation methods to the eigenvalue/eigenvector formulation for structural dynamic problems. The reduction or the condensation methods are based on transformations of the coordinates in the equations of motion that essentially maintain the invariance of the quadratic forms of the potential and kinetic energies. An important feature of these methods is that the reduced order model often loses the basic characteristics of the original system. Considerable progress was made by Likins, Ohkami, and wong5 in this respect. However, they failed to develop a general enough criterion that could reduce the system model in an sense without significantly affecting the eigenvalues of the original model. The optimization or the mathematical reduction procedure, on the other hand, is based on the reduction of the eigenvalue problem to a smaller size based on some optimality criterion (usually quadratic). In these techniques, the reductions are carried out without actually resorting to approximations, i .e. , without truncatiag any coordinates or states of the original system. Balanced model reduction of linear timeinvariant dynamical systems is essentially based on the controllability and observability relations of the states of the system. Subsystem models are obtained by deleting those states that contribute the least to the controllability and observability (or the impulse response) of the original system7 and thus are only in this sense. A more recent approach to model reduction is proposed in Skelton's work,* where each state of the system model is assigned a relative to a given basis, via a quadratic criterion, and the states with the least cost are deleted in a systematic manner. The resulting reduced model is a function of the state-space basis, and thus there is no guarantee for optimality for all choices. The latest development in model order reduction techniques is the work by Hyland and erns stein.^ Herein first order necessary conditions for reduced order modeling of linear time-invariant systems are derived via a pair of modified Lyapunov equations coupled by a nonorthogonal projection. This approach reveals the possibility of multiple extrema forsome of the abovementioned methods. Copyright @ 1988 by the American Institute of Aeronautics and Astronautics. Inc. All Rights Reserved.

Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems. Such models typically exhibit a second-order structure and their material properties as well as their excitation may be depending on the driving frequency. We demonstrate the effectiveness of all considered methods in terms of their accuracy and computational cost by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic problems. The results of the experiments are extensively discussed to derive guidelines for the choice of model reduction methods based on the problem setting.