Influence Coefficient Matrix Research Articles

Analysis of Dynamic Performance of 2-RUUS Mechanism

Configuration of 2-RUUS mechanism is analyzed. The influence coefficient matrix of the mechanism is obtained by using virtual mechanism method. Simulation curves of input speed and input acceleration of mechanism are obtained by adopting influence coefficient method and differential coefficient method, and the correctness of influence coefficient matrix is verified. Meanwhile, the unequal equation expressing the relation between robot mechanism inertia force and mechanism size and quality and the global performance index of inertia force are given. This performance index can be used to analyze the influence of mechanism size and quality on the dynamic performance of mechanism. At last, 2-RUSS mechanism’s dynamic performance is analyzed by using global performance indices of acceleration and inertia force, and the relative performance atlas is obtained. The relationship between 2-RUUS mechanism size and dynamic performance, and the size of mechanism with good dynamic performance are obtained through analyzing performance atlas.

Sensitivity analysis of a strongly coupled aero-structural system using the discrete direct and adjoint methods

This paper is dedicated to the sensitivity analysis of a static aeroelastic system with respect to design parameters governing its jig-shape. The gradients of interest are computed using either the discrete direct differentiation or adjoint vector methods. The aerodynamic load is predicted by the nonlinear Euler equations and transferred to the structure through a consistent and conservative procedure. The induced structural displacement field is computed using beam theory and the matrix of the aerodynamic influence coefficients. Finally, a threedimensional wing-body case is used to verify the successful implementation of the analytical sensitivity analysis methods.

Aeroelastic Analysis of Wing Structures Using Equivalent Plate Models

In this paper we formulate the Reissner-Mindlin first order shear deformation model based governing equation for a non-isotropic plate. The governing equations are cast as a set of coupled Helmholtz equations which are then expressed as integral equations where the Green’s functions are expressed in terms of the traditional Hankel functions of the first kind. The integral equations are then solved to determine the static and dynamic influence coefficients which are inverted to generate the stiffness and dynamic matrices. In order to demonstrate the application of these computations we consider the aeroelastic analysis of a wing structure, modeled as an equivalent plate. The unsteady aerodynamic generalized loads are estimated by employing the Doublet-Lattice method which is coupled with the compatible numerical evaluation of the structure’s dynamic influence coefficient matrix without any need for independent vibration analysis. We have demonstrated that by employing appropriate equivalent anisotropic plate models, and a variant of the classical Nyquist plot to assess the relative stability of the system, it is possible to capture, simulate and predict all the instability features of real aircraft wings. These models are proving to be particularly useful in the synthesis of active controllers for smart structures.

Sensitivity analysis of a strongly coupled aero-structural system using the discrete direct and adjoint methods

This paper is dedicated to the sensitivity analysis of a static aeroelastic system with respect to design parameters governing its jig-shape. The gradients of interest are computed using either the discrete direct differentiation or adjoint vector methods. The aerodynamic load is predicted by the nonlinear Euler equations and transferred to the structure through a consistent and conservative procedure. The induced structural displacement field is computed using beam theory and the matrix of the aerodynamic influence coefficients. Finally, a threedimensional wing-body case is used to verify the successful implementation of the analytical sensitivity analysis methods.

The dynamics of three-dimensional underwater explosion bubble

The fluid is assumed to be inviscid and incompressible and the flow irrotational. A time-integration boundary-integral method is used to solve the Laplace equation for the velocity potential to calculate the shape and position of the bubble. To improve the accuracy of the solution, the high-order triangular elements with curved sides and surfaces defined by six nodes are used to discretize the boundary surface in this investigation. Meanwhile, the singularity of the double-layer potential is eliminated by recasting the principal-value integral of the double-layer potential when the influence coefficient matrix is calculated. The material velocity vector at any node can be obtained by the potential of adjacent nodes with an appropriate weighted method. Elastic mesh technique (EMT), which is a new mesh regulation technique, is further applied to maintain the regularity of the triangular-element mesh used to discretize the dynamic boundary surface during the evolution of explosion bubble(s). All these efforts make the present approach viable and robust, and which is validated by computations of several bubble dynamics problems. Numerical analyses are carried out for the evolution of a bubble near a free surface and the interaction of two bubbles with a floating structure near a free surface. The robustness of the algorithm is demonstrated through simulating bubble jets near a free surface producing sharp free surface spikes and bubble(s) collapsing nearby a floating structure close to a free surface.

