Full three-dimensional investigation of structural contact interactions in turbomachines

Minimizing the operating clearance between rotating bladed-disks and stationary surrounding casings is a primary concern in the design of modern turbomachines since it may advantageously affect their energy efficiency. This technical choice possibly leads to interactions between elastic structural components through direct unilateral contact and dry friction, events which are now accepted as normal operating conditions. Subsequent nonlinear dynamical behaviors of such systems are commonly investigated with simplified academic models mainly due to theoretical difficulties and numerical challenges involved in non-smooth large-scale realistic models. In this context, the present paper introduces an adaptation of a full three-dimensional contact strategy for the prediction of potentially damaging motions that would imply highly demanding computational efforts for the targeted aerospace application in an industrial context. It combines a smoothing procedure including bicubic B-spline patches together with a Lagrange multiplier based contact strategy within an explicit time-marching integration procedure preferred for its versatility.The proposed algorithm is first compared on a benchmark configuration against the more elaborated bi-potential formulation and the commercial software Ansys. The consistency of the provided results and the low energy fluctuations of the introduced approach underlines its reliable numerical properties. A case study featuring blade-tip/casing contact on industrial finite element models is then proposed: it incorporates component mode synthesis and the developed three-dimensional contact algorithm for investigating structural interactions occurring within a turbomachine compressor stage. Both time results and frequency-domain analysis emphasize the practical use of such a numerical tool: detection of severe operating conditions and critical rotational velocities, time-dependent maps of stresses acting within the structures, parameter studies and blade design tests.     

Different pathways in mechanical unfolding/folding cycle of a single semiflexible polymer

Kinetics of conformational change of a semiflexible polymer under mechanical external field were investigated with Langevin dynamics simulations. It is found that a semiflexible polymer exhibits large hysteresis in mechanical folding/unfolding cycle even with a slow operation, whereas in a flexible polymer, the hysteresis almost disappears at a sufficiently slow operation. This suggests that the essential features of the structural transition of a semiflexible polymer should be interpreted at least on a two-dimensional phase space. The appearance of such large hysteresis is discussed in relation to different pathways in the loading and unloading processes. By using a minimal two-variable model, the hysteresis loop is described in terms of different pathways on the transition between two stable states.     

A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization I

We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. This class is an asymmetric generalization of the class of Hamiltonians (Fannes et al. Commun Math Phys 144:443–490, 1992). It can be characterized by five qualitative physical properties of ground state structures. In this Part I, we introduce the models and investigate their properties.     

Forced vibration of a thin flexible cylinder in viscous flow

A thin, infinitely flexible cylinder in viscous axial flow is forced to vibrate by transverse motion of its upstream boundary condition and hydrodynamic forces due to arbitrary cross-flow components. This models a large-aspect-ratio cylindrical instrumentation package being towed in the ocean in which the “towpoint” has transverse motion and cross-currents exist. The governing momentum equation is derived as an extension to previous work by Ortloff and Ives [1], and the solution is studied. The response of the cylindrical structure to the two different forcing functions is quite different, although common physical elements exist. When the cylinder diameter is small relative to the wavelength of the forcing element, hydrodynamic forces dominate structural forces, and a unidirectional wave propagating downstream results. In the opposite limit, tension stiffness and velocity damping modify and complicate the response, but do not change the basic downstream-propagating induced wave.     

The role of non-linear theories in transient dynamic analysis of flexible structures

Transient dynamic analysis of flexible structures undergoing large motions is considered. For rotating structures, it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non-linear (at least second-order) beam theory. Use of a first-order (linearized) linear beam theory results in a spurious loss of bending stiffness. For a rotating plane beam, a set of linear partial differential equations of motion—that includes all inertia effects (Coriolis, centrifugal, acceleration of revolution) and coupling between extensional and flexural deformations—is derived from the fully non-linear beam theory by consistent linearization. The analysis is subsequently extended to the more general case of a plate, accomodating shear deformation, and undergoing a general three-dimensional rotating motion. The discretization process of the resulting linear equations of motion for the beam and the plate is also discussed.     

