Showing papers in "Journal of Vibration and Acoustics in 1997"

A reduced-order modeling technique for mistuned bladed disks

Abstract: The analysis of the response statistics of mistuned turbomachinery rotors requires an expensive Monte Carlo simulation approach Simple lumped parameter models capture basic localization effects but do not represent well actual engineering structures without a difficult parameter identification Current component mode analysis techniques generally require a minimum number of degrees of freedom which is too large for running Monte Carlo simulations at a reasonable cost In the present work, an order reduction method is introduced which is capable of generating reasonably accurate, very low order models of tuned or mistuned bladed disks This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector It is shown that the phenomenon of mode localization is well captured by the reduced order modeling technique

Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems

Abstract: The analysis of systems subjected to periodic excitations can be highly complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-periodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates the periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solutions and locates system parameter ranges where aperiodic and chaotic responses bifurcate from the periodic response. Once the system response for a parameter is known, the solution for near range of the parameter is calculated efficiently using a pseudo-arc length continuation procedure. Practical procedures for continuation, numerical difficulties and some strategies for overcoming them are also given. The numerical scheme is used to study the imbalance response of a rigid rotor supported on squeeze-film dampers and journal bearings, which have nonlinear stiffness and damping characteristics. Rotor spinning speed is used as the bifurcation parameter, and speed ranges of sub-harmonic, quasi-periodic and chaotic motions are calculated for a set of system parameters of practical interest. The mechanisms of these bifurcations also are explained through Floquet theory, and bifurcation diagrams.

Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers

Abstract: Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.

Time domain simulation of jack-up dynamics with the extremes of a gaussian process

Abstract: Random simulations are often used to simulate the statistics of storm-driven waves. Work on Gaussian linear random signals has lead to a method for embedding a large wave into a random sequence in such a way that the composite signal is virtually indistinguishable (in a rigorous statistical limit) from a purely random occurrence of a large wave. We demonstrate that this idea can be used to estimate the extreme response of a jack-up in a severe sea-state in a robust and efficient manner. Results are in good agreement with those obtained from a full random time-domain simulation.

Chaotic Vibration of a Simple Model of the Machine Tool-Cutting Process System

Abstract: A study on a simple model of the machine tool-cutting process system is presented. As the system is non-linear and discontinuous, and exhibits intermittent cutting, non-linear dynamics techniques such as constructing bifurcation diagrams and Poincare maps were employed to ascertain a quality of motion. Untypical routes to chaos and unusual topology of Poincare sections were observed. New phenomena such as unidirectional bifurcation and births and deaths of periodic solutions were detected. It was also found out that the dynamic responses of the analysed system can be most effictively controlled by a magnitude of the cutting force.

Boundary Control of Beams Using Active Constrained Layer Damping

Abstract: A variational mathematical model is developed using Hamilton’s principle to describe the dynamics of beams fully-treated with Active Constrained Layer Damping (ACLD) treatments. The resulting distributed-parameter model is utilized in devising a globally stable boundary control strategy which is compatible with the operating nature of the ACLD treatments. The effectiveness of the ACLD in damping out the vibration of cantilevered beams is determined for different control gains and compared with the performance of conventional Passive Constrained Layer Damping (PCLD). The results obtained demonstrate the high damping characteristics of the boundary controller particularly over broad frequency bands.

Nonlinear piezothermoelasticity and multi-field actuations, part 1: Nonlinear anisotropic piezothermoelastic shell laminates

Abstract: Nonlinear characteristics, either material or geometrical nonlinearity, and temperature variations can significantly influence the performance and reliability of piezoelectric sensors, actuators, structures, and systems. This paper is intended to examine the nonlinear piezothermoelastic characteristics and temperature effects of piezoelectric laminated systems, and it is divided into two parts. Part 1 is concerned with a mathematical modeling of nonlinear anisotropic piezothermoelastic shell laminates and Part 2 is a study of static and dynamic control of a nonlinear piezoelectric laminated circular plate subjected to mechanical, electric, and temperature excitations. Geometric nonlinearity induced by large deformations is considered in both parts. A generic nonlinear piezothermoelastic shell lamination theory is proposed and its nonlinear thermo-electromechanical equations are derived based on Hamilton's principle. Thermo-electromechanical couplings among the elastic, electric, and temperature fields are discussed, and nonlinear components identified. Applications of the nonlinear theory to other materials, continua, sensors, actuators, and linear systems are discussed.

