Elastic Structural Elements Research Articles

Experimental probing of the configuration space of circular, clamped panels

A thin, post-buckled, circular plate is a classic exhibiter of bi-stability. That is, an elastic structural element that possesses more than a single (stable) equilibrium configuration. The key here is that the plate may be flat, or deflected in a given direction. In the latter case, this is a thoroughly nonlinear phenomenon that typically requires a relatively large perturbation (using a probing force) to deflect the system from one equilibrium configuration to the other, in which we can think of a structure exhibiting an initial configuration, but able to be pushed-through into an inverted, complementary stable configuration, or even into other shapes. The work described here is primarily experimental, exploiting the capabilities of digital image correlation. It points in the direction of identifying nonlinear, global features of the structural behavior, features that tend to have a strong influence on underlying behavior in an operational, dynamic environment. Some of the equilibrium configurations require a degree of interrogation to be revealed, i.e., they are not necessarily observed without some exploratory probing of the configuration space and we present results from a number of experimental studies of clamped, circular panels. The study is preceded by some experiments on initially flat panels, for which there is some access to analytic results and helps to set the stage for nonlinear environment in the post-buckled landscape.

Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation

This study is based on the Lie group method for the nonlinear elastic structural element equation (ESE Equation). We obtain a three-dimensional Lie algebra. By utilizing this Lie algebra a four-dimensional optimal system is constructed. The governing ESE Equation is converted to nonlinear ordinary differential equations (ODEs) via symmetry reduction. We use a modified auxiliary equation (MAE) procedure to deal with nonlinear ODEs. These ODEs reveal the dynamics of the periodic and soliton solutions. We obtain soliton solutions through rational, trigonometric, and hyperbolic functions. Wolfram Mathematica simulations vividly illustrate the wave characteristics of the derived solutions, affirming their properties as singular periodic solutions, a singular solution, an optical dark soliton solution, and a singular soliton solution. We also obtain the local conservation laws by a new conservation theorem introduced by Ibragimov.

Program complex for solving of some classes of aerohydroelasticity problems

On the basis of the developed mathematical models, a program complex was created for studying the dynamics and stability of an elastic pipeline, an elastic structural element in supersonic flow, elastic elements of wing profiles of several types with subsonic flow, elastic elements of vibration devices of several types. The complex generates three-dimensional graphs of element deformations, construction of animation graphs of element deformations, construction of flat graphs of deformations and strain rate at a given point or at a given time. On the basis of the constructed graphs, one can study the dynamics and draw conclusions about the stability of vibrations of elastic structural elements.

Анализ колебательных процессов в упругих и вязкоупругих средах и конструктивные элементы для прогнозирования останова оборудования

Анализ колебательных процессов в упругих и вязкоупругих средах и конструктивные элементы для прогнозирования останова оборудования

Effects of Elastic Supports on the Snap-through Buckling of Mises Trusses

The load-displacement relations and buckling loads of Mises trusses, which are used in a bistable structural element, has been investigated in this paper. For the snap-through struts, von Mises trusses are connected to the adjacent elastic structural elements that provide elastic types of supports to the ends of the trusses. The elastically supporting actions of the other elements on a truss were replaced by equivalent springs. Then the effects of the elastic supports on the behavior of von Mises trusses, which rarely appear to be reported in the open literature, were discussed.

Theoretical Analysis on the Effect of Surface Horizontal Traction on Top-Down Cracking of Flexible Pavement

Fatigue cracking of flexible pavement is one of the most important elements that should be considered due to the damage occurs in asphalt layer under the effect of wheel load repetitions. This research demonstrated theoretical study on top-down fatigue crackingusing the finite element method. A three- dimensional finite elastic structural element is used to modal pavement using (ABAQUS ver. 6.12.1) program. The results obtained from this studydemonstrated that maximum value of tensile strain developed at the surface of asphalt layer for flexible pavement due to the horizontal traction generated from wheel load application at contact area. Also, the horizontal tensile strain ( ) at surface of asphalt layer is increasing rapidly with load repetitions with values greater than that generated at bottom by (94%) at failure. This prescribed the basic or inherent features of top crack initiation and down propagates within asphalt layer in flexible pavement. The top horizontal tensile strains obtained from the finite element model is higher than the empirical relations by (20%); since the finite element analysis of flexible pavement considered the surface horizontal tensile strains due to contact traction force at tire pavement interface. Finally, according to the results of this study the horizontal tensile strains at the top of asphalt surface significantly increase the damage intensity of fatigue failure for flexible pavement.

