bluuebunny/crossref_metadata_2025 huggingface dataset:
A Method for Determining the Optimal Location of a Distributed Sensor/Actuator
Authors: Ko Byeongsik , Tongue Benson H. , Packard Andrew
Published: January 2014

The optimal location problem of distributed sensor/actuator for observation and control of a flexible structure is investigated. Using a property of controllability and observability grammian matrices, this approach employs a nonlinear optimization technique to determine the optimal placement of a distributed sensor/actuator. The effect of unimportant modes that do not strongly affect the structural behavior of a system is minimized and the effect of important modes is maximized. The final objective function is expressed as the combinational form of two different objective functions. This technique is applied to several types of beam support conditions and the corresponding optimal locations are determined.
Vibrations of a Beam Moving Over Supports with Clearance
Authors: Lee H.P.
Published: January 2014

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.
Response of Launch Pad Structures to Random Acoustic Excitation
Authors: Margasahayam Ravi N. , Caimi Raoul E.
Published: January 2014

The design of launch pad structures, particularly those having a large area-to-mass ratio, is governed by launch-induced acoustics, a relatively short transient with random pressure amplitudes having a non-Gaussian distribution. The factors influencing the acoustic excitation and resulting structural responses are numerous and cannot be predicted precisely. Two solutions (probabilistic and deterministic) for the random vibration problem are presented in this article from the standpoint of their applicability to predict the response of ground structures exposed to rocket noise. Deficiencies of the probabilistic method, especially to predict response in the low-frequency range of launch transients (below 20 Hz), prompted the development of the deterministic analysis. The relationship between the two solutions is clarified for future implementation in a finite element method (FEM) code.
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Authors: Bergamaschi Luca , Gambolati Giuseppe , Pini Giorgio
Published: January 2014

Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient) was developed, based on the conjugate gradient (CG) minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficientβkrequired at each DACG iteration for the computation of the new search directionPkare discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimalβkleads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimalβkand (LLT)−1as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
Nonlinear Resonance Behavior in the Human Exposed to Whole-Body Vibration
Authors: Smith Suzanne D.
Published: January 2014

The driving-point impedance technique was applied to identify nonlinear resonance behavior in the human exposed to sinusoidal vibration between 3 and 20 Hz at three acceleration levels. Up to four regions of resonance were observed. A significant decline in the first and fourth resonance frequency and the disappearance of the second resonance peak occurred with a fivefold increase in the acceleration level. A proposed, base-excited five degree-of-freedom model, representing major dynamic structures in the human, proved highly successful in simulating the typical impedance responses. The model was used to quantify the variations in the mass, stiffness, and damping characteristics associated with changes in the acceleration level.
Fully Coupled FE Analyses of Buried Structures
Authors: Baylot James T.
Published: January 2014

Current procedures for determining the response of buried structures to the effects of the detonation of buried high explosives recommend decoupling the free-field stress analysis from the structure response analysis. A fully coupled (explosive–soil structure) finite element analysis procedure was developed so that the accuracies of current decoupling procedures could be evaluated. Comparisons of the results of analyses performed using this procedure with scale-model experiments indicate that this finite element procedure can be used to effectively evaluate the accuracies of the methods currently being used to decouple the free-field stress analysis from the structure response analysis.
Eigensolution Derivatives for Arbitrarily Normalized Modes
Authors: Wang B.P.
Published: January 2014

Methods for computing eigenvector derivatives for arbitrarily normalized modes are derived. Formulations are presented for modal methods, Nelson's method, and a method for computing eigenvalue and eigenvector derivatives simultaneously. A simple numerical example is provided to illustrate various formulations.
Vibration Isolation: A Review, I. Sinusoidal and Random Excitations
Authors: Nelson F.C.
Published: January 2014

This article reviews the engineering theory and technology associated with the use of dicrete Isolators to protect Vibration-sensitive equipment or machinery against sinusoidal or random excitation. Special attention is given to protection against low frequency (<5 Hz) and high-frequency (>100 Hz) excitation. Both passive and active isolators systems are discussed.
Construction of Benchmark Problems for Solution of Ordinary Differential Equations
Authors: Lee Sangchul , Junkins John L.
Published: January 2014

