Response Of Coupled System Research Articles

Determination of system vibratory response characteristics applying a spectral-based inverse sub-structuring approach. Part I: analytical formulation

The frequency response functions of discretely connected structures, such as a vehicle system, are determined by inverting the spectral-based sub-structuring equation in dynamic compliance form, which is classically used to compute coupled system response in terms of the characteristics of the free sub-structures. The resulting formulation backs out the response spectra of the free sub-structures including the dynamic stiffness terms of the coupling elements. When analysing the vibration response of one sub-structure due to an externally applied harmonic excitation on an adjacent sub-structure, the proposed theory can express the force transmissibility and structural path contribution functions directly in terms of the coupled system response. This provides a convenient way to identify the critical elements of a physical structure containing multiple coupling points without having to disconnect the individual sub-structures. The salient features of this approach are demonstrated using an idealised lumped parameter dynamic system.

Determination of system vibratory response characteristics applying a spectral-based inverse sub-structuring approach. Part II: motor vehicle structures

The spectral-based inverse sub-structuring theory formulated in Part 1 is applied here to investigate the vibration transmissibility and frequency response characteristics of motor vehicle structures. Analysis assumes a vehicle model that comprised of two sub-structures representing the body and chassis/suspension. Measured structural-acoustic and vibration spectra acquired from a relatively direct experimental setup are utilised to compute the relevant force transmissibility and path contribution functions at the discrete coupling points. Furthermore, the free sub-structure response characteristics and mount dynamic stiffnesses are expressed directly in terms of coupled system responses. These studies are performed using four real-life vehicles. For each case, the constructed system response functions are shown to match well with experimental data. Comparisons of the results derived from these vehicle examples reveal useful relationships between coupled system responses, free sub-structure characteristics and coupling compliances.

A numerical model of deformation and fluid-flow in an evolving thrust wedge

To investigate deformation and fluid-flow in an actively deforming tectonic wedge, we model the evolution of a large, two-dimensional (100 km long, 5 km thick), mechanically and hydrologically homogeneous and isotropic pile of sedimentary strata that is deformed to become a thrust wedge. We compare both ‘dry’ and ‘wet’ cases, in order to illustrate: (1) the relative importance of fluids on wedge evolution, and (2) the effect of brittle deformation on fluid-flow. We use an elastic–plastic constitutive relation, including a Mohr–Coulomb failure criterion and a non-associated flow rule, and coupled fluid flow, with bulk rock properties that approximate typical foreland sedimentary strata. Simulations are made both with and without dilation. The model is fully dynamic, but inertial forces remain small. Results show that deformation within the wedge is accommodated by reverse-slip movement on shear bands, which migrate in both directions through the wedge as both fore- and back-thrusts. The model has features predicted by the critical-taper theory: (1) overall wedge geometry; (2) crudely self-similar growth during evolution; (3) more intense deformation toward the rear of the wedge. The models show strong overall in-sequence faulting behavior with major thrusts isolating relatively undeformed packages, which are moved in a piggyback manner upon the active thrusts. Intermittent out-of-sequence faulting does however occur, in order to maintain the wedge taper. Fluid-flow in the deforming wedge is dominated by topography, but is also strongly affected by dilational plastic deformation. In all simulations, there is focused fluid flow within fault zones. When mechanical time-stepping is shut off (uncoupled), flow systems evolve to steady-state where inflow equals outflow. By subtracting the two ‘states’ we isolate the mechanical fluid response from the total coupled system response. The mechanical fluid response is manifest as contours of head and pressure difference and focusing of fluid-flow in areas of active deformation. In non-dilational simulations, these zones are quite localized and are a result of the contrasting stresses in and adjacent to a brittle shear zone. In simulations with dilation, the zones of head and pressure difference are broad and regional in extent. They are ten times greater in magnitude than in non-dilation simulations, and they track a rock-damage front that moves through the wedge.