Nonlinear analysis of cylindrical and conical hysteretic whirl motions in rotor-dynamics

The internal friction of a rotor–shaft-support system is mainly due to the shaft structural hysteresis and to some possible shrink-fit release of the assembly. The experimentation points out the destabilizing effect of the internal friction in the over-critical rotor running. Nevertheless, this detrimental influence may be efficiently counterbalanced by other external dissipative sources located in the supports or by a proper anisotropic configuration of the support stiffness. The present analysis considers a rotor–shaft system which is symmetric with respect to the mid-span and is constrained by viscous-flexible supports with different stiffness on two orthogonal planes. The cylindrical and conical whirling modes are easily uncoupled and separately analysed. The internal dissipation is modelled by nonlinear Coulombian forces and moments, which counteract the translational and rotational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are solved by averaging approaches of the Krylov–Bogoliubov type. In both the over-critical whirling motions, cylindrical and conical, stable limit cycles may be attained whose amplitude is as large as the external dissipation applied by the supports is low. The stiffness anisotropy of the supports may be recognised as quite beneficial for the cylindrical whirl.     

Transverse hysteretic damping characteristics of a serpentine belt: Modeling and experimental investigation

In this paper, the transverse dynamic hysteretic damping characteristics (HDC) of a serpentine belt are investigated. The variable stiffness and variable damping model (VSDM) constituted of a variable-stiffness spring and a variable-damping damper is developed to estimate the HDC of the belt. A test rig is designed to test the force–displacement hysteresis damping curve and resonance frequencies of serpentine belts with different lengths under diverse loading conditions. The force–displacement hysteresis damping curve getting from the experiment is then used to determine the transverse stiffness and damping coefficients needed for the VSDM. The experiment particularly shows that the orientation of the hysteresis curve swings left and right around each natural frequency as it is a symmetrical point. This interesting phenomenon is explicated in detail with the loss angle which is calculated by two methods. Moreover, two sub-analytical models included in the VSDM are proposed to model the dependence of transverse dynamic stiffness and damping coefficient of a belt on belt length, pretension and excitation frequency. A comparison of the hysteresis curves obtained from the VSDM and experiment indicates that they are in good agreement.     

Internally resonating lattices for bandgap generation and low-frequency vibration control

The paper reports on a structural concept for high stiffness and high damping performance. A stiff external frame and an internal resonating lattice are combined in a beam-like assembly which is characterized by high frequency bandgaps and tuned vibration attenuation at low frequencies. The resonating lattice consists of an elastomeric material arranged according to a chiral topology which is designed to resonate at selected frequencies. The concept achieves high damping performance by combining the frequency-selective properties of internally resonating structures, with the energy dissipation characteristics of their constituent material. The flexible ligaments, the circular nodes and the non-central interactions of the chiral topology lead to dynamic deformation patterns which are beneficial to energy dissipation. Furthermore, tuning and grading of the elements of the lattice allows for tailoring of the resonating properties so that vibration attenuation is obtained over desired frequency ranges. Numerical and experimental results demonstrate the tuning flexibility of this concept and suggest its potential application for load-carrying structural members parts of vibration and shock prone systems.     

Controlling chaotic robots with kinematical redundancy

Robots with kinematical redundancy under the pseudoinverse control exhibit undesirable chaotic joint motion, which leads to erratic behaviors. In this study, we used the delayed feedback method to control chaotic motions of a planar 3R rigid and a planar 3R flexible redundant robot under the pseudoinverse control when the end-effector traces a closed-path repeatedly in the work space. It was demonstrated that chaotic motions of robots with kinematical redundancy can be turned into regular motion when the delayed feedback method was applied with some appropriate parameters. This study provides a new insight helpful to solve the repeatability problem of redundant manipulators.     

CAN: an example of nonclassical acoustic nonlinearity in solids

A new class of nonlinear acoustic phenomena has been observed for acoustic wave interaction with simulated and realistic nonbonded contact interfaces (cracked defects) in solids. "Nonclassical" effects are due to substantially asymmetric stiffness characteristics of the interface for normal stress that results in specific contact acoustic nonlinearity (CAN). The asymmetry in the contact restoring forces causes the stiffness parametric modulation and instability of oscillations, which results in acoustic wave fractional subharmonic generation. The CAN subharmonics and higher harmonics reveal threshold dynamic behaviour, evident hysteresis, and instability effects.     

