bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamic Modelling and Response Characteristics of a Magnetic Bearing Rotor System With Auxiliary Bearings
Authors: Free April M. , Flowers George T. , Trent Victor S.
Published: March 2021

Auxiliary bearings are a critical feature of any magnetic bearing system. They protect the soft iron core of the magnetic bearing during an overload or failure. An auxiliary bearing typically consists of a rolling element bearing or bushing with a clearance gap between the rotor and the inner race of the support. The dynamics of such systems can be quite complex. It is desired to develop a rotordynamic model which describes the dynamic behavior of a flexible rotor system with magnetic bearings including auxiliary bearings. The model is based upon an experimental test facility. Some simulation studies are presented to illustrate the behavior of the model. In particular, the effects of introducing sideloading from the magnetic bearing when one coil fails is studied. These results are presented and discussed.
Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing
Authors: Mosher Phillip , Childs Dara W.
Published: March 2021

This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in highspeed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to be somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.
The Effects of Converging and Diverging Axial Taper on the Rotordynamic Coefficients of Liquid Annular Pressure Seals: Theory Versus Experiment
Authors: Lindsey W. Todd , Childs Dara W.
Published: March 2021

Experimental results are compared to predictions for turbulent flow, short (D = 76.2mm, L/D = .17), smooth annular seals with converging and diverging axial taper. Results are presented for four geometries: two convergent, two divergent, and a constant-clearance. Measurements were taken at seal pressure differentials and shaft rotation rates ranging from 1.34 to 3.54 MPa and 10,200 to 24,600 rpm, respectively.

Measurements parameters include leakage, direct stiffness, cross-coupled stiffness, and direct damping coefficients. Results show that direct stiffness generally increases with converging axial taper and decreases with diverging axial taper. Direct damping and cross-coupled stiffness were shown to decrease with increasing convergent or divergent taper. Measured damping values increase with increased running speed and decreasing average clearance. Theoretical predictions for rotordynamic coefficients are in good overall agreement with measured results. The theory consistently underpredicts leakage by ranges of 10 ∼ 30%. The accuracy of predictions for leakage and rotordynamic coefficients was not influenced by running speed.
Dynamical Behaviors of Hybrid Squeeze Film Damper for Rotor System Vibration Control
Authors: Changsheng Zhu
Published: March 2021

The behaviors of oil film stiffness and damping coefficients of the deep multi-recessed hybrid squeeze film damper (HSFD) with the orifices compensated are first analysed in this paper. The control ability of the HSFD on the rotor system vibrations is studied theoretically and experimentally with a rigid rotor system supported on the HSFD, and compared with that of the conventional squeeze film damper (SFD). Investigation shows that the HSFD not only can significantly improve the high nonlinearity of the SFD, but also can effectively control the rotor vibrational amplitudes, especially for larger rotor unbalance levels and radial clearance ratios, as compared with the SFD.
Vibration Analysis of Bladed Disc Assemblies
Authors: Minas C. , Kodiyalam S.
Published: March 2021

The dynamic behavior of a bladed disc assembly was determined by developing a finite element model (FEM). The object of this work is to develop an understanding of the dynamic behavior of the system with respect to the various boundary conditions. The analysis included variation of the boundary conditions at the blade-disc interface, between adjacent blades, and the shroud. It was clearly shown that only certain mode patterns are affected with respect to a particular boundary condition, leaving the remaining modes unchanged. The quantitative effect of the various boundary conditions was calculated by finite element analysis of a cyclic symmetric model. A methodology is also presented where the associated modes of the higher harmonics natural frequencies of the assembly, are identified in a systematic and automated way without being plotted and viewed. This methodology which uses the cross-orthogonality equations, is valuable to systems with a large number of nodal diameters, where the complete set of the associated mode shapes can be analyzed in an efficient and systematic way. The technique is illustrated through an example, where a complete analytical Campbell diagram for the lower order modes is developed.
Study on the Unbalanced Effect of Rotary Systems
Authors: Huang Yuan Mao , Wang Chin-Ming
Published: March 2021

The transient dynamic analysis of rotary systems is very important because the maximum displacements of components due to the unbalanced effect may occur during the transient state. This study develops a numerical method by combining the methodologies of the finite element method, the transfer matrix method, the time marching numerical integration method and the Houbolt numerical method. The effects of rotary inertia, gyroscopic phenomenon, shear deformation and internal damping on the dynamic behaviors of a rotor-bearing system are analyzed. The transient displacements of components in the system are calculated and show good agreement with the available data.
Multi-Dimensional Directional Spectrograms and Campbell (ZMOD) Diagrams for Rotating Machinery
Authors: Bucher I. , Ewins D. J. , Robb D. A. , Schmiechen P.
Published: March 2021

