bluuebunny/crossref_metadata_2025 huggingface dataset:
Blade Design Trade-Offs Using Low-Lift Airfoils for Stall-Regulated HAWTs
Authors: Gigue`re P. , Selig M. S. , Tangler J. L.
Published: February 2008

A systematic blade design study was conducted to explore the trade-offs in using low-lift airfoils for a 750-kilowatt stall-regulated wind turbine. Tip-region airfoils having a maximum-lift coefficient ranging from 0.7-1.2 were considered in this study, with the main objective of identifying the practical lower limit for the maximum-lift coefficient. Blades were optimized for both maximum annual energy production and minimum cost of energy using a method that takes into account aerodynamic and structural considerations. The results indicate that the effect of the maximum-lift coefficient on the cost of energy is small with a slight advantage to the highest maximum lift coefficient case considered in this study. As a consequence, higher maximum lift coefficient airfoils for the tip-region of the blade become more desirable as machine size increases, provided the airfoils yield acceptable stall characteristics. The conclusions are applicable to large wind turbines that use passive or active stall to regulate peak power.
The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response
Authors: Felszeghy S. F.
Published: February 2008

The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.
The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 2: Transient Response
Authors: Felszeghy S. F.
Published: February 2008

The transient response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions were developed in Part 1 of this article for all load speeds greater than zero. The solution to the homogeneous equations of motion is developed here in Part 2. It is shown that the latter solution can be obtained by numerical integration using the method of characteristics. Particular attention is given to the cases when the load travels at the critical speeds consisting of the minimum phase velocity of propagating harmonic waves and the sonic speeds. It is shown that the solution to the homogeneous equations combines with the steady-state solution in such a manner that the beam displacements are continuous and bounded for all finite times at all load speeds including the critical speeds. Numerical results are presented for the critical load speed cases.
Damping of Composite Tubes With Embedded Viscoelastic Layers
Authors: Zhou Haiming , Rao Mohan D.
Published: February 2008

In this paper, the results of analytical investigation into the effects of cocuring fiber composite tubes with commercially available damping materials are presented. A comprehensive theory has been developed for studying the vibration of a composite tube with multiple viscoelastic damping layers. The effects of transverse shear deformation, transverse normal stress and strain, rotary inertia, and higher-order stiffness terms are included in the modeling along with shear correction factors. Resonance frequency and loss factor results as a function of various geometric and physical parameters are presented for composite tubes with single and double damping layers. It is demonstrated through a parametric study that in all these systems, careful selection of damping and pre-preg material is needed to optimize the damping benefits desirable and the stiffness reductions that can be tolerated.
On Vibrations of a System With an Eigenfrequency Identical to That of One of Its Subsystems, Part 2
Authors: Pesterev A. V. , Bergman L. A.
Published: February 2008

The problem of free vibration of a complex system with a natural frequency identical to that of one of its subsystems is further discussed. Such eigenvibrations need special consideration in many modal synthesis methods, as the Green’s operator of the resonating subsystem does not exist at subsystem natural frequencies. A general treatment of this problem has been given by the authors in a companion paper. In this supplement, the previous work is extended to include the case of interaction forces applied to the resonating subsystem at points where the corresponding eigenfunction of the subsystem has maxima. Examples of such eigenvibrations are presented for two simple systems. The differences between these examples and those of the previous paper are noted and discussed.
Threaded Components Under Axial Harmonic Vibration, Part 2: Kinematic Analysis
Authors: Hess D. P.
Published: February 2008

A kinematic analysis is presented for the twisting of threaded components loaded by gravity and subjected to axial harmonic vibration. It is shown that the complex motions of twisting due to the interaction of the applied vibration and the resulting unsteady friction can be broken down and described as a sequence of simple motion forms. The analysis provides significant insight into the mechanisms of twisting both with and against load experimentally explored in Part 1 of this paper. Several solutions which are representative of the observed phenomena are developed and simulation results are presented.
Identification of Failure Modes of Carbon-Carbon Composites at Various Processing Stages Using the Acoustic Emission Technique
Authors: Vaidya U. K. , Raju P. K.
Published: February 2008