Free Vibrations of Thick Hollow Circular Cylinders From Three-Dimensional Analysis

Abstract: A three-dimensional (3-D) method of analysis is developed for the free vibration frequencies of hollow circular cylinders of elastic material. The method is based upon local coordinates whose origin is attached to the center of cylindrical wall. It assumes for the three displacement components a Fourier series in the circumferential (θ) direction and algebraic polynomials in the radial (q) ) and axial (z) directions. Convergence studies for completely free cylinders show that the analysis can yield frequencies which are exact to five or six significant figures. These accurate frequencies are compared with those from other 3-D analyses available for free hollow circular cylinders having various length-to-outside diameter (L/D o ) and inside-to-outside diameter (D i /D o ) ratios. Extensive, accurate data are presented for the first 10 frequencies of each circumferential wave number 0 through 5 for hollow circular cylinders having D i /D o of 0.1, 0.5, and 0.9, with L/D o = 0.2, 1 and 5 and a Poisson's ratio (v) = 0.3.

On the Active-Passive Hybrid Control Actions of Structures With Active Constrained Layer Treatments

Abstract: This paper is concerned with the analysis of active and passive hybrid actions in structures with active constrained damping layers (ACL). A system model is derived via Hamilton's Principle, based on the constitutive equations of the elastic, viscoelastic, and piezoelectric materials. The model converges to a purely active piezotronic system as the thickness of the viscoelastic material (VEM) layer approaches zero. A mixed Galerkin-GHM (Golla-Hughes-McTavish) method is employed to discretize and analyze the model in time domain. With an LQR (linear quadratic regulator) optimal control, the effects of the active constrained layer configuration on the system vibration suppression performance and control effort requirements are investigated. Analysis illustrates that the active piezoelectric action with proper feedback control will always enhance the damping ability of the passive constrained layer. When compared to a purely active configuration, while the viscoelastic layer of the ACL treatment will enhance damping, it will also reduce the direct control authorities (active action transmissibility) from the active source to the host structure. Therefore, whether the ACL treatment is better than a purely active configuration depends on whether the effect of damping enhancement is greater than that of transmissibility reduction caused by the VEM layer. The significance of these effects depends very much on the viscoelastic layer thickness and material properties. With some parameter combinations, the ACL configuration could require more control effort while achieving less vibration reductions compared to a purely active system. Through analyzing the performance and control effort indices, the conditions where this active-passive hybrid approach can outperform both the passive and active configurations are quantified. Based on this study, design guidelines can be set up to effectively integrate the host structure with the piezoelectric and viscoelastic materials, such that a truly beneficial active-passive hybrid control system could be achieved.

Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part 2: Control of Nonlinear Deflection, Buckling and Dynamics

Abstract: Linear dynamics and distributed control of piezoelectric laminated continua have been intensively investigated in recent years. In this study, dynamics, electromechanical couplings, and control of thermal buckling of a nonlinear piezoelectric laminated circular plate with an initial large deformation are investigated. It is assumed that the transverse nonlinear component is much more prominent than the other two in-plane components-the von Karman type geometrical nonlinearity. In addition, the piezoelectric layers are uniformly distributed on the top and bottom surfaces of the circular plate. Accordingly, the control effect is introduced via an equivalent control moment on the circumference. Dynamic equations and boundary conditions including the elastic and piezoelectric couplings are formulated, and solutions are derived. Active control of plate nonlinear deflections, thermal buckling, and natural frequencies using high control voltages are studied, and their nonlinear effects are evaluated.