Determination of the frequency response functions of complex systems using spectral-based inverse substructuring approach

The structural-acoustic response of discretely connected complex structures, such as a motor vehicle, are determined by inverting the spectral-based substructuring matrix equation in dynamic compliance form, which is classically used to compute coupled system response in terms of the dynamic characteristics of free substructures. The resulting formulation backs out the response spectra of the free substructures and the dynamic stiffness matrix representing the coupling elements. This provides a useful way to dissect a fairly complex system into two or more substructures. When analyzing the dynamic interaction between two adjacent substructures, the proposed theory can be conveniently used to express the transmissibility and path contribution functions directly as measurable coupled system response functions. Therefore, critical elements of a complex system can be identified easily without having to physically disconnect the substructures. The salient features of this approach are demonstrated using a motor vehicle example. The study specifically addresses the road noise problem by examining the sensitivity of the motor vehicle structure response to tire patch excitation. In the analysis, the body structural-acoustic functions, and excitation transfer functions between the spindle and chassis mounts are determined. [Work supported by CAVT and Ford.]

Advancements in vibroacoustic evaluation of satellite structures

The importance of the launcher vibroacoustic environment is increasing with respect to satellite loads due to the increase in size and decrease in surface mass of lightweight appendages like antennas and solar arrays. The loads generated by the vibroacoustic environment need to be covered adequately to ensure satellite structural integrity. This is of particular importance in the low-frequency range where the low frequencies of light appendages and equipment couple with the acoustic environment. In order to cope with the increasing demand for prediction of structural loads due to the acoustic environment, various methods have been developed in the frame of ESA research and development activities. These range from simplified approaches with partial fluid–structure coupling, e.g. the POSTAR package provided by INTESPACE (France) to more sophisticated approaches with full fluid–structure coupling. In the frequency domain this includes pure finite element modelling techniques, where specific tools have been developed by FFA (Sweden) using the ASKA package, as well as coupled finite element—boundary element approaches that have been developed in cooperation with DASA–Dornier (Germany), STRACO (France) and FFA using the commercial packages ASKA and RAYON. For fully coupled fluid structure analysis in the time domain the ASTRYD code from METRAVIB (France) is employed where advancements have been supported by CNES. Applications of these tools range from simple benchmarks such as simply supported plates, cavity enclosures or generic satellite-fairing models to complex satellite structure configurations. Evaluations of antenna reflector structures (Artemis communication antenna) and satellite equipment panels (polar platform) are presented. The paper covers also the investigation of payload/fairing effects (influence of fairing helium purging on the coupled-system response) together with DASA–Dornier, FFA and STRACO, as well as the vibroacoustic analysis of solar array stacks carried out by FOKKER (The Netherlands) and METRAVIB, where the air effects in the inter panel gaps are being taken into account.

Development of an Antarctic Regional Climate System Model. Part I: Sea Ice and Large-Scale Circulation

Abstract A coupled atmosphere–ice regional model previously used for simulations in the Arctic has been implemented in the Antarctic. Three 14-month simulations were performed for 1988–89, with different oceanic specifications. The year 1988 was interesting as there were several sensible heat polynya events in the Cosmonaut Sea region, the investigation of which is the goal of future finer-resolution simulations. Overall, the regional climate model produces reasonable simulations of the Antarctic at 100-km resolution. Root-mean-square errors range from 4 hPa in surface pressure, 4 K in near-surface air temperature, and 3 m s−1 in near-surface winds, to 1 K in air temperature and 2 m s−1 in winds at the 500-hPa level. Tests of the coupled system response to oceanic heat flux suggest that the sea-ice simulation is more sensitive than the atmospheric circulation, but it could be expected that the atmosphere would respond to these changes in sea ice over longer time periods than those of interest here. This s...

Analytical Model of Tire Cavity Resonance and Coupled Tire/Cavity Modal Model

Abstract The acoustic resonance of the air cavity in the tire/wheel assembly may be a contributor to vehicle interior noise through the structure-borne noise transmission path. This problem has been examined in the past using approximate closed form solutions (based on plane wave theory for a two-tube model) and numerically, using FEA. The coupling between the cavity resonance and structural resonance of the wheel may result in higher levels of interior noise as noted previously. The two primary goals of this paper are (1) to develop simple analytical models to gain fundamental understanding of some observed phenomena and for a quick estimation of cavity resonance frequency to assist in the design process, and (2) to develop tire modal models incorporating the acoustic cavity to predict coupled system natural frequencies and response. An improved analytical model for accurate calculation of acoustic cavity resonance frequencies of a static, unloaded tire is developed using variational principles. The sensitivities of the cavity resonance frequencies to tire width and aspect ratio are examined. For the case of a loaded tire, an improved analytical formulation based on plane wave propagation (for linearly varying cross-sectional area) is developed. Deformed structure geometry from FEA is used as input to the analytical model. The FEA-based methodology used in the tire/cavity coupling analysis is as follows: The tire structural modes are calculated, ignoring the effect of the acoustic cavity. The tire cavity modes are calculated using deformed cavity geometry only. Next, the structural/acoustic coupling matrix is calculated. Finally, a coupled cavity-structure modal model is generated from modal mass and stiffness of the tire/wheel assembly, the cavity modal matrices, and the coupling matrix. This process is an improvement over conventional tire modal models, which only include structural modes.