In the fabrication of carbon-carbon (C/C) composites, the first carbonization process is crucial, as the mechanical properties of the composite are completely altered at this stage. Some predominant effects of this process, in the composite, are development of delaminations, fiber breaks, distributed porosity and formation of transverse cracks in the matrix. These effects are to some extent, beneficial, during latter processing of the composite. However, excessive occurrence of any of these effects is undesirable. Keeping this in view, the present study focuses on the utilization of acoustic emission (AE) (as a nondestructive evaluation (NDE)) technique for identification and characterization of failure modes of C/C composites at several processing stages of C/C composites. Primarily, acoustic emission (AE) has been used to study the failure modes of C/C composites at the as-cured, carbonized and densified stages using AE parameters such as the peak amplitude, event duration and energy content of the AE signals. These parameters have been related to the initiation and progression of matrix cracking, fiber breakage and delaminations which occur in the composite at the as-cured, carbonized and densified stages.
An Inverse Vibration Method Applied to Bond Evaluation of Space Shuttle Tiles
Authors: Mueller S. A. , Moslehy F. A.
Published: February 2008

This paper describes an inverse vibration method for determining unknown parameters of the physical system by using partial modal information. The method is based on knowing the complete mass matrix of the system and part of its stiffness matrix. The unknown parameters in the stiffness matrix are related to the physical system. This method is applied to the bond evaluation of the space shuttle tiles. The tiles are excited by audible acoustic energy and the response is measured by a noncontact laser vibrometer. The inverse solution is incorporated into a user-friendly computer program to determine the size and location of disbonded regions in the tile assembly. The program allows for any tile geometry as well as the orthotropic properties of the the material. Both simulated data, provided by finite element analysis, and experimentally acquired data are used to verify the proposed method.
Free and Forced Vibrations of a Spinning Viscoelastic Beam
Authors: Sturla F. A. , Argento A.
Published: February 2008

The free and forced response of spinning, viscoelastic, Rayleigh shafts is studied. Viscoelasticity is included using the three parameter solid model. The closed form polynomial frequency equation and integral expressions for the response to a general forcing function are derived. A convenient decay parameter is described. Results are given for natural frequencies and decay rates as functions of shaft rotation speed, stiffness, and viscosity. It is found that shaft materials are possible which have desirable damping and natural frequency characteristics. A parameter case is discussed in which natural frequency and damping simultaneous increase, while stiffness is held constant. Also, the special case of forced response to a step load is derived and used to illustrate the combined effects of viscoelasticity and gyroscopic forces.
Optimal Design of Acoustical Foam Treatments
Authors: Kang Yeon June , Bolton J. Stuart
Published: February 2008

A finite element model for elastic porous materials is presented that allows for interfaces with adjacent acoustical media that are arbitrarily oriented with respect to the global coordinate system. The foam finite element is based on a complete elastic porous material theory that can account for all the three wave types known to be significant in foams. Example problems are used to illustrate the application of foam finite elements to the optimal design of a foam wedge terminating a waveguide. The wedge angle is used as a design parameter (while the wedge volume is held constant) and the performance measure is the frequency-averaged absorption coefficient.
An Energy-Based Parametric Control Approach for Structural Vibration Suppression via Semi-Active Piezoelectric Networks
Authors: Wang K. W. , Lai J. S. , Yu W. K.
Published: February 2008

A structural vibration control concept, using piezoelectric materials shunted with real-time adaptable electrical networks, has been investigated. The variable resistance and inductance in an external RL circuit are used as control inputs. An energy-based parametric control scheme is created to reduce the total system energy (the main structure mechanical energy plus the electrical and mechanical energies of the piezoelectric material and electrical circuit) while minimizing the energy flowing into the main structure. Stability of the closed-loop system is proved. The performance of the controller is examined through analyzing a beam example. It is shown that the structure energy level and vibration amplitude can be suppressed effectively.
On Efficient Computation of the Steady-State Response of Linear Systems With Periodic Coefficients
Authors: Selstad T. J. , Farhang K.
Published: February 2008