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed in this fashion have a known exact solution, even though analytical solutions are generally not obtainable. The process leading to the exact solution makes use of an initially available approximate numerical solution. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Five illustrative examples are presented.
Design of Damping and Control Matrices by Modification of Eigenvalues and Eigenvectors
Authors: Neubert Vernon H.
Published: January 2014

Direct methods are presented, in state space, for design of control matrices for structures with and without initial viscous damping. given the desired changes in the eigenvalues and eigenvectors. The equations with full-state variable feedback areMz¨+Cz˙+Kz=−Gz˙−Hz. Advantage is taken of the special state-space form of the structural plant and eigenvector matrices to develop efficient numerical procedures. Essential relationships are derived between the upper and lower portions of the left and right eigenvector matrices for systems with simple eigenvalues. We distinguish between displacement mode shapes and eigenvectors in state space. A unique method is presented by which the[C+G]matrices are designed to achieve specified real parts of the eigenvalues, with no change in mode shapes or eigenvectors. In addition, two general methods are discussed. suitable for systems with nonproportional damping, where the eigenvalues are specified with or without change in mode shapes.
Effect of Surface Coatings on Cylinders Exposed to Underwater Shock
Authors: Kwon Y.W. , Bergersen J.K. , Shin Y.S.
Published: January 2014

The response of a coated cylinder (metallic cylinder coated with a rubber material) subjected to an underwater explosion is analyzed numerically. The dynamic response of the coated cylinder appears to be adversely affected when impacted by an underwater shock wave under certain conditions of geometry and material properties of the coating. When adversely affected, significant deviations in values of axial stress, hoop stress, and strain are observed. The coated cylinder exhibits a larger deformation and higher internal energy in the metallic material. Rubber coatings appeared to inhibit energy dissipation from the metallic material to the surrounding water medium. A parametric study of various coatings was performed on both aluminum and steel cylinders. The adverse effect of the coating decreased when the stiffness of the rubber layer increased, indicating the existence of a threshold value. The results of this study indicate that the stiffness of the coating is a critical factor to the shock hardening of the coated cylinder.
Optimal Location of Plate Damped Parts by Use of a Genetic Algorithm
Authors: Marcelin J.-L. , Trompette Ph.
Published: January 2014

Optimal damping of plates (or beams) partially covered by viscoelastic constrained layers is presented. The design variables are the locations and the sizes of the damped parts. The objective function is a linear combination of the first modal damping factors calculated from a specific finite element analysis. The discrete design variable optimization problem is solved using a genetic algorithm.
Transient Response of an Impacted Beam and Indirect Impact Force Identification Using Strain Measurements
Authors: Park Hyungsoon , Park Youn-sik
Published: January 2014

The impulse response functions (force-strain relations) for Euler–Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force, including reflection at the boundary, is obtained with the convolution approach using the impulse response function obtained by a Laplace transform and a numerical scheme. Using this relation, the impact force history is determined in the time domain and results are compared with those of Hertz's contact law. In the case of an arbitrary impact, the location of the impact force and the time history of the impact force can be found. In order to verify the proposed algorithm, measurements were taken using an impact hammer and a drop test of a steel ball. These results are compared with simulated ones.
Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation
Authors: Leung A.Y.T. , Qichang Zhang , Yushu Chen
Published: January 2014

A method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system. The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler and can easily be implemented: that is, given the coefficients of the governing equations, the response is obtained directly by substitution.
Actuator Placement in Multi-Degree-of-Freedom Vibration Simulators
Authors: Fitz-Coy Norman , Chatterjee Anindya
Published: January 2014

A method for comparing candidate actuator configurations for multi-degree-of-freedom (MDOF) vibration simulators is presented. The method has its roots in the comparison of achievable subspaces and maximum error bounds; the comparison is accomplished via a QR decomposition. In instances where two configurations yield the same error bound, the ratio of the largest to smallest singular value is used to determine the “best” configuration. Both amplitude bounds at given sensor locations and relative significance of each sensor's output, if known, can be incorporated in the analysis. Through numerical examples, it is demonstrated that no simple rule of thumb criterion appears to exist for the selection of actuator placement in MDOF vibration simulators.
Noise Source Location Optimization
Authors: O’Keefe Ed , Graves Russ
Published: January 2014