Numerical modeling of the strain of elastic rubber elements

A comparative analysis of the results of experimental investigation of mechanical behavior of the rubber sample during biaxial compression testing and numerical simulation results obtained by the finite element method was carried out to determine the correctness of the model applied in the engineering calculations of elastic structural elements made of the rubber. The governing equation represents the five-parameter Mooney-Rivlin model with the constants determined from experimental data. The investigation results showed that these constants reliably describe the mechanical behavior of the material under consideration. The divergence of experimental and numerical results does not exceed 15%.

Methodology of determining design parameters for vibration damping in spacecraft structures

Modern spacecraft designs use elastic outrigger-type structural elements to accommodate equipment and devices. When the angular position of spacecraft changes and they stabilise in their orbits, these elements start to vibrate. In order to decrease the effect these vibrations have on the spacecraft dynamics, vibration damping delay time is introduced, amounting to several minutes. We present a methodology of determining design parameters for vibration damping systems that make it possible to damp vibrations in milliseconds

Nonlinear guided bulk waves in heterogeneous elastic structural elements

Guided nonlinear bulk strain waves are considered in heterogeneous composite materials, containing macro- or micro(nano)inclusions as the main sources of nonuniformity. Theory is based on the combination of the finite deformation and the 5-constant (Murnaghan) nonlinear elasticity, that leads under several assumptions to the only nonlinear doubly dispersive equation with variable coefficients (DDE) for a component of longitudinal strain in rod and in shell. Numerical simulations performed and experimental data are discussed, and lead to conclusions concerning dramatic influence of heterogeneity in dynamic behaviour of strain solitons in solids. We have shown how different smooth variations in elasticity may lead to either amplification or decay of strain solitons in both polymer rod and shell. These date can be useful in the NDT problems, and in problems of the solids integrity under intense elastic pulse loading.

Interaction dynamics of pulsating viscous liquid with the walls of the conduit on an elastic foundation

Bending oscillations of walls of conduit on Winkler foundation under the influence of pulsating flow of viscous liquid have been studied. The statement and solution of hyper-elasticity problem have allowed analytical expressions for channel wall bends and pressure in liquid to be defined, as well as the distribution functions for bend amplitudes and pressures along the channel to be plotted. The performed calculations showed the significant impact of taking into consideration the elastic compliance of the channel foundation on the bend amplitude of channel walls and pressure in the channel. The obtained results present the possibilities of studying the dynamic processes conditioned by the interactions of elastic structural elements with viscous liquid in hydraulic drives, assemblies, and devices.

Modeling of Microaccelerations Caused by Running of Attitude-Control Engines of Spacecraft with Elastic Structural Elements

The article deals with the task to estimate microaccelerations caused by natural oscillations of big elastic elements after impulse firing of an orientation system engine. Offered estimation is useful for development of space-system engineering intended for realization of gravity-sensitive processes. It can be applied for taking a decision about appropriateness of one or another process on the board of spacecraft.

Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids

Abstract In this article, the prolongation structure technique is applied to a generalised inhomogeneous Gardner equation, which can be used to describe certain physical situations, such as the stratified shear flows in ocean and atmosphere, ion acoustic waves in plasmas with a negative ion, interfacial solitary waves over slowly varying topographies, and wave motion in a non-linear elastic structural element with large deflection. The Lax pairs, which are derived via the prolongation structure, are more general than the Lax pairs published before. Under the Painlevé conditions, the linear-damping coefficient equals to zero, the quadratic non-linear coefficient is proportional to the dispersive coefficient c(t), the cubic non-linear coefficient is proportional to c(t), leaving no constraints on c(t) and the dissipative coefficient d(t). We establish the prolongation structure through constructing the exterior differential system. We introduce two methods to obtain the Lax pairs: (a) based on the prolongation structure, the Lax pairs are obtained, and (b) via the Lie algebra, we can derive the Pfaffian forms and Lax pairs when certain parameters are chosen. We set d(t) as a constant to discuss the influence of c(t) on the Pfaffian forms and Lax pairs, and to discuss the influence of d(t) on the Pfaffian forms and Lax pairs, we set c(t) as another constant. Then, we get different prolongation structure, Pfaffian forms and Lax pairs.

Vibrations of the walls of a slot channel with a viscous fluid formed by three-layer and solid disks

An axisymmetric problem of hydroelastic vibrations of the walls of a channel with a pulsating layer of a viscous incompressible fluid is investigated. The channel walls are formed by the concentric circular three-layer elastic plate and absolutely solid disk with an elastic coupling. The laws of motion of the channel walls, their amplitude and phase frequency characteristics, as well as the hydrodynamic parameters of the fluid layer in the channel are found. An example of the computation of resonance vibrations of a hydromount with a three-layer elastic structural element is shown.