An efficient method for obtaining the steady-state response of linear systems with periodically time varying coefficients is developed. The steady-state solution is obtained by dividing the fundamental period into a number of intervals and establishing, based on a fourth-order Rung-Kutta formulation, the relation between the response at the start and end of the period. Imposition of periodicity condition upon the response facilitates computation of the initial condition that yields the steady-state values in a single pass; i.e., integration over only one period. Through a practical example, the method is shown to be more accurate and computationally more efficient than other known methods for computing the steady-state response.
Determination of Far-Field Pattern of Rigid Scatterers Using Independent Finite Element Method and Eigenfunction Expansion, Part 2: Nonaxisymmetric Scattering
Authors: Prabavathi C. , Vendhan C. P.
Published: February 2008

The near- and far-field steady state scattered potentials around a rigid arbitrary obstacle subjected to plane incident wave are computed by FE and eigenfunction expansion approach. The near-field is bounded by a truncation surface which is spherical. The nonaxisymmetric damper equation developed by Bayliss et al. (SIAM J. Appl. Math. Vol. 42, pp. 430–451, 1982) is employed on this surface. The computed FE near-field potential on the truncation boundary is employed as a Dirichlet boundary condition to obtain the expansion coefficients which eventually help in obtaining the complete solution in the entire outer domain including the far-field. The numerical technique is applied to problems of rigid scattering of beam-on- and oblique-incident waves by rigid prolate spheroid and hemispherically capped cylinder and contour plots of far-field scattered potential are presented.
Dynamic Analysis of Folded Plate Structures
Authors: Danial A. N. , Doyle J. F. , Rizzi S. A.
Published: February 2008

A spectral element method for analyzing wave propagation in multiply connected plates oriented at arbitrary angles is presented. These plate elements may be joined to model structures with stiffeners, open or closed thin-walled tubes, corrugated plates, channels, and ducts. The element models exactly both in-plane and out-of-plane responses over large domains. Results for point impact of a plate with stringers and a thin-walled box beam show excellent agreement with finite element solutions.
Vibration of a Rotating Timoshenko Beam
Authors: White M. W. D. , Heppler G. R.
Published: February 2008

Timoshenko beam theory is used to model a flexible slewing link with an attached payload using two different rotating frames of reference: pseudo-pinned and pseudo-clamped. The boundary conditions are presented for both formulations; these lead naturally to the frequency equation for the link. The infinite dimensional model of the slewing link is then approximated by a finite dimensional model. Finally, these two formulations are shown to be equivalent through a simple transformation.
Relating Turbulence to Wind Turbine Blade Loads: Parametric Study with Multiple Regression Analysis
Authors: Kashef T. , Winterstein S. R.
Published: February 2008

Different wind parameters are studied to find a set that is most useful in estimating fatigue loads on wind turbine blades. The histograms of rainflow counted stress ranges are summarized through their first three statistical moments and regression analysis is used to estimate these moments in various wind conditions. A systematic method of comparing the ability of different wind parameters to estimate the moments is described and results are shown for flapwise loads on three HAWTs. In the case of two of these turbines, the stress ranges are shown to be highly correlated with a turbulence measure obtained by removing a portion of the low-frequency content of the wind.
Wave Mixing Effects on a Periodically Ribbed Cylindrical Shell
Authors: Photiadis D. M.
Published: February 2008

An examination of the response of a periodically ribbed cylindrical shell shows several effects due to the mixing of fast and slow waves on the shell. In wavenumber-frequency space, this mixing manifests itself in the formation of hybrid modes, for example, mixtures of part shear and part flexural vibration. The mixing is strongest when the phase speeds of the different wave types coincide and so reflect the dispersion curves of the flexural Bloch wavenumber. The dispersion curves may be significantly altered by mixing effects, and even for weak wave mixing the polarization of the fast waves can be changed significantly. This effect greatly alters the coupling of the fast waves to an external fluid.
Free Bending Vibrations of Adhesively Bonded Orthotropic Plates With a Single Lap Joint
Authors: Yuceoglu U. , Toghi F. , Tekinalp O.
Published: February 2008