A fast algorithm for soil dynamics calculations by wavelet decomposition

The article presents a fast numerical algorithm for calculating the response of a halfspace under any surface loads. Under certain conditions there exists an analytical solution to the problem in the Fourier domain. To get the desired response, a numerical inverse Fourier transform of this analytic solution has to be made. By using a wavelet decomposition, the proposed algorithm can reduce the calculation time significantly, thus allowing the computation of complex problems. As an example, the response of the beam-halfspace coupled system under moving load is presented.

Numerical analysis of the interaction of soil-structure under earthquake loading

In this paper, the dynamical response of soil-structure coupled system was studied by the continuum theory of soild-fluid mixtures, the building foundation system subjected to rapid earthquake excitation were calculated by using finite element method. In the results, the deformation patterns and corresponding contour diagrams of pore pressure at various time levels are given, time variations of displacement in a certain node and shear stress in a certain element are also presented. The results of this study have provided an improved understanding of coupled behaviour of porous media. The procedure developed in this paper can be effectively used under a wide range of loading conditions from very slow quasi-static to very rapid earthquake excitations.

Dynamics of coupled nonlinear maps and its application to ecological modeling

This paper investigates the behavior of coupled nonlinear dynamical systems. We take two such dynamical systems (or units), couple them together, and study the effect of coupling on the dynamics. We demonstrate that coupling two chaotic units can indeed stabilize both of them. Several results describing the global dynamics of the coupled nonlinear system are established. Using them, we show that, by-and-large, the presence of coupling appears to increase the orderliness of the coupled system's response, producing periodicity, synchronicity, and quasi-symmetry. Using exponential maps which are commonly used to simulate-population dynamics, we establish the applicability of our results to population dynamics.

NEW ANALYSIS METHOD FOR GENERAL ACOUSTIC-STRUCTURAL COUPLED SYSTEMS

A new solution procedure has been developed for the analysis of the most general cases of vibro-acoustic problems, using a one-dimensional system as the model. The responses of the acoustic-structural coupled system with viscous and structural damping elements as well as absorbing material can be easily obtained. The solution algorithm utilizes the generalized orthogonality of the system eigenvectors to decouple the system matrix equation. The procedure is not only numerically efficient, but it also provides more insights to the system characteristics. The Sherman-Morrison formula is applied to the one-dimensional case, which reveals some interesting aspects of the effect of absorbing materials on the system response. The validity of the developed procedure is verified by comparing its results to the exact solutions.

TLM diakoptics for coupled-mode analysis of GaAs MESFET distributed amplifier

A new model of the application of diakoptics in the transmission-line-matrix (TLM) method for the coupled-mode analysis of GaAs MESFET distributed amplifiers is proposed. The model takes into account the major coupling effect caused by C/sub dg/ and g/sub m/ of the active devices. Techniques are developed by representing the whole system as two coupled lossy transmission lines. The numerical effort required can be reduced by representing the response of the resultant coupled system as that of superposition of two independent modes. The scattering matrix of the system obtained in the time domain leads to a process of discrete time domain convolutions based on the TLM numerical procedure. The results are compared with other analytical and computed results and show good agreement.

Dynamic Response of Coupled Structural-Acoustic Systems

A new approach, based on Lagrange's energy equations, is described for the derivation of the generalized equations of motion of coupled structural-acoustic systems. Furthermore attention is given to consideration of the acoustic properties of sound absorbing materials and damping pads in the generalized formulation of the coupled equations of motion.

Steady-State Response of Disk-Beam Coupled System Having Cyclically Symmetric Structure.