Optimal balancing of flexible rotors by minimizing the condition number of influence coefficients

Abstract The Hermitian matrix of influence coefficients is one indicator of a balancing experiment’s overall effectiveness. The condition number of this matrix is determined by the sensor locations and balancing planes selected for the balancing procedure. In this research, we use finite element analysis to simulate the balancing of flexible rotor-bearing systems under various arrangements of sensors and planes. The condition number turns out to be inversely related to the accuracy of the balancing and directly related to the sum of correction masses; in other words, the accuracy and efficiency of rotor balancing can be improved by selecting sensor locations and balancing planes which reduce the condition number. This result is validated by experimental measurements of a physical rotor system.

Explicit algebraic influence coefficients: a one-dimensional transient aquifer model

This work makes explicit an algebraic expression giving the matrix of transient influence coefficients associated with a one-dimensional semi-confined aquifer model. The domain studied is divided into a series of connected and completely mixed compartments over which the governing equation is discretized. The discrete equations obtained are solved for the compartmental hydraulic head and used to derive the algebraic expression in question. The basic properties of the so-called algebraic influence coefficients are investigated. In particular, their consistency with the exact Green function is highlighted. Finally, the newly derived influence coefficients are applied to a simplified aquifer system in order to formulate and solve the problem of identifying illegal groundwater pumping.

An efficient computational method for nonlinear three-dimensional wave-wave and wave-body interactions

We develop and apply a highly efficient computational method for the study of three-dimensional nonlinear wave dynamics and interactions with floating bodies and bottom topography. Similarly to the classical boundary element methods, this method is based on the boundary integral equation formulation in the context of potential flow assumptions. In solving the integral equation, however, it employs a highly efficient fast Fourier transform technique for the calculation of far-field influences of boundary source/dipole distributions without an explicit realization of the influence coefficient matrix. As a result, the computational cost associated with the boundary-value solution at each time in the simulation of nonlinear wave-wave and wave-body interactions is reduced to O( Nln N) in comparison to the requisite O( N 2 ) effort of the classical methods, where N is the total number of boundary unknowns. The focus of this paper is on the development of the method and investigation of the features and dependence of its efficiency and accuracy on physical and computational parameters.

Extension of the g-Method Flutter Solution to Aeroservoelastic Stability Analysis

Extension of the g-Method Flutter Solution to Aeroservoelastic Stability Analysis

A study of hydrodynamics of three-dimensional planing surface

The hydrodynamic problem of 3D planing surface is studied by a finite element approach. The planing surface is represented by a number of pressure patches whose strengths are constant at each element. The unknown pressure strength is obtained by using the free surface elevation condition under the planing surface and Kutta condition at the transom stern. Previous studies indicate that, when the constant pressure distribution method is used, the number of buttocks should be less than five or six, otherwise the calculated pressure distribution will start to oscillate and even become divergent. In the present study, after careful examination of the influence coefficients, it is found that the accuracy of the influence coefficients matrix is very important to the convergence of the solution, especially when the number of elements is relatively high. The oscillation of the pressure distribution can be avoided by constant element method if the influence coefficients are sufficiently accurate. The predicted results of the present paper with more number of buttocks are in good agreement with other researchers'. It is concluded that the irregularity of the pressure distribution found in previous studies is most likely caused by the low accuracy in their calculation of the influence coefficients, not by the method itself.

The Application of Support Vector Machines to Gas Turbine Performance Diagnosis

SVMs (support vector machines) is a new artificial intelligence methodology derived from Vapnik's statistical learning theory, which has better generalization than artificial neural network. A C-support vector classifiers Based Fault Diagnostic Model (CBFDM) which gives the 3 most possible fault causes is constructed in this paper. Fivefold cross validation is chosen as the method of model selection for CBFDM. The simulated data are generated from PW4000-94 engine influence coefficient matrix at cruise, and the results show that the diagnostic accuracy of CBFDM is over 93% even when the standard deviation of noise is 3 times larger than the normal. This model can also be used for other diagnostic problems.

Research on a Novel Parallel Engraving Machine and its Key Technologies

In order to compensate the disadvantages of conventional engraving machine and exert the advantages of parallel mechanism, a novel parallel engraving machine is presented and some key technologies are studied in this paper. Mechanism performances are analyzed in terms of the first and the second order influence coefficient matrix firstly. So the sizes of mechanism, which are better for all the performance indices of both kinematics and dynamics, can be confirmed and the restriction due to considering only the first order influence coefficient matrix in the past is broken through. Therefore, the theory basis for designing the mechanism size of novel engraving machine with better performances is provided. In addition, method for tool path planning and control technology for engraving force is also studied in the paper. The proposed algorithm for tool path planning on curved surface can be applied to arbitrary spacial curved surface in theory, control technology for engraving force based on fuzzy neural network(FNN) has well adaptability to the changing environment. Research on teleoperation for parallel engraving machine based on B/S architecture resolves the key problems such as control mode, sharing mechanism for multiuser, real-time control for engraving job and real-time transmission for video information. Simulation results further show the feasibility and validity of the proposed methods.