This study is concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The influence of shear deformation and rotatory inertia in plates are taken into account in the equations according to the Mindlin plate theory. The effects of both thickness and shear deformations in the thin adhesive layer are included in the formulation. Plates are assumed to have simply supported boundary conditions at two opposite edges. However, any boundary conditions can be prescribed at the other two edges. First, equations of motion at the overlap region are derived. Then, a Levy-type solution for displacements and stress resultants are used to formulate the problem in terms of a system of first order ordinary differential equations. A revised version of the Transfer Matrix Method together with the boundary and continuity conditions are used to obtain the frequency equation of the system. The natural frequencies and corresponding mode shapes are obtained for identical and dissimilar adherends with different boundary conditions. The effects of some parameters on the natural frequencies are studied and plotted.
Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method
Authors: Gorrepati K. M. , Rao M. D.
Published: February 2008

This paper presents the analysis of modal parameters (natural frequencies, damping and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joints with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.
Stability and Controllability of Euler-Bernoulli Beams With Intelligent Constrained Layer Treatments
Authors: Shen I. Y.
Published: February 2008

This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer function approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.
Maximizing the Fundamental Natural Frequency of Triangular Composite Plates
Authors: Abrate S.
Published: February 2008

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.
Complementarity Problems of Stick-Slip Vibrations
Authors: Pfeiffer F.
Published: February 2008

Multibody systems with many friction contacts not being decoupled by some force laws afford a special treatment with respect to the uniqueness of the solution after a contact event. This problem can be solved by an optimization technique including unequality constraints which corresponds exactly to the physical properties of stick-slip vibrations. The theoretical background to this complementarity problem is presented and illustrated by examples from machine dynamics.
The Effects of Stingers on Receptance Function Measurements
Authors: Lee Jyh-Chiang , Chou Yuan-Fang
Published: February 2008

When using a shaker to conduct receptance function measurements, it is usual to put a stinger between the shaker and a force transducer that is attached to a test structure. Ideally, a stinger can transmit desired axial force to excite the structure and isolate excitations in all other DOFs in order not to bias the testing results. The selections of stingers were made by trial-and-error, by chance, or by experience. This may cause test errors especially when the magnitude of receptance function of the excitation system is significant compared with that of the structural system at the correspondent frequency. In this work, substructure synthesis algorithm was used to calculate the effects of stingers on the receptance function measurements. The dynamic characteristics of a shaker, a shaker suspension system, a stinger, and a test structure were considered in the analysis. If the shaker is fixed, the method can predict the effects of the stinger on measured receptance functions. Finally, a cantilever beam and seven different sizes of stingers were used to verify this method. Good agreements were found between the predictions and testing results.
Torsional Vibrations in Electrical Induction Motor Drives During Start-up
Authors: Ran L. , Yacamini R. , Smith K. S.
Published: February 2008

When electrical induction motors are started direct on-line they generate a considerable pulsating torque. This start up torque can create problems when the motor is connected to mechanical loads such as fans or pumps and there are reported cases of the interconnecting shafts having been sheared on start-up. This paper examines the inter-relationship between the electric motor and the mechanical system which is effectively a multi-mass oscillatory system. It will be shown that large transients of both torque and speed occur immediately on start-up due to excitation of the oscillatory system. It will also be shown that later during the run up process, large vibrations can occur due to the negative damping of the rotor winding. A time domain model of the intercoupled electromechanical system is presented and the effect of ac system impedance, rotor resistance and the size of the motor relative to the driven mass is investigated.
Structural Control Using Analog Phase-Locked Loops
Authors: Niezrecki C. , Cudney H. H.
Published: February 2008