Identification of crack-like defects in elastic structural elements on the basis of evolution algorithms

A method for the identification of defects in elastic structural elements (SEs) on the basis of artificial neural network (ANN) tools was proposed. The problems of constructing a simulation model of an object, the optimal arrangement of transducers with the use of a genetic algorithm, and the subsequent identification of a defect were solved. The application of different learning architectures and algorithms to feed-forward neural networks (FFNs) was studied and the influence of errors on the estimation accuracy of the parameters of a defect was analyzed.

Accurate inversion of high‐resolution snow penetrometer signals for microstructural and micromechanical properties

Measurements of snow using a high‐resolution micropenetrometer can be used to discriminate between different snow types; in lower‐density snow the signal is sensitive to microstructure, and micromechanical properties can be estimated. Although a physics‐based snow penetration theory was first developed almost a decade ago, since that time the majority of studies using snow micropenetrometers have focused on using direct hardness measurements in statistical relationships. We use Monte‐Carlo simulations to rigorously test the existing physics‐based snow micropenetration theories over a wide range of parameters. These tests revealed four major sources of error in the inversion, which are corrected in this analysis. It is shown that this improved inversion algorithm can recover micromechanical parameters in synthetic data with much greater accuracy over the entire range of micromechanical properties observed in natural snow. Detailed examples of the inversion results are shown for eight different snow types, collected in both Alaskan and alpine snowpacks. The resulting micromechanical properties are distinctly different, indicating that a snow characterization from snow micropenetrometer estimates of micromechanical properties is likely possible. Estimates of the microscale elastic modulus, microscale strength, and structural element length make sense physically when compared to the qualitative descriptions of the different snow types. Microscale strength estimates are used to estimate macroscale strength values, and results from 33 different snow samples, covering a wide range of densities and snow types, are consistent with previously reported values from macroscale tests.

Structure of the Cytosolic Part of the Subunit b-Dimer of Escherichia coli F0F1-ATP Synthase

The structure of the external stalk and its function in the catalytic mechanism of the F0F1-ATP synthase remains one of the important questions in bioenergetics. The external stalk has been proposed to be either a rigid stator that binds F1 or an elastic structural element that transmits energy from the small rotational steps of subunits c to the F1 sector during catalysis. We employed proteomics, sequence-based structure prediction, molecular modeling, and electron spin resonance spectroscopy using site-directed spin labeling to understand the structure and interfacial packing of the Escherichia coli b-subunit homodimer external stalk. Comparisons of bacterial, cyanobacterial, and plant b-subunits demonstrated little sequence similarity. Supersecondary structure predictions, however, show that all compared b-sequences have extensive heptad repeats, suggesting that the proteins all are capable of packing as left-handed coiled-coils. Molecular modeling subsequently indicated that b2 from the E. coli ATP synthase could pack into stable left-handed coiled-coils. Thirty-eight substitutions to cysteine in soluble b-constructs allowed the introduction of spin labels and the determination of intersubunit distances by ESR. These distances correlated well with molecular modeling results and strongly suggest that the E. coli subunit b-dimer can stably exist as a left-handed coiled-coil.

Solitary wave in a nonlinear elastic structural element of large deflection

General form nonlinear governing equations for the wave traveling in a nonlinear elastic structural element of large deflection are derived in the present research. An asymptotic solution of solitary wave in the elastic element is derived and investigated by means of a modified complete approximate method. Numerical computations for the solution are carried out. Characteristics of the solitary wave are investigated with various system parameters and initial conditions. Shapes and the propagation of the nonlinear elastic wave are also illustrated with figures. Based on the theoretical and numerical analyses of the research, quantitative conclusions are obtained for the wave motion of the elastic structural element.

Design of the Suboptimal Profiled Relay Control of Orientation of the Spacecraft Having Elastic Structural Elements with Regard for Two Oscillation Tones

A speed-optimal formulation of the control of angular spacecraft motion with regard for two tones of oscillations of its elastic structural elements was considered. A new approach based on the relay profiling of control was proposed. It provides the minimum oscillation amplitudes of the tones under consideration.