Design sensitivity analysis of structure-induced noise and vibration

Abstract: A continuum design sensitivity analysis (DSA) method for dynamic frequency responses of structural-acoustic systems is developed using the adjoint variable and direct differentiation methods. A variational approach with a non-self-adjoint operator for complex variables is used to retain the continuum elasticity formulation throughout derivation of design sensitivity results. It is shown that the adjoint variable method is applicable to the variational equation with the non-self-adjoint operator. Sizing design variables such as the thickness and cross-sectional area of structural components are considered for the design sensitivity analysis. A numerical implementation method of continuum DSA results is developed by postprocessing analysis results from established finite element analysis (FEA) codes to obtain the design sensitivity of noise and vibration performance measures of the structural-acoustic systems. The numerical DSA method presented in this paper is limited to FEA and boundary element analysis (BEA) is not considered. A numerical method is developed to compute design sensitivity of direct and modal frequency FEA results. For the modal frequency FEA method, the numerical DSA method provides design sensitivity very efficiently without requiring design sensitivities of eigenvectors. The numerical method has been tested using passenger vehicle problems. Accurate design sensitivity results are obtained for analysis results obtained from established FEA codes.

Regenerative Systems for Vibration Control

Abstract: The potential for energy regeneration in vibration control systems is investigated. Such control systems hold the possibility of self-sustainability by alternately extracting and releasing energy originating from the vibrating system in a controlled non-passive manner. To be self-sustaining, more energy must on average flow into the control system than flows out. Generally speaking, the performance of such a system will approach that of an active system while theoretically requiring no externally supplied power. As research progresses in this area, an increasing number of viable applications for regenerative vibration control systems are being uncovered. This paper examines two broad applications: base-excited suspensions and periodically excited compound mounts. Some experimental results of the former are presented to support our claims.

Parameter Selection Strategies in Finite Element Model Updating

Abstract: In FE model updating, as in any identification procedure, we select some parameters in the model, and try to fine-tune them to minimize the discrepancy between the model predictions and the measured data. The paper compares the performance of the generic element matrices, recently introduced by the authors, with other selection strategies for finite element model updating. The updated models obtained from these methods are compared with the measured data and rated according to their ability to produce the measured data within and beyond the frequency range used in the updating, and more importantly, according to their ability to predict the effect of design changes.

A Variational Formulation, a Work-Energy Relation and Damping Mechanisms of Active Constrained Layer Treatments

Abstract: The purposes of this paper are to formulate active constrained layer (ACL) damping treatments through a variational approach, to study the work-energy relation of ACL, and to identify damping mechanisms of ACL treatments. Application of the extended Hamilton principle to ACL results in the equations of motion of ACL and the charge equation of electrostatics for the piezoelectric constraining layer. The work-energy equation together with the charge equation shows that the power dissipated through the active damping is the product of the electric field and the axial velocity of the piezoelectric constraining layer at the boundaries. This unique feature suggests that a set-sensing and actuating piezoelectric constraining layer may be an appropriate design in dissipating vibration energy without causing instability. To identify the damping mechanisms, a sensitivity analysis shows that the effectiveness ofA CL damping primarily depends on the active and passive damping forces transmitted to the vibrating structure through the viscoelastic layer. The active damping force transmitted depends on the controller transfer function as well as a system parameter, termed active damping sensitivity factor, which depends entirely on the configuration of the passive constrained layer and the sensor. Finally, numerical results on ACL beams are obtained to illustrate the theoretical predictions above.

Modelling of a Hybrid Constrained Layer/Piezoceramic Approach to Active Damping

Abstract: It has been shown that significant reductions in structural vibration levels can be achieved using a hybrid system involving constrained layer damping and active control with piezoceramics. In this paper, mathematical models based on the Rayleigh Ritz approach, are developed to describe the longitudinal and flexural vibration behaviour of a cantilevered beam when excited using piezoceramic patches bonded to a constrained layer damping treatment. Predictions of static and steady state dynamic behaviour, obtained using the models are validated by comparison with results from finite element analysis and laboratory experiments. The models are then used in open loop and closed loop velocity feedback control simulations to demonstrate the improvements in stability and performance achieved using this method over that achieved using conventional active control.