This article describes a method to determine locations of noise sources that minimize modal coupling in complex acoustic volumes. Using the acoustic source scattering capabilities of the boundary element method, predictions are made of mode shape and pressure levels due to various source locations. Combining knowledge of the pressure field with a multivariable function minimization technique, the source location generating minimum pressure levels can be determined. The analysis also allows for an objective comparison of “best/worst” locations. The technique was implemented on a personal computer for the U.S. Space Station, predicting 5–10 dB noise reduction using optimum source locations.
On the Effectiveness of Using Only Eigenvalues in Structural Model Updating Problems
Authors: Nobari A.S. , Ewins D.J.
Published: January 2014

In this article the subject of model updating using the inverse eigensensitivity method that uses only eigenvalues in the calculation is examined. The problem of creating an underdetermined set of equations is studied and ways of preventing it are addressed.
Evaluation of Eigenvalue Routines for Large Scale Applications
Authors: Tischler V.A. , Venkayya V.B.
Published: January 2014

The NASA structural analysis (NASTRAN∗) program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this article is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the block Lanczos aLgorithm. This eigenvalue routine is now availabLe in several mathematics libraries as well as in severaL commerciaL versions of NASTRAN. In addition, the eRA Y library maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The block Lanczos algorithm was found to be extremely efficient, particularly for very large problems.
Power Spectral Density Conversions and Nonlinear Dynamics
Authors: Rassaian Mostafa
Published: January 2014

To predict the vibration environment of a payload carried by a ground or air transporter, mathematical models are required from which a transfer function to a prescribed input can be calculated. For sensitive payloads these models typically include linear shock isolation system stiffness and damping elements relying on the assumption that the isolation system has a predetermined characteristic frequency and damping ratio independent of excitation magnitude. In order to achieve a practical spectral analysis method, the nonlinear system has to be linearized when the input transportation and handling vibration environment is in the form of an acceleration power spectral density. Test data from commercial isolators show that when nonlinear stiffness and damping effects exist the level of vibration input causes a variation in isolator resonant frequency. This phenomenon, described by the stationary response of the Duffing oscillator to narrow-band Gaussian random excitation, requires an alternative approach for calculation of power spectral density acceleration response at a shock isolated payload under random vibration. This article details the development of a plausible alternative approach for analyzing the spectral response of a nonlinear system subject to random Gaussian excitations.
Characterization and Simulation of Transient Vibrations Using Band Limited Temporal Moments
Authors: Smallwood David O.
Published: January 2014

A method is described to characterize shocks (transient time histories) in terms of the Fourier energy spectrum and the temporal moments of the shock passed through a contiguous set of band pass filters. The product model is then used to generate of a random process as simulations that in the mean will have the same energy and moments as the characterization of the transient event.
Structural Synthesis in the Frequency Domain: A General Formulation
Authors: Gordis Joshua H.
Published: January 2014

A general formulation for frequency domain structural synthesis is presented. The formulation is based on a physical coordinate transformation of the presynthesis frequency response system model and addresses modification, general coupling, and constraint imposition. Notable features of the formulation includes the ability to directly synthesize response quantities such as displacements, stresses, and strains, and the accommodation of Boolean matrices that organize the connectivity in the synthesis of complex systems. The theory is shown to be a highly efficient and exact means of doing static and complex dynamic reanalysis.
A Computer Program for a Canonical Problem in Underwater Shock
Authors: Geers Thomas L. , Ju Teh-Hua
Published: January 2014

Finite-element/boundary-element codes are widely used to analyze the response of marine structures to underwater explosions. An important step in verifying the correctness and accuracy of such codes is the comparison of code-generated results for canonical problems with corresponding analytical or semianalytical results. At the present time, such comparisons rely on hardcopy results presented in technical journals and reports. This article describes a computer program available from SAVIAC that produces user-selected numerical results for a step-wave-excited spherical shell submerged in and (optionally) filled with an acoustic fluid. The method of solution employed in the program is based on classical expansion of the field quantities in generalized Fourier series in the meridional coordinate. Convergence of the series is enhanced by judicious application of modified Cesàro summation and partial closed-form solution.
Feedforward Control of Gear Mesh Vibration Using Piezoelectric Actuators
Authors: Montague Gerald T. , Kascak Albert F. , Palazzolo Alan , Manchala Daniel , Thomas Erwin
Published: January 2014