Active H Control of Sound Radiation from Thin Cylindrical Panels

Activecontrol of sound radiated by thin-walled cylindrical panels using arrays of spatially discrete piezoelectric sensors and actuators is addressed. A new general methodology for the design of controllers to reduce structure radiated noise is presented. The methodology utilizes e nite element modeling to perform structural discretization. The structure dynamics model, presented in state-space form, incorporates simplie ed models of the piezoelectric sensing and actuation and accounts for the mass and stiffness of the piezoelectric elements. The acoustic power radiated by thestructureinto thefare eld is expressed asa quadraticform ofthesystem statesthatis used to dee ne an acoustic performance criterion in an H1 disturbance rejection controller design setup. The methodology is applied for active control of sound radiated by a vibrating thin cylindrical panel excited by a persistent external force. The controller performance is evaluated using numerical simulations of the controlled structure. It is shown that the sound radiated by the panel into the far e eld is effectively controlled and reduced. CTIVE structural acoustic control (ASAC) has been exten- sively addressed in the literature. In essence, ASAC can be interpreted as attenuation of structure radiated sound resulting from a persistent excitation/disturbance. In controller design terms, it can be viewed as a disturbance rejection problem, the control objective of which is to minimize structure radiated sound, specie ed by an analytical sound radiation model. This is closely related to conven- tional vibration suppression control, often obtained by increasing (passivelyoractively )thedampingofthecontrolledstructure,which also reduces the structure radiated sound. Because effective ASAC should tackle the sound radiation mechanisms directly, which, in addition to the vibrational power, includes additional important pa- rameters such as vibrationalmodeshapes, excitation frequency,and others, use of a controller specie cally designed to minimize the sound radiation should be more effective. As an application of intelligent structures technology, ASAC re- lies on integrating piezoelectric sensors and actuators, for example, PVDF and PZT, into the structure. Modeling of such an integrated structure has been the subject of on-going research, with initial re- sultsreportedbyCrawleyanddeLuis, 1 followedbyWang 2 andmore recently by Pletner and Abramovich, 3 to name but a few. The sound radiated by a vibrating structure into the far e eld from measure- ments of the structural velocity e eld was investigated, both analyt- ically and experimentally, by Clark and Fuller, 4 Mathur and Tran, 5 and others. The analytical formulation presented in these studies was exclusively performed on simple structures (simply supported beams and plates ), while neglecting the mass and stiffness of the sensors and actuators. More complex structures, such as cylindri- calshells 6 and airplane fuselage, 7 were treated only experimentally. The ASAC controller designs documented in the literature are lim- ited to proportional and least mean squares algorithms, which are used to control the experimental structure. TomakeASACapplicableforcommercialapplications,areliable methodology that covers the design and analysis of adaptive struc- tures with complex geometric and material properties, incorporates a model of the sound radiation mechanism, and includes appropri- ate control synthesis algorithms is needed. This goal is undertaken in this study, which presents a new methodology that attempts to address ASAC objectives. This methodology, which utilizes e nite element(FE) tools to obtain a discrete representation of the contin- uous structure dynamics of (almostany)linearly elastic thin-walled structural element, incorporating piezoelectric sensing and actua- tion, uses the recent results of Pletner and Abramovich. 3 Because FEmodelsofcontinuousstructurestendtobeverylarge,makingthe synthesis, analysis, and implementation of the controlled structure extremely dife cult, static condensation and/or balanced truncation 8 techniques are employed to reduce the model dimensions. The acoustic power radiated by the structure into the far e eld can be expressed as a quadratic form of the system states. This formsthebasisfor a controllerdesign setup,where the performance specie cations are given by requirements on the allowable acoustic power.The controllersynthesis,whichincludes thesoundreduction criteria, sensor noise, and actuation limits, is stated as a disturbance rejection problem in the H1 framework. Theadvantageofthemethodologyproposedhereinisinitsgener- ality. It is applicable to any linearly elastic structure and permits the application of the latest techniques in state-space multi-input/multi- output control design tools. This study aims at demonstrating the performanceandeffectivenessoftheresultingcontrollerinreducing the sound radiated by a vibrating cylindrical panel.

VIBRATION AND NOISE GENERATION BY ELASTIC ELEMENTS EXCITED BY A TURBULENT FLOW

Vibration and sound generation by elastic structural elements (membrane, strip and plate) of streamlined surfaces excited by low Mach number turbulent flow is considered. The models of Corcos, Chase, Ffowcs Williams and Smol'yakov-Tkachenko for the wavenumber-frequency spectrum of the wall pressure field beneath a turbulent boundary layer are used to describe random excitation. A comparative analysis of the models is carried out. The Chase and Smol'yakov-Tkachenko models are shown to have the best agreement with the Martin and Leehey experimental data. The differences in the predictions of sound fields of turbulence excited elastic elements for all the above models are demonstrated and analyzed. The roles of the acoustic, low wavenumber, and convective wall pressure components are studied. The convective components are shown to make a significant contribution to the vibration and acoustic fields produced by turbulence. The ranges of parameters of the flow and the elastic structure are found (away from structural resonances) where the differences between the wall pressure models are not important for predictions of the sound radiated. At the same time these differences are important when the sound field is estimated near structural resonances.