Natural Frequencies and Stability of an Axially-Traveling String in Contact With a Stationary Load System

Abstract: The natural frequencies and stability of a string traveling between two fixed supports and in contact with a stationary load system, which contains such parameters as dry friction, inertia, damping, and stiffness, are investigated both numerically and analytically. After establishing the orthogonality properties between. the eigenfunctions of a freely traveling string, the eigenvalues of the coupled system are calculated by a numerical procedure based on eigenfunction expansion method. It is found that the stiffness in the load system tends to increase the natural frequencies of the traveling string, while the inertia tends to decrease the natural frequencies. When the load system contains both inertia and stiffness elements with natural frequency W z , inertia effect is dominant for the modes with natural frequencies higher than W z , and stiffness effect is dominant for the modes with natural frequencies lower than W z . Large dry friction causes flutter instability in the high speed range, which cannot be suppressed by the damping element in the load system. The expressions for the derivatives of eigenvalues with respect to various load parameters are derived to verify the numerical results.

Active Vibration Absorption Using Delayed Resonator With Relative Position Measurement

Abstract: A novel active vibration absorption technique, the Delayed Resonator, has been introduced recently as a unique way of suppressing undesired oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with a time delay. Its strengths consist of extremely simple implementation of the control algorithm, total vibration suppression of the primary structure against a harmonic force excitation and full effectiveness of the absorber in a semi-infinite range of disturbance frequency, achieved by real-time tuning. All this development work was done using the absolute displacements of the absorber in the feedback. These measurements, however, may be difficult to obtain and for some applications impossible. This paper deals with the operating and design repercussions caused by the substituting of an easier measurement: the relative motion of the absorber with respect to the primary structure. Although the proposition sounds like a trivial extension to the prior work it gives rise to important concerns such as system stability. Theoretical foundations for the Delayed Resonator (DR) are briefly recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a harmonic force is discussed utilizing both absolute and relative position measurement of absorber mass. Methods for stability range analysis and transient behavior are presented as design tools. Properties observed for the same system with these two different feedbacks are compared. Another important advantage of the relative position feature is is to decouple the operation of the absorber from the primary structure entirely.

Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems

Abstract: A precise integration algorithm has recently been proposed by Zhong (1994) for dynamic stiffness matrix computations, but he did not give a corresponding eigenvalue count method. The Wittrick-Williams algorithm gives an eigenvalue count method for pure displacement formulations, but the precise integration method uses a mixed variable formulation. Therefore the Wittrick-Williams method is extended in this paper to give the eigenvalue count needed by the precise integration method and by other methods involving mixed variable formulations. A simple Timoshenko beam example is included.

The Effect of Thermal Prestress on the Free Vibration Characteristics of Clamped Rectangular Plates: Theory and Experiment

Abstract: In a combined theoretical and experimental approach, the free vibration characteristics ofa uniformly heated, fully clamped (out-of-plane), rectangular plate are considered. Specifically, this work focuses on the behavior of the small amplitude natural frequencies as the temperature is increased from the ambient. The effects of initial geometric imperfections, modal coupling, imperfect clamping (in-plane) and post-buckling are addressed. Comparisons between theory and experiment show excellent agreement.

Control of Forced Vibration Using Multi-Electrode Electro-Rheological Fluid Dampers

Abstract: Vibration control of cylindrical, electro-rheological fluid (ERF) dampers were studied. Single- as well as multi-electrode cylindrical ERF dampers were designed, built and tested under a forced vibration motion. Closed-loop, on-line control systems utilizing bang-bang and linear proportional controller were implemented to control the damping capacity of the ERF dampers. In addition, the designs were modified to reduce the required activation voltage. These modifications include increasing the electrode surface area as well as the number of electrodes. The damping ability of the dampers was further enhanced by using two identical dampers in series connection.