The steady-state response of a disk-beam coupled system having cyclically symmetric structure subjected to a sinusoidal point force is investigated analytically. The orthogonal polynomials generated using the Gram-Schmidt process and the eigenfunction of a uniform disk are employed as admissible functions, and artificial springs are introduced between the components to satisfy their continuity condition. The equations for steady-state response are derived by means of the Lagrange equation. The response curves of the system are calculated numerically to examine the effect of damping factors, the location of the driving point, the existence of the shroud, and the stiffness ratio of the disk and beams.

The forced response of an acoustic-structural coupled system

The sound-pressure response of an acoustic-structural coupled system to both air-borne and structure-borne excitations has been studied. Both steady-state and transient-state sound field responses of the system can be characterized by the system modal behaviors and by the nature of the driving forces. This paper presents a method to describe the sound and vibration fields of the coupled system in terms of modal coupling analysis. In particular, analytical expressions for steady-state and transient-state sound-pressure fields in a panel–cavity coupled system are obtained. They are used to calculate the frequency response and transient decay of the sound field in the cavity. The effect of the system eigenvalue distributions (or the pole locations in the sound field transfer functions) upon the sound field response is demonstrated by numerical examples.

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

On the dynamic response of flexible structures coupled through viscous fluid layers

The dynamic response of planar flexible structures that are coupled to each other through viscous fluid layer forces is considered. The fluid-structural interaction can occur over a partial or over the complete span of the structures. The linear vibration of the coupled system is analyzed in the frequency domain using the Green's function method. Interactions between the structural response and the fluid layer are described by the impedance function. The impedance function depends on the structural response, the frequency of the coupled system response, and the spatial location of the fluid layers. As an illustrative example for the proposed method, the vibration response of two stringlike structures (second-order problem) that are placed very close to each other and separated by a fluid layer is studied. The fluid is assumed to be incompressible, and the impedance function is given in a recent publication [C. A. Tan and C. D. Mote, Jr., ASME J. Tribology (to appear)]. The frequency response of this coupled system under different excitation forces is examined.

Nonlinear fluid slosh coupled to the dynamics of a spacecraft

The dynamics of a linear spacecraft mode coupled to the nonlinear low-gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft system are derived through an assumed mode Lagrangian method. Unlike a linear model, this nonlinear model retains two fundamental slosh modes and three secondary slosh modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. An experiment was developed to verify and complement this analysis. Scale model fluid tanks were coupled to an electromechanical analog for the second-order oscillatory spacecraft mode. Moderate and low gravity were simulated in 1 g using capillary scale models, and zero gravity was simulated in parabolic flight tests on the NASA KC-135 Reduced Gravity Test Facility. The experimental results substantiated the analytical predictions. The dependence of the coupled nonlinear response on the coupled system parameters and the gravity level is illustrated and discussed.

A Numerical Study of Tropical Large-Scale Air-Sea Interaction

Abstract In a series of numerical experiments using a simplified, domain-averaged, coupled air-sea model, some aspects of the low-latitude large-scale interaction between the atmosphere and the ocean are investigated. Experiments are designed with a view toward elucidating basic mechanisms involved in the coupled processes. In this paper, we focus on the response of coupled system to 1) steady forcing, 2) seasonal variations and 3) large perturbations and continuous short-period random forcings. Results indicated that the sea surface temperature (SST) distribution, which is strongly controlled by the oceanic upwelling, is the primary factor in determining the location and transition of the tropical rainbelt. The strongest convective activities in the ITCZ, however, depend mainly on the moisture supply from horizontal convergence and the static stability of lower atmosphere, and do not necessarily coincide with the occurrence of maximum SST. It is also demonstrated that the positive feedback processes betw...

The Coupled Response of a Dynamic Element Riding on a Continuously Supported Beam

The dynamic interaction between a Linear Induction Motor primary, modeled as a spring-mass-damper element, and its secondary-rail, modeled as a prestressed, continuously supported, infinitely long beam, is studied theoretically. The existence of two transition speeds is established. At the lower transition speed, the frequency and damping ratio of the coupled system response attain their minimum and maximum values, respectively. The system is unstable at speeds higher than the second transition speed. Using a rotating annular disk to simulate the secondary rail, measured values of the frequency and damping ratio confirm the validity of the mathematical model for speeds up to nearly the lower transition speed.