This article presents a novel means for suppressing gear mesh related vibrations. The key components in this approach are piezoelectric actuators and a high-frequency, analog feed forward controller. Test results are presented and show up to a 70% reduction in gear mesh acceleration and vibration control up to 4500 Hz. The principle of the approach is explained by an analysis of a harmonically excited, general linear vibratory system.
Free and Forced Vibrations of Periodic Multispan Beams
Authors: Zhu Liping , Elishakoff Isaac , Lin Y.K.
Published: January 2014

In this study, the following two topics are considered for uniform multispan beams of both finite and infinite lengths with rigid transversal and elastic rotational constraints at each support: (a) free vibration and the associated frequencies and mode shapes; (b) forced vibration under a convected harmonic loading. The concept of wave propagation in periodic structures of Brillouin is utilized to investigate the wave motion at periodic supports of a multispan beam. A dispersion equation and its asymptotic form is obtained to determine the natural frequencies. For the special case of zero rotational spring stiffness, an explicit asymptotic expression for the natural frequency is also given. New expressions for the mode shapes are obtained in the complex form for multispan beams of both finite and infinite lengths. The orthogonality conditions of the mode shapes for two cases are formulated. The exact responses of both finite and infinite span beams under a convected harmonic loading are obtained. Thus, the position and the value of each peak in the harmonic response function can be determined precisely, as well as the occurrence of the so-called coincidence phenomenon, when the response is greatly enhanced.
Experimental Investigation of Effects of Vibration upon Elastic and Cohesive Properties of Beds of Wet Sand
Authors: Alsop S. , Matchett A. J. , Coulthard J. M.
Published: January 2014

The transmission of sinusoidal vibrations through beds of cohesive particulate solids was measured. Results were interpreted in terms of a critical state model to predict the elastic swelling constant k, and the cohesive stress C. Factorial experimental design was used to identify significant parameters. Factors that affect k include percent moisture, bulk density, sample size, sample shape, the presence of a supporting membrane, and loading order. Factors that affect C include percent moisture and particle size distribution. Factors affecting k were interpreted in terms of their effects upon bed structure and factors affecting C in terms of an equivalent pore water pressure due to capillary and liquid bridge effects. The critical state model was modified to incorporate general relationships between axial and radial strains.
Air Bag Momentum Force Including Aspiration
Authors: Nusholtz Guy , Wang Deguan , Wylie E. Benjamin
Published: January 2014

A gas-jet momentum force drives the air bag into position during a crash. The magnitude of this force can change as a result of aspiration. To determine the potential magnitude of the effect on the momentum force and mass flow rate in an aspirated system, a series of experiments and simulations of those experiments was conducted. The simulation consists of a two-dimensional unsteady isentropic CFD model with special “infinite boundaries”. One of the difficulties in simulating the gas-jet behavior is determining the mass flow rate. To improve the reliability of the mass flow rate input to the simulation, a sampling procedure involving multiple tests was used, and an average of the tests was adopted.
Dynamics and Control of Adaptive Shells with Curvature Transformations
Authors: Tzou H.S. , Bao Y.
Published: January 2014

Adaptive structures with controllable geometries and shapes are rather useful in many engineering applications, such as adaptive wings, variable focus mirrors, adaptive machines, micro-electromechanical systems, etc. Dynamics and feedback control effectiveness of adaptive shells whose curvatures are actively controlled and continuously changed are evaluated. An adaptive piezoelectric laminated cylindrical shell composite with continuous curvature changes is studied, and its natural frequencies and controlled damping ratios are evaluated. The curvature change of the adaptive shell starts from an open shallow shell (30°) and ends with a deep cylindrical shell (360°). Dynamic characteristics and control effectiveness (via the proportional velocity feedback) of this series of shells are investigated and compared at every 30° curvature change. Analytical solutions suggest that the lower modes are sensitive to curvature changes and the higher modes are relatively insensitive.
Active Vibration Control of a Thin Steel Sheet
Authors: Okada Yohji , Matsuda Ken-Ichi , Tani Junji
Published: January 2014