Flexural Vibration of Cylindrical Shells Partially Coupled With External and Internal Fluids

Abstract: In this paper, the free flexural vibrations of a partially fluid-loaded simply supported circular cylindrical shell are studied; the fluid is assumed to be inviscid and to present a free-surface parallel to the shell axis. The presence of external and internal fluids are both studied and the problem for incompressible and compressible fluid are both discussed by using the added virtual mass approach. Circumferential dependence of displacement is extended in a Fourier series. The maximum potential energy of the cylinder is evaluated using a sum of reference kinetic energies of the shell vibrating in vacuum; this fact allows the proposed method to be independent from the theory of shells used. Then, the Rayleigh quotient for fluid-shell coupled vibration is formulated and minimized to obtain the Galerkin equation whose solution gives the natural frequencies and mode shapes. Numerical computations are performed to obtain the modal characteristics as functions of the level of water in contact with the shell in the range of good accuracy of the theory, that is around the half-wet shell level. Results for both a shell partially surrounded and filled with water are obtained and compared.

A Subharmonic Vibration Absorber for Rotating Machinery

Abstract: We demonstrate a dynamic vibration absorber system which can be used to reduce speed fluctuations in rotating machinery. The primary system is modeled as a simple rotating disk, and the idealized absorber system consists of a pair of equal point masses which are free to move along identical, prescribed paths relative to the disk. The unique features of the proposed arrangement are that the absorbers are tuned to one-half of the frequency of the applied torque and, more importantly, that they are effective in the fully nonlinear operating range. These absorbers can, in the undamped case, exactly cancel a pure harmonic applied torque of a given order without inducing any higher harmonics, thus rendering a perfectly constant speed of rotation. A perturbation method is used to extend the results to the small damping case and to investigate the dynamic stability of the desired motion. Simulations are used to verify the analysis and to demonstrate the effectiveness of the device.

Identification of Structural Parameters in Mistuned Bladed Disks

Abstract: The present investigation focused on the estimation of the parameters of a structural model to represent at best a set of measurements of the steady state response of a mistuned bladed disk. The applicability of the least squares and maximum likelihood approaches to the identification of the bladed disk model from this data is first investigated. The advantages and drawbacks of these techniques motivate the introduction ofa new mixed least squares-maximum likelihood formulation which is shown to recover well the true model parameters from noisy simulated response data.

Modal sensitivity analysis of coupled acoustic-structural systems

Abstract: Modal analysis of coupled acoustic-structural systems leads to unsymmetric eigenproblem of special form which introduce different left and right eigenvectors. In this paper, the relation between left and right eigenvectors is first established by symmetrization of the unsymmetric eigensystem, and then Nelson's method is extended to coupled acoustic-structural systems for calculating the sensitivities of the eigenvalues and eigenvectors. The method only needs to calculate the sensitivities of the right eigenvectors and can treat the Helmholtz resonance mode naturally. Numerical examples of an acoustic box model solved by the proposed approach are compared with finite difference approach and good agreement is noted.

Natural Vibrations of a Clamped-Clamped Arch With an Open Transverse Crack

Abstract: The paper presents a finite element model of the arch with a transverse, one-edge crack. A part of the cracked arch is modelled by a curved beam finite element with the crack. Parts of the arch without the crack are modelled by noncracked curved beam finite elements. The crack occurring in the arch is nonpropagating and open. It is assumed that the crack changes only the stiffness of the arch, whereas the mass is unchanged. The method of the formation of the stiffness matrix of a curved beam finite element with the crack is presented. The effects of the crack location and its length on the changes of the in-plane natural frequencies and mode shapes of the clamped-clamped arch are studied.

Dynamic loosening and tightening of a single-bolt assembly

Abstract: Previous analyses of threaded fasteners under vibration are based on static equilibrium conditions with supporting data limited to low frequency loading. Such analyses predict only a net loosening action. This paper presents a dynamic model of a single-bolt assembly with moderate pre-load subjected to axial harmonic vibration. Simulations with this model predict that threaded fasteners can, on the average, loosen or tighten in the presence of vibration; and that the applied vibration, as well as other system parameters, can be tuned so that either action occurs. Measurements from a single-bolt assembly apparatus are presented and compared with the simulations.