A new method for decomposition of vibration signals measured on rotating machinery is presented in this paper. The method uses a signal measured from a number of sensors to decompose the spatial response according to the direction of the progression of motion, the frequency content and the various wavelengths. For the simple case of shaft vibration, two sensors, horizontal and vertical, are used to separate the vibration pattern into forward and backward progressing components. For the case of a rotating disc, more sensors are required to further decompose the response into different wavelengths. This allows one to monitor and to identify potentially dangerous vibration patterns exhibiting large backward components. The method is shown to provide better resolution in the time-frequency (speed of rotation) and spatial domains by separating several, usually overlapping patterns. Several analytical and experimental results demonstrate the usefulness of the proposed method.
Determination of Rotating Assembly Synchronous Response Characteristics Using Blade Tip-Timing Techniques
Authors: Heath Steve , Imregun Mehmet
Published: March 2021

This paper presents an improved analysis method for the interpretation of the vibration data measured at turbomachinery blade tips using optical laser probes. A multi-degree-of-freedom numerical simulator, which includes the structural and geometric properties of the bladed-disk assembly, the external forcing terms and the characteristics of the optical probe, has been developed to assess the reliability of the various data processing techniques to identify the natural frequencies and mode shapes of bladed-disk assemblies. It has been demonstrated that the Zablotsky-Korostelev single parameter technique, which is a de-facto standard in the aerospace industries, has inherent limitations associated with it. An improved and more rigorous method is presented for deriving the blade arrival times and a non-linear solution technique is suggested for their numerical determination. Finally, the effect of blade mistuning on the accuracy of the proposed method is also investigated.
Application of ESPI in the Vibration Analysis of Turbine Blading
Authors: Wang Robert X. , Chapman Graham M.
Published: March 2021

This paper reports on the application of Electronic Speckle Pattern Interferometry (ESPI) technique in vibration measurement of turbine blading. Using the time-averaged mode of ESPI, the first six modes of a turbocharger blade with airfoil profile were identified. The effect of the complicated profile of the blade was established by studying simplified model blades. Coupled modes were identified and successfully separated. Experimental results are compared with those obtained using finite element analysis.
Adaptive Virtual Autobalancing for a Magnetic Rotor With Unknown Mass Imbalance: Part II — Dynamic Balancing
Authors: Lum Kai-Yew , Bhat Sanjay P. , Bernstein Dennis S. , Coppola Vincent T.
Published: March 2021

In Lum et al. (1995), an adaptive control algorithm for the stabilization of a rigid, statically unbalanced rotor moving in the plane was proposed. The control strategy consisted in emulating a mechanical autobalancer using magnetic actuation so as to directly cancel the effects of static mass imbalance. In this present paper, this strategy is extended to the case of a rigid, dynamically unbalanced rotor in six degree-of-freedom motion. The state equations of the controller are based on the equations of motion of a multiple-plane autobalancer, and the control forces partially emulates the interaction between rotor and autobalancer. It is shown in simulation that the adaptive virtual autobalancing control can achieve stabilization of rotor motion as well as adaptation to changes in imbalance.
Transient Vibration of Gyroscopic Systems With Unsteady Superposed Motion
Authors: Wickert J. A.
Published: March 2021

The equations of motion for a gyroscopic system with unsteady superposed motion are derived for the prototypical problem in which motion of an oscillating particle is measured relative to a non-inertial frame. The resulting coefficient matrices are time-dependent, and skew-symmetric acceleration terms are present both as Coriolis acceleration and as a component of net stiffness. Such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems, including flexible media that translate with time-dependent speed. Following the asymptotic approach of Krylov, Bogoliubov and Mitropolsky, a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the natural periods of oscillation. First-order approximations for the modal amplitude and phase are obtained in closed form. The method is illustrated through two examples of technical interest: a two degree-of-freedom model of a rotating shaft, and a distributed parameter model of a moving tape.
Generalized Characteristic Method for Orthotropic Media
Authors: Su Shigong , Su Xianzhong
Published: March 2021