The commercial rolling process used in the steel industry to manufacture thin steel sheets tends to cause plate vibrations that lower the quality of the surface finish. This article introduces a noncontact method of active vibration control for reducing the flexural vibrations of a thin steel sheet. The proposed electromagnetic method of control has been implemented in a simple experimental setup where the signal from a motion sensor regulates the attractive force of the magnets that produce a damping force on the steel sheet.
Limiting Vibroisolation Control of an Oscillating String on a Moving Base
Authors: Balandin Dmitry V.
Published: January 2014

The vibroisolating capability of an elastic object that is assumed to be protected against a class of excitations is studied. It is proposed that this capability be estimated by a quadratic functional. The solution method gives an estimate of the optimal isolation with a criterion of minimum guaranteed quality. A numerical example of the solution technique is presented.
An Analytical Study of Self-Compensating Dynamic Balancer with Damping Fluid and Ball
Authors: Lee Jongkil
Published: January 2014

The self-compensating dynamic balancer (SCDB) is composed of a circular disk with a groove containing ball and a low viscosity damping fluid. The equations of motion of the rotating system with SCDB were derived by the Lagrangian method. To consider dynamic stability of the motion, perturbation equations were investigated. Based on the results of stability investigation, ball positions that result in a balanced system are stable above the critical speed with small damping (β′>3.8 case). At critical speed the perturbed motion is said to be stable for large damping (β′>2.3 case). However, below critical speed the balls cannot stabilize the system in any case.
Free Vibration of Thick Multilayer Cylinders
Authors: Hamidzadeh H. R. , Sawaya N. N.
Published: January 2014

In this study of the free vibration of multilayer thick cylinders, the medium is modeled by laminated linear viscoelastic cylinders of an infinite extent. The analytical modeling is based on three-dimensional wave propagation utilizing constant complex elastic moduli. The solution is achieved by determining the displacements and stresses for each interface and by complying with requirements at the interfaces. A propagator matrix relating the boundary displacements to boundary stresses is developed. Dimensionless natural frequencies and modal loss factors for different circumferential and axial wave numbers are determined. The validity of the proposed method is verified by comparing the results for one-, two-, and three-layer elastic cylinders with properties similar to those reported for an equivalent single layer.
Effective Method for Analysis of Electrothermally Coupled Fields
Authors: Korytkowski Jacek , Wincenciak Stanisław
Published: January 2014

An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. A numerical model of this physical phenomenon was obtained by the finite element method, which takes into account the temperature-dependent characteristics describing the material parameters and conditions of heat transmission outside of the analyzed objects. These characteristics and conditions make the problem strongly nonlinear. The solution uses the Newton-Raphson method with the appropriate procedure for determining the Jacobian matrix elements. The main idea of the proposed method is the use of an automatic time step selection algorithm to solve heat conduction equations. The influence of the assumed accuracy value on the final result of the nonlinear calculation is discussed. The theoretical results were confirmed by the numerical experiments performed with selected physical objects.
Performance Characteristics of Active Constrained Layer Damping
Authors: Baz A. , Ro J.
Published: January 2014

Theoretical and experimental performance characteristics of the new class of actively controlled constrained layer damping (ACLD) are presented. The ACLD consists of a viscoelastic damping layer sandwiched between two layers of piezoelectric sensor and actuator. The composite ACLD when bonded to a vibrating structure acts as a “smart” treatment whose shear deformation can be controlled and tuned to the structural response in order to enhance the energy dissipation mechanism and improve the vibration damping characteristics. Particular emphasis is placed on studying the performance of ACLD treatments that are provided with sensing layers of different spatial distributions. The effect of the modal weighting characteristics of these sensing layers on the broad band attenuation of the vibration of beams fully treated with the ACLD is presented theoretically and experimentally. The effect of varying the gains of a proportional and derivative controller and the operating temperature on the ACLD performance is determined for uniform and linearly varying sensors. Comparisons with the performance of conventional passive constrained layer damping are presented also. The results obtained emphasize the importance of modally shaping the sensor and demonstrate the excellent capabilities of the ACLD.
Computer Simulations of Contact Forces for Airbags with Different Folding Patterns During Deployment Phase
Authors: Yang King H. , Li Yun-Qiang , Sun Danyu
Published: January 2014