A study of the application of the phase-locked loop (PLL) to modal control of mechanical structures is performed. An analog PLL circuit is used to control the vibration of a cantilevered beam with piezoelectric sensors and actuators. By using the PLL controller, strain rate feedback is provided within a narrow and distinct frequency range about the fourth mode of the beam. The controller ignores all other modes and does not affect the phase outside of the frequency range. The PLL controller provides a simple, inexpensive, and effective method to control an individual structural mode or set of modes without causing spillover.
A Separation Principle for Gyroscopic Conservative Systems
Authors: Meirovitch L.
Published: February 2008

Closed-form solutions to differential eigenvalue problems associated with natural conservative systems, albeit self-adjoint, can be obtained in only a limited number of cases. Approximate solutions generally require spatial discretization, which amounts to approximating the differential eigenvalue problem by an algebraic eigenvalue problem. If the discretization process is carried out by the Rayleigh-Ritz method in conjunction with the variational approach, then the approximate eigenvalues can be characterized by means of the Courant and Fischer maximin theorem and the separation theorem. The latter theorem can be used to demonstrate the convergence of the approximate eigenvalues thus derived to the actual eigenvalues. This paper develops a maximin theorem and a separation theorem for discretized gyroscopic conservative systems, and provides a numerical illustration.
Modelling of a Hybrid Constrained Layer/Piezoceramic Approach to Active Damping
Authors: Rongong J. A. , Wright J. R. , Wynne R. J. , Tomlinson G. R.
Published: February 2008

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.
Pole Assignment Self-tuning Control for a Multivariable Vibrating System
Authors: Huang Shiuh-Jer , Shu Biing-Tay
Published: February 2008

A dynamic absorber with DC servo motors for actuation is designed and built as an actively suppressing vibration system. This is a two-stage spring-lumped mass system with sliding guide. Each mass has an internal vibration source. The discrete time state space model is identified from the input and output data of this system by using a modified recursive least square method. Then a multivariable adaptive control strategy is derived by combining the concept of the pole assignment with a multivariable stability theorem. Finally, the feasibility of employing this control method is evaluated based upon experimental results.
3-D Vibration Analysis of Fiber Reinforced Composite Laminated Cylindrical Shells
Authors: Xiaoyu Jiang
Published: February 2008

In this paper, 3-D solutions of free vibrations are presented for isotropic and composite laminated cylindrical shells. The perturbation method and a variational principle are used to obtain the solutions which satisfy the 3-D differential equations of motion, the strain-displacement relations, the stress-strain relations, the boundary conditions and the continuity conditions at layer interfaces. The distributions of displacements and stresses in the shells are shown in figures. The free vibration frequencies are listed in tables. In the thickness direction of the shells, continuous displacements and stresses are obtained. And the importance of transverse shear stresses and transverse normal stress is analyzed.
Acoustic Radiation From Multi-Span Baffled Panels
Authors: Hawwa M. A. , Nayfeh A. H.
Published: February 2008

The objective of this study is to evaluate the acoustic radiation from a multi-span baffled panel having certain types of irregularities, including intermediate torsional springs and/or displaced intermediate supports. These irregularities lead to the confinement of motion to a limited part of the structure, as evident from the mode shapes. The radiation efficiency is calculated for both ordered and disordered panels in order to measure the tendency of the panel to radiate sound. It is found that the modes of disordered panels radiate slightly more than those of the ordered ones.
Stability Analysis and Complex Dynamics of a Gear-Pair System Supported by a Squeeze Film Damper
Authors: Chen Chin-Shong , Natsiavas S. , Nelson H. D.
Published: February 2008

The stability properties of periodic steady state response of a nonlinear geared rotordynamic system are investigated. The nonlinearity arises because one support of the system includes a cavitated squeeze film damper, while the excitation is caused by mass unbalance. The dynamical model and the procedure which leads to periodic steady state response of the system examined have been developed in an earlier paper. Here, the emphasis is placed on analyzing the stability characteristics of located periodic solutions. Also, within ranges of the excitation frequency where no stable periodic solutions are detected, the long time behavior of the system is investigated by direct integration of the equations of motion. It is shown that large order subharmonic, quasiperiodic and chaotic motions may coexist with unstable periodic response in these frequency ranges. Finally, attention is focused on practical consequences of these motions.
Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems
Authors: Sundararajan P. , Noah S. T.
Published: February 2008