A new method is developed to solve two dimensional transient problems of elastodynamics in orthotropic media. The real solutions of the characteristic equation for the Navier equations in orthotropic media can be analytically continued to the complex domain in which they are called generalized characteristics. The generalized characteristics are employed to prove that a set of algebraic equations of the velocity components is equivalent to the Navier equations. To illustrate how to use the present method in elastodynamics for orthotropic media, the problems of time domain Green’s functions in an unbounded medium, and Lamb’s problem for a buried concentrated line force are solved by applying the derived algebraic equations. The reflection coefficients and Snell’s law on the surface of a half-space are obtained for incident non-plane transient waves. The direct waves, reflected waves, and head wave in a half-space are analyzed directly in terms of generalized characteristics. Finally, some numerical results for the particle displacement at receivers (on and below the surface) are shown for four typical crystals and composite materials.
Shape Optimization of Unconstrained Beam and Plate Damping Layers
Authors: Lumsdaine Arnold , Scott Richard A.
Published: March 2021

The aim of this paper is to determine the optimum shape of a symmetric unconstrained viscoelastic damping layer for a laminated composite structure undergoing harmonic excitation. The objective is to minimize the peak displacement at the first damped natural frequency. The material loss factor is monitored to determine the improvement in performance. Beam and plate structures are examined for several boundary conditions. The common assumption of constant viscoelastic material properties is investigated by comparing optimization results for cases with constant properties to those with varying properties. ABAQUS finite element code is used to model the structures. The optimization code uses a Sequential Quadratic Programming algorithm. Results show dramatic improvement in the loss factor for optimized shapes. In addition, the use of frequency dependent viscoelastic properties is insignificant in the cases examined. Finally, results indicate that minimizing the displacement at one frequency may cause significantly worse performance at other frequencies.
Active Vibration Absorption Using Delayed Resonator With Relative Position Measurement
Authors: Olgac Nejat , Hosek Martin
Published: March 2021

A novel active vibration absorption technique, the Delayed Resonator, has been introduced recently as a unique way of suppressing undesired oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with a time delay. Its strengths consist of extremely simple implementation of the control algorithm, total vibration suppression of the primary structure against a harmonic force excitation and full effectiveness of the absorber in a semi-infinite range of disturbance frequency, achieved by real-time tuning. All this development work was done using the absolute displacements of the absorber in the feedback. These displacement measurements may be difficult to obtain and for some applications impossible. This paper deals with a substitute and easier measurement: the relative motion of the absorber with respect to the primary structure. Theoretical foundations for the Delayed Resonator (DR) are briefly recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a harmonic force is introduced utilizing both absolute and relative position measurement of absorber mass. Methods for stability range analysis and transient behavior are presented. Properties acquired for the same system with these two different feedback are compared. Relative position measurement case is found to be more advantageous in most applications of the Delayed Resonator method.
Digital Optimal Multivariable Control of a Smart Structure Featuring Piezoelectric Sensors and Actuators
Authors: Sannah Muhammad , Smaili Ahmad , Lahdhiri Tarek
Published: March 2021

In this paper, a digital regulator is designed and experimentally implemented for a smart structure featuring piezoelectric sensors and actuators using optimal multivariable control techniques. The controller consists of a linear quadratic regulator with output weightings and a state estimator, Luenberger observer. The structure is a cantilever beam synthesized with two sets of sensor/actuator PZT ceramic piezoelectric plates bonded to the beam surface at the high strain locations corresponding to the first and second vibration modes. Equations of motion of the beam are developed using finite beam element model. The model includes the mass and rigidity of the PZT ceramics. Experimental results of two regulators differing in the number of modes considered are presented and discussed. The results proved the applicability of the concept and the stability and robustness of the control algorithm.
Effects of Desired Transmissibility Functions on the Performance and Design of Control Systems for Microgravity Isolation Systems
Authors: Tsai N.-C. , Sinha A.
Published: March 2021

This paper examines the performance of active isolation systems for micrograviry space experiments as a function of desired transmissibilities which are chosen to be either much below or close to what can be tolerated. The control system utilizes two feedback signals: absolute acceleration and relative displacement of the mass. The controller transfer function for acceleration feedback is chosen to avoid marginally stable pole-zero cancellations. The controller transfer function for relative displacement feedback is determined to achieve the desired transmissibility function. The issue of stability and properness of this controller transfer function are addressed. The required input forces and “equivalent” closed-loop stiffness are examined for various examples of desired transmissibilities.
Chaotic Response of a Hard Duffing Type Vibration Isolator With Combined Coulomb and Viscous Damping
Authors: Leung A. Y. T. , Ravindra B. , Mallik A. K. , Chan C. W.
Published: March 2021