Overset Field-Panel Method for Unsteady Transonic Aerodynamic Influence Coefficient Matrix Generation

The overset field-panel method presented solves the integral equation of the time-linearized transonic small disturbance equation by an overset field-panel scheme for rapid transonic aeroelastic applications of complex configurations. A block-tridiagonal approximation technique is developed to greatly improve the computational efficiency to solve the large size volume-cell influence coefficient matrix. Using the high-fidelity computational-fluid-dynamics solution as the steady background flow, the present method shows that simple theories based on the small disturbance approach can yield accurate unsteady transonic flow predictions. The aerodynamic influence coefficient matrix generated by the present method can be repeatedly used in a structural design loop, rendering the present method as an ideal tool for multidisciplinary optimization.

Simulation of temperature distribution of point contacts in mixed lubrication

The numerical simulation of temperature distribution of point contacts in mixed lubrication is presented. The calculating includes two steps. First, temperature rises on two surfaces are obtained by a temperature integration method of transient point heat source. Second, the partition coefficients of heat flux are determined by matching the temperature of two surfaces. Similar to the calculation of elastic deformation, double linear interpolation function is used to get a better accuracy, and moving grid method is used to increase the efficiency of the computation. Due to the symmetry of influence coefficient matrix in the direction perpendicular to the velocity, storage and computational work are further reduced by 50%. Numerical samples validate the algorithm and program. The calculating results of the cases of smooth surface and isotropic sinusoidal surface are presented.

Nonlinear transient wave–body interactions in steady uniform currents

Fully nonlinear monochromatic wave three-dimensional body interactions are studied with and without the presence of steady uniform currents. The mixed initial boundary value problem is set-up in a numerical wave tank (NWT) and solved by an indirect desingularized boundary integral equation method (DBIEM). The Laplace equation is solved at each time-step and time-dependent nonlinear free surface boundary conditions are simultaneously integrated by a mixed Eulerian–Lagrangian (MEL) method. A piston-type wave maker is used for generating the incident waves and a steady current is imposed everywhere in the computational domain at t=0 +. A spatially varying sponge layer on the free surface is devised to dissipate the outgoing waves. The resulting influence coefficient matrix is divided into sub-matrices by domain decomposition technique and solved simultaneously by block line Jacobi method (BJM). A specially devised preconditioning matrix is used to accelerate the convergence rate of the matrix equation by obtaining the minimized condition number of the influence coefficient matrix. Computations are performed for the nonlinear diffractions of steep monochromatic waves by a truncated vertical cylinder both without currents and in the presence of uniform coplanar or adverse currents. A φ n -type adaptive beach is developed and its performance compared with some beaches in the literature. Results of NWT simulations are compared with the first-order potential theory (Buchmann et al., Proceedings of the Seventh International Offshore and Polar Engineering Conference, Honolulu, Hawaii, USA, 1997), second-order diffraction theory [Kim and Yue, J. Fluid Mech. 200 (1989) 235–264], modified marker and cell (MAC) method (Park et al., International Journal for Numerical Methods in Fluids 29 (1999) 685–703) and the experimental and second-order potential theory results of Mercier and Niedzwecki [Proceedings of the Seventh International Conference on Behavior of Offshore Structures, vol. 2, TX, USA, 1994, pp. 265–287].

An Evaluation of Engine Faults Diagnostics Using Artificial Neural Networks

Application of artificial neural network (ANN)-based method to perform engine condition monitoring and fault diagnosis is evaluated. Back-propagation, feedforward neural nets are employed for constructing engine diagnostic networks. Noise-contained training and testing data are generated using an influence coefficient matrix and the data scatters. The results indicate that under high-level noise conditions ANN fault diagnosis can only achieve a 50–60 percent success rate. For situations where sensor scatters are comparable to those of the normal engine operation, the success rates for both four-input and eight-input ANN diagnoses achieve high scores which satisfy the minimum 90 percent requirement. It is surprising to find that the success rate of the four-input diagnosis is almost as good as that of the eight-input. Although the ANN-based method possesses certain capability in resisting the influence of input noise, it is found that a preprocessor that can perform sensor data validation is of paramount importance. Autoassociative neural network (AANN) is introduced to reduce the noise level contained. It is shown that the noise can be greatly filtered to result in a higher success rate of diagnosis. This AANN data validation preprocessor can also serve as an instant trend detector which greatly improves the current smoothing methods in trend detection. It is concluded that ANN-based fault diagnostic method is of great potential for future use. However, further investigations using actual engine data have to be done to validate the present findings.