A Finite Element Geometrically Nonlinear Dynamic Formulation of Flexible Multibody Systems Using a New Displacements Representation

Abstract: In previous work (Mayo, 1993), the authors developed two geometrically nonlinear formulations of beams inflexible multibody systems. One, like most related methods, includes geometric elastic nonlinearity in the motion equations via the stiffness terms (Mayo and Dominguez, 1995), but preserving terms, in the expression for the strain energy, of a higher-order than most available formulations. The other formulation relies on distinguishing the contribution of the foreshortening effect from that of strain in modelling the displacement of a point. While including exactly the same nonlinear terms in the expression for the strain energy, the stiffness terms in the motion equations generated by this formulation are exclusively limited to the constant stiffness matrix for the linear analysis because the terms arising from geometric elastic nonlinearity are moved from elastic forces to inertial, reactive and external forces, which are originally nonlinear. This formulation was reported in a previous paper (Mayo et al, 1995) and used in conjunction with the assumed-modes method. The aim of the present work is to implement this second formulation on the basis of the finite-element method. If, in addition, the component mode synthesis method is applied to reduce the number of degrees of freedom, the proposed formulation takes account of the effect of geometric elastic nonlinearity on the transverse displacements occurring during bending without the need to include any axial vibration modes. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms.

A Driver’s Seat With Active Suspension of Electro-pneumatic Type

Abstract: The aim of this article is to summarize some of the results of a study of a driver's seat with an electro-pneumatic active suspension utilizing a pneumatic spring and a proportional electro-pneumatic transducer. Discussion of the system's simplified mathematical description is followed by a short explanation of the full scale dummy driver's seat with active pneumatic suspension and discussion of some experimental results.

Torsional Vibration Control of a Shaft Through Active Constrained Layer Damping Treatments

Abstract: This paper proposes a hybrid damping design to control torsional vibration of a shaft with a circular cross section through use of actively constrained layer (ACL) damping treatments proposed by Baz (1993) and Shen (1993, 1994a). The ACL damping treatment consists of a piezoelectric constraining layer and a viscoelastic shear layer wrapping around the shaft in the form of a helix. In addition, the angular displacement of the shaft is fed back to regulate the helical motion of the piezoelectric constraining layer. The equation of motion of this design is derived, and its stability and controllability are discussed. Finally, numerical examples show that this ACL design can reduce torsional vibration of a shaft. A sensitivity analysis shows that ACL is most effective in suppressing those modes with significant torsional vibration response. Stability, in general, is not a critical factor in designing ACL systems, because the piezoelectric strain of the constraining layer at the threshold of instability is too large to occur.

Putting Statistics into the Statistical Energy Analysis of Automotive Vehicles

Abstract: Sound and vibration transmission modeling methods are important to the design process for high quality automotive vehicles. Statistical Energy Analysis (SEA) is an emerging design tool for the automotive industry that was initially developed in the 1960's to estimate root-mean-square sound and vibration levels in structures and interior spaces. Although developed to estimate statistical mean values, automotive design application of SEA needs the additional ability to predict statistical variances of the predicted mean values of sound and vibration. This analytical ability would allow analysis of vehicle sound and vibration response sensitivity to changes in vehicle design specifications and their statistical distributions. This paper will present an algorithm to extend the design application of the SEA method through prediction of the variances of RMS. responses of vibro-acoustic automobile structures and interior spaces from variances in SEA automotive model physical parameters. The variance analysis is applied to both a simple, complete illustrative example and a more complex automotive vehicle example. Example variance results are verified through comparison with a Monte Carlo test of 2,000 SEA responses whose physical parameters were given Gaussian distributions with means at design values. Analytical predictions of the response statistics agree with the statistics generated by the Monte Carlo method but only require about 1/300 of the computational effort.