Numerical simulations of the response of a harmonically excited mass on an isolator with a cubic, hard, non-linear restoring force and combined Coulomb and viscous damping are presented. For a base-excited system, the inclusion of a Coulomb damper with a suitable break-loose frequency can suppress the secondary resonances and chaotic motion. However, for a force-excited system, the introduction of Coulomb damping does not alter the bifurcation structure. Transmissibility indices have been defined for the solution obtained by numerical integration and the role of the subharmonic resonances and chaotic motion on the performance of the system is pointed out.
Energy Flow Control of Interconnected Structures: I — Modal Subsystems
Authors: Kishimoto Yasuo , Bernstein Dennis S. , Hall Steven R.
Published: March 2021

Dissipative energy flow controllers are designed for inter-connected modal subsystems. Active feedback controllers for vibration suppression are then viewed as either an additional subsystem or a dissipative coupling. These controllers, which are designed by the LQG positive real control approach, maximize energy flow from a specified modal subsystem.
Spherical Compliant Model for Vibration Estimation and Control
Authors: Thompson Thomas J.
Published: March 2021

Proposed space missions involve large structures which must maintain precise dimensional tolerances during dynamic maneuvers. In order to attenuate disturbances in the many modes of vibration of such structures, active and passive vibration control has been proposed. Passive control is to be achieved by placing viscous or viscoelastic members in a structure to absorb energy, while active control similarly could involve structural members (struts) capable of sensing axial displacement and exerting axial control force.

With conventional modal analysis, the effect of a control element on a system is computed by summing its influence on many immutable modes. Since changes in mode shape must be described by this summation, truncation of higher modes results in inaccuracies.

The compliant model of vibration to be presented accurately accounts for the effects of locally-acting control elements without inclusion of high-frequency modes. The motion of each spring-mass system representing a structural mode is modified by a control element in series with another stiffness inherent to the structure for that mode and control position. In order to predict the influence of several control elements or dampers on closely-spaced modes, the compliant models for those modes are integrated into a spherical model in which one lumped mass is acted upon by orthogonal modal stiffnesses. In the spherical model, control elements influent the lumped mass from orientations determined by mode participation factors. The resulting equations of motion are stated in standard state-space form.

To test accuracy, the compliant model is used to predict eigenvalue shifts due to springs and dampers acting upon an axially-vibrating rod, and the spherical model is used to predict damping accurately in a lumped-mass system with closely-spaced modes.
Hybrid Vibration Control of a Cable-Stayed Bridge
Authors: Bell Mark , Shoureshi Rahmat A.
Published: March 2021

Hybrid vibration control, involving the combined use of feedforward and feedback control, is developed for a cable-stayed bridge using passivity-based control. The control objective is to reject all disturbances that cause unwanted motion in the bridge structure, namely seismic activity, wave loading and wind loading, while keeping energy consumption at a very low level. An experimental bridge prototype has been developed and simulations involving an analytical model derived from real data are presented. A three dimensional finite element model was developed of the bridge for verification purposes. A multiple time step ahead estimator is also developed using neural networks that is used in the feedforward loop to predict future bridge motion using past values of disturbance and output. Simulation results of the neural estimator are presented.
Tuning of a Rear Electronic Control Engine Mount
Authors: Galvin Daniel D.
Published: March 2021

This paper refers to mathematical tuning, by the sinusoidal steady-state transfer function method, of an adjustable hydraulic rear engine mount for reduction of perceived vibration during engine idle situations. The problem being addressed, in particular, is the reduction of “idle shake”. The accuracy of this method is confirmed by individual component testing along with in situ vibration measurements.