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.
Natural Vibrations of a Clamped-Clamped Arch With an Open Transverse Crack
Authors: Krawczuk M. , Ostachowicz W.
Published: February 2008

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.
Application of Center Manifold Theory to Regulation of a Flexible Beam
Authors: Khajepour Amir , Golnaraghi M. Farid , Morris Kirsten A.
Published: February 2008

In this paper we consider the problem of regulation of a flexible lumped parameter beam. The controller is an active/passive mass-spring-dashpot mechanism which is free to slide along the beam. In this problem the plant/controller equations are coupled and nonlinear, and the linearized equations of the system have two uncontrollable modes associated with a pair of pure imaginary eigenvalues. As a result, linear control techniques as well as most conventional nonlinear control techniques can not be applied. In earlier studies Golnaraghi (1991) and Golnaraghi et al. (1994) a control strategy based on Internal resonance was developed to transfer the oscillatory energy from the beam to the slider, where it was dissipated through controller damping. Although these studies provided very good understanding of the control strategy, the analytical method was based on perturbation techniques and had many limitations. Most of the work was based on numerical techniques and trial and error. In this paper we use center manifold theory to address the shortcomings of the previous studies, and extend the work to a more general control law. The technique is based on reducing the dimension of system and simplifying the nonlinearities using center manifold and normal forms techniques, respectively. The simplified equations are used to investigate the stability and to develop a relation for the optimal controller/plant natural frequencies at which the maximum transfer of energy occurs. One of the main contributions of this work is the elimination of the trial and error and inclusion of damping in the optimal frequency relationship.
Boundary Control of Beams Using Active Constrained Layer Damping
Authors: Baz A.
Published: February 2008

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.
A Variational Formulation, a Work-Energy Relation and Damping Mechanisms of Active Constrained Layer Treatments
Authors: Shen I. Y.
Published: February 2008

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 self-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 of ACL 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.
A Two-Step Structural Damage Detection Approach With Limited Instrumentation
Authors: Kim Hyoung M. , Bartkowicz T. J.
Published: February 2008

This paper describes a two-step damage detection and health monitoring approach that was developed for large and complex structures with a limited number of measurements. The first step identifies a general area of structural damage using the optimal model update method and a hybrid model reduction/eigenvector expansion technique. The second step locates a specific damaged structural component using a design sensitivity technique based on a priori information from the first damage detection step. Performance of the proposed damage detection approach was demonstrated with testing and analysis of a ten-bay hexagonal truss structure. Procedures developed for the damage detection are also directly applicable to test/dynamic math model correlation when the number of measurements is limited.
Resonant-Frequency-Distribution of Internal Mass Inferred From Mechanical Impedance Matrices, With Application to Fuzzy Structure Theory
Authors: Pierce A. D.
Published: February 2008

The partitioning of internal mass among bands of resonant frequencies is addressed for a prototype internal vibrating structure with small damping, attached via an arbitrary number NA of attachment points to an external structure. Insofar as the dynamics of the latter are concerned, the internal structure is adequately described by a frequency-dependent impedance matrix, any given column of which lists the ratios of the 3NA force components induced by one of the attachment points’ velocity components when all of the other velocity components are held to zero. The properties of matrix elements and their frequency dependence are discussed in relation to principles of mechanics, especially the requirements of translational and rotational invariance of the potential energy functions. Among the deductions are that modal masses can be defined with values calculable solely from the impedance matrix measurements, and that the modal masses sum to the total mass of the internal vibrating system.
Prediction of Periodic Response of Rotor Dynamic Systems With Nonlinear Supports
Authors: Wang Yu
Published: February 2008