A Numerical Three-Dimensional Model for the Contact of Layered Elastic/Plastic Solids With Rough Surfaces by a Variational Principle

A new numerical model for the three-dimensional contact analysis of a layered elastic–perfectly plastic half space with another rough surface is presented. The model is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. A quasi-Newton method is used to find the minimum. The influence coefficients matrix is determined using the Papkovich–Neuber potentials with fast Fourier transformation. The model is extended to elastic–perfectly plastic contacts in dry and wet conditions. Contact analyses have been performed to predict contact statistics of layered elastic/plastic solids with rough surfaces using this model. The effects of the stiffness of the layer and the substrate, layer thickness, as well as normal load are studied. Optimum layer parameters are identified to provide low friction/stiction and wear.

COMPUTATION OF TRANSIENT NONLINEAR SHIP WAVES USING AN ADAPTIVE ALGORITHM

An indirect boundary integral method is used to solve transient nonlinear ship wave problems. A resulting mixed boundary value problem is solved at each time-step using a mixed Eulerian– Lagrangian time integration technique. Two dynamic node allocation techniques, which basically distribute nodes on an ever changing body surface, are presented. Both two-sided hyperbolic tangent and variational grid generation algorithms are developed and compared on station curves. A ship hull form is generated in parametric space using a B-spline surface representation. Two-sided hyperbolic tangent and variational adaptive curve grid-generation methods are then applied on the hull station curves to generate effective node placement. The numerical algorithm, in the first method, used two stretching parameters. In the second method, a conservative form of the parametric variational Euler–Lagrange equations is used the perform an adaptive gridding on each station. The resulting unsymmetrical influence coefficient matrix is solved using both a restarted version of GMRES based on the modified Gram–Schmidt procedure and a line Jacobi method based on LU decomposition. The convergence rates of both matrix iteration techniques are improved with specially devised preconditioners. Numerical examples of node placements on typical hull cross-sections using both techniques are discussed and fully nonlinear ship wave patterns and wave resistance computations are presented.

The Hall Acoustics Computer Model and its Application to the Acoustic Design of a Theater and an Assembly Hall

The Hall Acoustics computer model presented here carries out the computation of the acoustic response of rooms and large multipurpose volumes. The model is based on the 3 D representation of the volume. The surfaces are each assigned an absorption coefficient and are subdivided into smaller elements. A matrix of influence coefficients between elements is first calculated. Given a sound source, the energy received by each element is calculated, and from this, the sound level at any point in the volume can be determined, making it possible to calculate a) the attenuation with distance, b) the acoustic illumination on any plane, and c) the reception directivity of the sound energy received at any given point. Echograms at any chosen point in the volume can be calculated, as well as the evolution with time of the reception directivity at the receiver: such a feature enables checking the possible discrepancy between the visual picture and the sound picture. This software makes it possible to modify the shape of the room at will, in order to optimize its acoustic features. Two examples of hall acoustics design are presented (the Théâtre de la Cité in Toulouse, and the Al Shura Main Assembly Hall in Riyadh, Saudi Arabia).

Approximation Methods in the Nonlinear Analysis of Planar Tracked Vehicles

SUMMARY In many chain drives and tracked vehicle system applications, the shape of a closed chain may not significantly change during the functional operation of the system. This paper presents certain approximation methods which assume that the chain shape does not change. Because of the high frequency contact and impact forces, using approximate numerical schemes based solely on the kinematic descriptions of the closed chain, may lead to erroneous results. Different procedures for the numerical solution of the dynamic equations of motion of the tracked vehicles are presented. The tracked vehicles are modeled as two kinematically decoupled subsystems; the first is the chassis subsystem which consists of the chassis, rollers, idlers, and sprockets, and the second is the track subsystem which consists of the track links, interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the equations of the two subsystems are not kinematically coupled. The objective of the procedures developed in this investigation is to examine the feasibility of improving computational efficiency by observing that the shape of a track does not significantly change even though its links undergo significant displacements. In such cases the magnitudes of the nonlinear terms propagate along the diagonals of a velocity influence coefficient matrix which is the only source of nonlinearity in the generalized inertia matrix of the track subsystem. Optimized numerical methods, based on coordinate permutations and reduction of the degrees of freedom of the track chain, are introduced and their effectiveness in the dynamic modeling of tracked vehicles is examined. Numerical results obtained using the two methods of coordinate prediction and coordinate reduction are presented and compared to the results obtained using the recursive kinematic equations in which all degrees of freedom of the track chain are considered. The analysis procedure developed in this investigation is applied to only a planar tracked vehicle model.