An explicit finite element method was used to study the neck load and the contact force between an occupant and an airbag during an out-of-position frontal automobile crash. Two different folding patterns and two different mounting angles of the airbag were simulated. For the four cases simulated, the occupant’s neck axial force ranged from 156 to 376% of the data obtained from in-position sled tests using the Hybrid III dummy. The neck shear force ranged from 87 to 229% and the neck flexion moment ranged from 68 to 127% of in-position experimental results. In both 300 mounting angle simulations, the neck axial forces were higher than that of the two simulations with 00 mounting angles, but the trend for the neck shear force was the opposite. Although the kinematics of the model appear reasonable, the numbers generated by the model must be reviewed with great caution because the model has not been fully validated.
Debris Cloud Material Characterization for Hypervelocity Impacts of Single- and Multimaterial Projectiles on Thin Target Plates
Authors: Schonberg William P.
Published: January 2014

The key to conducting an accurate damage assessment of a target impacted by a high speed projectile is the use of a robust assessment methodology. To accurately determine total target damage, a damage assessment methodology must include the effects of discrete impacts by solid debris cloud fragments as well as impulsive loadings due to molten and vaporous debris cloud material. As a result, the amount of debris cloud material in each of the three states of matter must be known to accurately assess total target damage and break-up due to a high speed impact. This article presents a first-principles based method to calculate: the amount of material in a debris cloud created by a perforating hypervelocity impact that is solid, molten, and vaporous; the debris cloud leading edge, trailing edge, center-of-mass, and expansion velocities; and the angular spread of the debris cloud material. The predictions of this methodology are compared against those of empirically based lethality assessment schemes as well as numerical and empirical results obtained in previous studies of debris cloud formation.
Periodic and Near-Periodic Structures
Authors: Mester S. S. , Benaroya H.
Published: January 2014

Extensive work has been done on the vibration characteristics of perfectly periodic structures. This article reviews the different methods of analysis from several fields of study, for example solid-state physics and civil, mechanical, and aerospace engineering, used to determine the effects of disorder in one-dimensional (1-D) and 2-D periodic structures. In the work examined, disorder has been found to lead to localization in 1-D periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. The implications of localization for control are also examined.
Optimal Constrained Layer Damping of Beams: Experimental and Numerical Studies
Authors: Marcelin J.-L. , Shakhesi S. , Pourroy F.
Published: January 2014

This article deals with the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. The design variables are the dimensions and locations of the viscoelastic layers and the objective function is the maximum damping factor. The discrete design variable optimization problem is solved using a genetic algorithm. Numerical results for minimum and maximum damping are compared to experimental results. This is done for a various number of materials and beams.
Positive Real Zeros in Flexible Beams
Authors: Maslen Eric H.
Published: January 2014

Feedback control of flexible structures naturally involves actuators and sensors that often cannot be placed at the same point in the structure. It has been widely recognized that this noncollocation can lead to difficult control problems and, in particular, difficulty in achieving high robustness to variation in the dynamic properties of the structure. This problem has previously been traced to transmission zeros in the dynamic transfer function between sensor location and actuator location, especially those lying on the positive real axis in the complex plane. In this artie/e, the physical significance of these zeros is explored and the dynamic properties of beams that give rise to real positive zeros are contrasted to those of torsional and compressive systems that do not.
Development of a Method for Characterizing Joint Stiffness, Deadband, and Hysteresis
Authors: Ferney G.D. , Folkman S.L.
Published: January 2014

This article documents the development of a procedure for characterizing the stiffness, deadband, and hysteretic behavior of struts with pinned joints. A test setup utilized procedures recommended by other authors. The test results included a calibration specimen with linear stiffness and near zero hysteretic behavior that identified the capabilities and limitations of the procedure. Tension/compression pull tests of the truss joints were conducted. The load vs. displacement curves showed stiffness, deadband, and hysteresis loops consistent with theory. Vibration damping was inferred from the hysteresis loops and compared with measured data from a three bay truss.
Parametrically Excited Nonlinear Two-Degree-of-Freedom Systems with Repeated Natural Frequencies
Authors: Nayfeh A. H. , Chin C. , Mook D. T.
Published: January 2014