A numerical-analytical method for estimating steady-state periodic behavior of nonlinear rotordynamic systems is presented. Based on a finite element formulation in the time domain, this method transforms the nonlinear differential equations governing the motion of large rotor dynamic systems with nonlinear supports into a set of nonlinear algebraic equations with unknown temporal nodal displacements. A procedure is proposed to reduce the resulting problem to solving nonlinear algebraic equations in terms of the coordinates associated with the nonlinear supports only. The result is a simple and efficient approach for predicting all possible fundamental and sub-harmonic responses. Stability of the periodic response is readily determined by a direct use of Floquet’s theory. The feasibility and advantages of the proposed method are illustrated with two examples of rotor-bearing systems of deadband supports and squeeze film dampers, respectively.
Redesign of Ultrasonic Block Horns for Improved Vibration Performance
Authors: Lucas M. , Smith A. C.
Published: February 2008

Ultrasonic block horns are prone to reliability problems associated with modal activity close to the tuned operating frequency. This paper presents an approach to block horn design, which relies on two laser based vibration measurement techniques, electronic speckle pattern interferometry (ESPI) and laser doppler velocimetry (LDV) modal analysis, to validate finite element (FE) models. Block horn vibration characteristics are interpreted from experimental and theoretical data such that successful horn redesign can be achieved from modifications to the FE models.
Effects of Normal Strain in Core Material on Modal Property of Sandwich Plates
Authors: Lee Byung-Chan , Kim Kwang-Joon
Published: February 2008

In vibration analysis of sandwich beam/plates, it is often assumed that there is shear deformation only, without extension or compression in the viscoelastic layer. Certainly, this assumption may have limitations, for example, with increase of the core thickness or frequency range of vibration. The purpose of this paper is to consider the normal, as well as shear strain of the core material for modal parameter estimation of the sandwich plates and to investigate how much error will be caused by neglecting the extension or compression in the core material. Natural frequencies and modal loss factors are estimated for a simply supported square plate by taking the normal as well as shear deformation into account for dynamic modeling. Nondimensional characteristic equations are formulated and solved numerically for various ratios of the base layer thickness to plate length, core layer thickness to base layer, constraining layer thickness to base layer, and shear modulus of core material to elastic modulus of base layer. The effects of the various parameters on the modal properties are shown to be intercorrelated to each other and hence difficult to summarize in one phrase. Normal deformation of the core material plays an important role when the thickness ratio of constraining layer to base layer is 0.5 and its Poisson’s ratio is smaller than 0.49, and hence need to be included in the dynamic modeling especially for estimation of modal damping when one of the following conditions are met; 1) the ratio of base layer thickness to plate length is greater than 0.02, 2) the thickness ratio of core layer to base layer is greater than 0.01, 3) the wavelength of a mode is less than one third of the plate length, 4) the ratio of shear modulus of core material to elastic modulus of base material is less than 10−5.
Torsional Vibration Control of a Shaft Through Active Constrained Layer Damping Treatments
Authors: Shen I. Y. , Guo Weili , Pao Y. C.
Published: February 2008

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.
Nonlinear Decentralized Control of a Flexible Cable-stayed Beam Structure
Authors: Magan˜a M. E. , Volz P. , Miller T.
Published: February 2008

A decentralized controller that suppresses the vibrations of a flexible cable-stayed beam structure induced by an external random disturbance is presented. The controller is designed based on a lumped-mass model representation of the distributed parameter flexible beam structure. It contains a linear part and a nonlinear part. The linear part is used to introduce damping into the beam structure and the nonlinear part is used to further reduce the vibrations caused by the external disturbance. Its performance is assessed via digital computer simulation.
Control of Forced Vibration Using Multi-Electrode Electro-Rheological Fluid Dampers
Authors: Gordaninejad F. , Ray A. , Wang H.
Published: February 2008

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-hang 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.
Putting Statistics into the Statistical Energy Analysis of Automotive Vehicles
Authors: Radcliffe C. J. , Huang X. L.
Published: February 2008

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.