A computational approach to calculating frequency-dependent structural operators using the spectral finite element method and a wavenumber-based gridding technique

Spectral finite element methods are used to compute exact vibration solutions of structural models at specific frequencies. The applicability of these methods to certain areas of structural dynamics is limited by two major factors: the lack of separate structural operators (mass, damping, and stiffness matrices), and the subsequent difficulty in computing mode shapes via eigenvalue decomposition. In the work presented in this article, a method is investigated to accurately calculate spectral finite elements while overcoming these limitations. The approach incorporates a two-dimensional, discrete solution utilizing a wavenumber-based gridding technique to compute frequency-dependent local mass, damping, and stiffness matrices which can be assembled into the global structural operators. Computed models are able to be used for precise vibration analysis as well as modal analysis via eigenvalue decomposition of the structural operators.     

振动结构耦合动刚度的间接逆子结构辨识方法

耦合动刚度是复杂耦合结构振动分析中的一个非常关键的参数,其精确辨识对于结构振动特性评估与控制设计非常重要。为将逆子结构动态分析方法推广应用于振动结构耦合动刚度辨识,在建立了耦合动刚度逆子结构分析模型后,提供一种通过频率响应函数反演耦合结构动刚度的方法——间接逆子结构辨识法。最后采用单点和三点耦合二级子结构“质量-胶垫”实验模型,验证了逆子结构辨识方法的理论有效性,包括辨识精度的误差分析.实验与理论分析结果的一致性表明,与现有的直接逆子结构动态分析方法相比,该方法较常规辨识方法具有适用条件范围更宽、辨识精度更高的优点,可以提高工程结构参数的辨识精度,具有更好的工程应用可行性与有效性,为逆子结构动态分析方法辨识振动结构耦合动刚度进一步提供理论依据。     

隔离段激波串流场特征的试验研究进展

高超声速推进技术是国际前沿研究, 其中双模态超燃冲压发动机的发展受到极大关注. 作为超燃冲压发动机的重要部件, 隔离段对发动机的性能和高超声速飞行的实现至关重要, 其中所涉及的流动机理问题也极为复杂. 自从高超声速飞行的概念被提出和论证以来, 相关的理论、试验和仿真研究不断取得进展, 但是对其中的机理问题研究仍有待进一步深入. 本文将从试验研究的角度回顾并综述近年来超燃冲压发动机隔离段的研究进展, 结合精细流动测试技术(Nano-tracer Planar Laser Scattering, NPLS)的发展分析了隔离段流场特征, 包括了激波串流场复杂的三维时空结构特点、湍流特性、非线性迟滞运动、不启动流场特征以及激波前缘检测等. 从风洞设备、隔离段设计、测试技术等方面对隔离段的试验研究进行了分类比较和论述, 对今后隔离段试验研究提出了建议.     

大口径光学元件重力变形补偿的设计分析

根据弹性板壳理论,建立了大口径光学元件的几种理论模型。提出了一种补偿大口径光学元件重力变形的方法,该方法通过在透镜镜框边缘施加作用力,使透镜产生与重力变形反向的挠性变形,抵消重力变形的影响。建立了带镜框的大口径透镜的分析模型,证明了通过优化施加力的大小和支撑点位置使透镜产生挠性变形的方法能有效消除重力变形的影响。     

Free vibrations of spatial Timoshenko arches

This paper addresses the evaluation of the exact natural frequencies and vibration modes of structures obtained by assemblage of plane circular arched Timoshenko beams. The exact dynamic stiffness matrix of the single circular arch, in which both the in-plane and out-of-plane motions are taken into account, is derived in an useful dimensionless form by revisiting the mathematical approach already adopted by Howson and Jemah (1999 [18]), for the in plane and the out-of-plan natural frequencies of curved Timoshenko beams. The knowledge of the exact dynamic stiffness matrix of the single arch makes the direct evaluation of the exact global dynamic stiffness matrix of spatial arch structures possible. Furthermore, it allows the exact evaluation of the frequencies and the corresponding vibration modes, for the distributed parameter model, through the application of the Wittrick and Williams algorithm. Consistently with the dimensionless form proposed in the derivation of the equations of motion and the dynamic stiffness matrix, an original and extensive parametric analysis on the in-plane and out-of-plane dynamic behaviour of the single arch, for a wide range of structural and geometrical dimensionless parameters, has been performed. Moreover, some numerical applications, relative to the evaluation of exact frequencies and the corresponding mode shapes in spatial arched structures, are reported. The exact solution has been numerically validated by comparing the results with those obtained by a refined finite element simulation.     