The method of normal forms is used to study the nonlinear response of two-degree-of-freedom systems with repeated natural frequencies and cubic nonlinearity to a principal parametric excitation. The linear part of the system has a nonsemisimple one-to-one resonance. The character of the stability and various types of bifurcation including the formation of a homoclinic orbit are analyzed. The results are applied to the flutter of a simply supported panel in a supersonic airstream.
Three Case Studies in Finite Element Model Updating
Authors: Imregun M.
Published: January 2014

This article summarizes the basic formulation of two well-established finite element model (FEM) updating techniques for improved dynamic analysis, namely the response function method (RFM) and the inverse eigensensitivity method (IESM). Emphasis is placed on the similarities in their mathematical formulation, numerical treatment, and on the uniqueness of the resulting updated models. Three case studies that include welded L-plate specimens, a car exhaust system, and a highway bridge were examined in some detail and measured vibration data were used throughout the investigation. It was experimentally observed that significant dynamic behavior discrepancies existed between some of the nominally identical structures, a feature that makes the task of model updating even more difficult because no unequivocal reference data exist in this particular case. Although significant improvements were obtained in all cases where the updating of the FE model was possible, it was found that the success of the updated models depended very heavily on the parameters used, such as the selection and number of the frequency points for RFM, and the selection of modes and the balancing of the sensitivity matrix for IESM. Finally, the performance of the two methods was compared from general applicability, numerical stability, and computational effort standpoints.
Dynamic Stiffness Matrix for a Beam Element with Shear Deformation
Authors: Pilkey Walter D. , Kitiş Levent
Published: January 2014

A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cross section. These new matrices are needed because, for a Timoshenko beam with an arbitrarily shaped cross section, deflections due to shear in the two perpendicular planes are coupled even when the coordinate axes are chosen to be parallel to the principal axes of inertia.
H-Adaptive Methods for Nonlinear Dynamic Analysis of Shell Structures
Authors: Lee Sang-Ho , Belytschko Ted
Published: January 2014

The implementation and application of h-adaptivity in an explicit finite element program for nonlinear structural dynamics is described. Particular emphasis is placed on developing procedures for general purpose structural dynamics programs and efficiently handling adaptivity in shell elements. New projection techniques for error estimation and projecting variables on new meshes after fission or fusion are described. Several problems of severe impact are described.
Random Vibration of Space Shuttle Weather Protection Systems
Authors: Elishakoff Isaac , Baruch Menahem , Zhu Liping , Caimi Raoul
Published: January 2014

The article deals with random vibrations of the space shuttle weather protection systems. The excitation model represents a fit to the measured experimental data. The cross-spectral density is given as a convex combination of three exponential functions. It is shown that for the type of loading considered, the Bernoulli-Euler theory cannot be used as a simplified approach, and the structure will be more properly modeled as a Timoshenko beam. Use of the simple Bernoulli-Euler theory may result in an error of about 50% in determining the mean-square value of the bending moment in the weather protection system.
An Algorithm for Higher Order Hopf Normal Forms
Authors: Leung A.Y.T. , Ge T.
Published: January 2014

Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.
Coupled Dynamics of a Rotor-Journal Bearing System Equipped with Thrust Bearings
Authors: Lie Yu , Bhat R.B.
Published: January 2014

The rotordynamic coefficients of fixed-pad thrust bearing are introduced and calculated by using the out-domain method, and a general analysis method is developed to investigate the coupled dynamics of a rotor equipped with journal and thrust bearings simultaneously. Considerations include the effects of static tilt parameters of the rotor on rotordynamic coefficients of thrust bearing and the action of thrust bearing on system dynamics. It is shown that thrust bearing changes the load distribution of journal bearings and the static deflection of the rotor and delays the instability of the system considerably in lateral shaft vibration.
Analysis of Multiaxis Vibration Simulators
Authors: Fitz-Coy Norman
Published: January 2014

A mathematical procedure that quantitatively addresses issues critical to the design and operation of multiaxis vibration simulators is presented. Both kinematic and dynamic issues are considered. The analysis is applied to both 3 and 6 degrees of freedom configurations. The existence of singular configurations is mentioned and appropriate corrective measures are recommended. A methodology for determining the required actuator commands is also presented.
Dynamic Analysis of Shells
Authors: Steele Charles R. , Tolomeo Jason A. , Zetes Deborah E.
Published: January 2014

Shell structures are indispensable in virtually every industry. However, in the design, analysis, fabrication, and maintenance of such structures, there are many pitfalls leading to various forms of disaster. The experience gained by engineers over some 200 years of disasters and brushes with disaster is expressed in the extensive archival literature, national codes, and procedural documentation found in larger companies. However, the advantage of the richness in the behavior of shells is that the way is always open for innovation. In this survey, we present a broad overview of the dynamic response of shell structures. The intention is to provide an understanding of the basic themes behind the detailed codes and stimulate, not restrict, positive innovation. Such understanding is also crucial for the correct computation of shell structures by any computer code. The physics dictates that the thin shell structure offers a challenge for analysis and computation. Shell response can be generally categorized by states of extension, inextensional bending, edge bending, and edge transverse shear. Simple estimates for the magnitudes of stress, deformation, and resonance in the extensional and inextensional states are provided by ring response. Several shell examples demonstrate the different states and combinations. For excitation frequency above the extensional resonance, such as in impact and acoustic excitation, a fine mesh is needed over the entire shell surface. For this range, modal and implicit methods are of limited value. The example of a sphere impacting a rigid surface shows that plastic unloading occurs continuously. Thus, there are no short cuts; the complete material behavior must be included.
Numerical Analysis for Dynamic Instability of Electrodynamic Maglev Systems
Authors: Cai Y. , Chen S.S.
Published: January 2014

Suspension instabilities in an electrodynamic maglev system with three- and five-degrees-of-freedom DOF vehicles traveling on a double L-shaped set of guideway conductors were investigated with various experimentally measured magnetic force data incorporated into theoretical models. Divergence and flutter were obtained from both analytical and numerical solutions for coupled vibration of the three-DOF maglev vehicle model. Instabilities of five direction motion (heave, slip, roll, pitch, and yaw) were observed for the five-DOF vehicle model. The results demonstrate that system parameters such as system damping, vehicle geometry, and coupling effects among five different motions play very important roles in the occurrence of dynamic instabilities of maglev vehicles.
Waves, Solids, and Nonlinearities
Authors: Engelbrecht Jüri
Published: January 2014

In this article nonlinearity is taken as a basic property of continua or any other wave-bearing system. The analysis includes the conventional wave propagation problems and also the wave phenomena that are not described by traditional hyperbolic mathematical models. The basic concepts of continuum mechanics and the possible sources of nonlinearities are briefly discussed. It is shown that the technique of evolution equations leads to physically well-explained results provided the basic models are hyperbolic. Complicated constitutive behavior and complicated geometry lead to mathematical models of different character and, as shown by numerous examples, other methods are then used for the analysis. It is also shown that propagating instabilities possess wave properties and in this case the modeling of energy redistribution has a great importance. Finally, some new directions in the theory and applications are indicated.
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Authors: Chu Chih-Liang , Lin Yih-Hwang
Published: January 2014

A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
Symplectic Integration and Nonlinear Dynamic Symmetry Breaking of Frames
Authors: Mao S.G. , Leung A.Y.T.
Published: January 2014

An accurate beam finite element is used to solve nonlinear vibration of arched beams and framed structures. The nonlinear governing equations of a skeletal structure are integrated numerically using symplectic integration schemes so that the Poincaré integral invariant of a Hamiltonian flow are preserved during the evolution. The element stiffness matrices are not required to be assembled into global form, because the integration is completed on an element level so that many elements can be handled in core by a small computer. Testing examples include arched beams and frames with and without damping in free and forced vibration. The dynamic symmetry breaking phenomena are noted at the dynamic buckling point.
Testing Procedures for High Output Fluid Viscous Dampers Used in Building and Bridge Structures to Dissipate Seismic Energy
Authors: Taylor Douglas P. , Constantinou Michael C.
Published: January 2014

Today's economic climate demands that conversion of military technology for commerical applications be a part of an aerospace and defense company's strategic planning. Toward this goal, a successful defense conversion has occurred recently with the application of high capacity fluid damping devices from the defense community for use as seismic energy dissipation elements in commercial buildings, bridges, and related structures. These products have been used by the military for many years for attenuation of weapons grade shock, typically applied to shipboard equipment or land based strategic weapons. Commercial energy dissipation devices historically have involved heavy yielding sections or hysteretic joints.