A multi-input multi-output adaptive feed-forward controller for vibration alleviation on a large blended wing body airliner

Turbulent atmosphere, gusts, and manoeuvres significantly excite aircraft rigid body motions and structural vibrations, which leads to reduced ride comfort and increased structural loads. In particular BWB (Blended Wing Body) aircraft configurations, while promising a significant fuel efficiency improvement compared to wing-tube configurations, exhibit severe sensitivity to gusts. In general, a flexible aircraft represents a lightly damped structure involving a large variety of uncertainties due to fuel mass variations during flight, control system nonlinearities, aerodynamic nonlinearities, and structural nonlinearities, to name just a few. Especially at the beginning of flight testing of a newly developed aircraft type, plant models generally require a lot of verification and adjustment based on obtained flight test data, before they can be used reliably for control law design. Adaptive control already is a well-established method for many active noise and vibration control problems, and thus is proposed here for application to the problem of gust load alleviation. However, safety requirements are significantly higher for gust load alleviation systems than for most noise and vibration control systems. This paper proposes a MIMO (Multi-Input Multi-Output) adaptive feed-forward controller for the alleviation of turbulence-induced rigid body motions and structural vibrations on aircraft. The major contribution to the research field of active noise and vibration control is the presentation of a detailed stability analysis of the MIMO adaptive algorithm in order to support potential certification of this method for a safety-critical application. Finally, the proposed MIMO adaptive feed-forward vibration controller is applied to a longitudinal flight dynamics model of a large flexible BWB airliner in order to verify the derived vibration controller on a challenging control problem.     

Resonant enhancement in nanostructured thermoelectric performance via electronic thermal conductivity engineering

The use of an asymmetric broadening in the transport distribution, a characteristic of resonant structures, is proposed as a route to engineer a decrease in electronic thermal conductivity thereby enhancing the electronic figure of merit in nanostructured thermoelectrics. Using toy models, we first demonstrate that a decrease in thermal conductivity resulting from such an asymmetric broadening may indeed lead to an electronic figure of merit well in excess of 1000 in an idealized situation and in excess of 10 in a realistic situation. We then substantiate with realistic resonant structures designed using graphene nano-ribbons by employing a tight binding framework with edge correction that match density functional theory calculations under the local density approximation. The calculated figure of merit exceeding 10 in such realistic structures further reinforces the concept and sets a promising direction to use nano-ribbon structures to engineer a favorable decrease in the electronic thermal conductivity.     

Gamma-resonance and X-ray investigations of slow motions in macromolecular systems

Information on slow motions of atomic complexes in proteins and other large molecules can be obtained from X-ray and from Mössbauer type experiments. This paper deals with the information on the motional behavior within macromolecular systems, which is contained in the line intensities and in the line widths observed in such experiments. The particular suitability of the gamma resonance method for studies of structural fluctuations in biomolecules is emphasized.     

Inverse vibration problem for un-damped 3-dimensional multi-story shear building models

Various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional (2-D) shear building structural models for a given set of vibratory frequencies. The suggested methods are based on the specific characteristics of the Jacobi matrices, i.e., symmetric, tri-diagonal and semi-positive definite matrices. However, in case of three dimensional (3-D) structural models, those methods are no longer applicable, since their stiffness matrices are not tri-diagonal. In this paper the inverse problem for a special class of vibratory structural systems, i.e., 3-D shear building models, is investigated. A practical algorithm is proposed for solving the inverse eigenvalue problem for un-damped, 3-D shear buildings. The problem is addressed in two steps. First, using the target frequencies, a so-called normalized eigenvector matrix, which is a banded matrix containing the information related to the frequencies and mode shapes of the target structural system, is determined. In this regard, similar to the solution of inverse problem for 2-D shear building structural models in which an auxiliary structure is constructed by adding constraints (or springs) to the original system, three auxiliary structures are proposed to solve the problem for 3-D cases. In the second step, the normalized eigenvector matrix is utilized to obtain the normalized stiffness matrix; in turn, this matrix is decomposed into the stiffness and mass matrices of the system. Finally, a numerical example is presented to demonstrate the efficiency of the proposed algorithm in determining the mass and stiffness matrices of a 3-D structural model for a given set of target vibrational frequencies.