During this work, a general approach to transfer function calculation is given by evaluating the system components with the linear-graph system of modeling. This is complemented by component verification and curve-fitting to arrive at the final transfer function which reveals the inherent tendencies of the overall system. Secondary measurements are then employed to rectify the contradiction between mathematical values and subjective results.
Development of V-Shaped Hybrid Mass Damper and its Application to High-Rise Buildings
Authors: Imazeki Masanori , Tanida Koji , Mutaguchi Masao , Koike Yuji , Murata Tamotsu , Kobori Takuji , Yamada Tosikazu , Tagami Jun , Sasaki Katsuyasu , Ohrui Satoshi
Published: March 2021

A hybrid mass damper system has been developed with a view to counteracting wind- and earthquake-excited vibrations of large high-rise building structures. In order to eliminate the large space needed to accommodate a pendulum-type mass damper adapted to the long period of high-rise building, mechanism has been devised for suspending the auxiliary mass on a V-shaped rail sliding on rollers. The base angle of the V-shaped rail is varied for adjusting the natural period of the mass damper system. A suboptimal algorithm based on the minimum norm method has been adopted for designing the auxiliary mass driving system. Three units of this damper system, each equipped with auxiliary mass weighing 110 tons, have been installed on a 52-story building. Satisfactory performance conforming in all practical aspects with design has been verified from vibration test on actual building after installation. As sequel, the functioning of the system during the first year of service is also reported.
Hydraulic Actuator Tuning in the Control of a Rotating Flexible Beam Mechanism
Authors: Panza Michael J. , Mayne Roger W.
Published: March 2021

The end point position and vibration control of a rotating flexible beam mechanism driven by a hydraulic cylinder actuator is considered. An integrated nonlinear system model comprised of beam dynamics, hydraulic actuator, control valves, and control scheme is presented. Control based on simple position feedback along with a hydraulic actuation system tuned to suppress beam vibration over a wide range of angular motion is investigated. For positioning to small to moderate mechanism angles, a linear system model with the actuator tuned for good open loop performance is developed. Actuator tuning is accomplished by varying the system hydraulic resistance according to a dimensionless parameter defining the interaction between the actuator and flexible beam. Simulation results for a closed loop system indicate that this simple tuned control provides comparable performance and requires less control effort than an untuned system with a more complex state feedback optimal controller. To compensate for geometric nonlinearities that cause instability when positioning to large mechanism angles, an active actuator tuning scheme based on continuous variation of hydraulic resistance is proposed. The active variable resistance controller is combined with simple position feedback and designed to provide a constant dimensionless actuator-flexible beam interaction parameter throughout the motion. Simulation results are presented to show the stabilizing effect of this control strategy.
Hybrid Feedback-Feedforward Control for Vibration Suppression
Authors: De Man P. , Preumont A.
Published: March 2021

This paper evaluates a hybrid feedback-feedforward controller for vibration suppression. The feedback controller uses colocated actuator and sensor and a fixed compensator with guaranteed stability. The feedforward controller uses the same actuator as the feedback one. The x-filtered LMS algorithm is used to adapt the FIR filter coefficients. For the application considered in this paper, the hybrid controller enjoys the advantages of both types of controllers.
A Design Method of Robust Controller for a Flexible Structure Using H∞/μ Control Theory
Authors: Watanabe Toru , Yoshida Kazuo
Published: March 2021

This paper discusses about robust vibration control of a flexible structure that has transverse and torsional vibration modes. A design method of a controller taking account of the parameter variations and the residual dynamics is presented. The transverse-torsional coupling is translated into parameter variations, and other model errors of structural dynamics of the system are interpreted as frequency-shaped weighting functions. The H∞/μ control theory is applied to synthesize controller and these perturbations are formulated in the generalized plant. To examine the capability of the obtained controller, computer simulations and control experiments are carried out and the effectiveness of the presented method is verified.
Vibration Control Using Combined Independent Modal Space Control and Fuzzy Logic
Authors: Asdigha Mehran , Greif Robert
Published: March 2021

Independent Modal Space Control (IMSC) is an established technique in active suppression of vibrations, in which the control law is developed exclusively in the modal space, allowing for independent design of the modal control forces. These forces can be transformed to the physical domain through modal transformation. The resulting controller is fixed-gain, with the active damping introduced to the system determined independently for each mode and is a function of the velocity for the under-damped case. In this work we propose to modify IMSC using fuzzy reasoning. The result is a new non-linear control law, embedding fuzzy reasoning and an implicit fuzzy rule-base that transforms the traditional algorithm from a fixed-gain to a variable-gain controller. The algorithm uses information about the displacement profile across the sensed locations to distribute the active damping rationally among the modal controllers. This new algorithm complements the “local” view of the traditional algorithm in the modal space, with a “global” view of the displacements in the physical space. The results show significant improvement in the settling time as the performance criterion.
Experimental Verification of Time-Varying Impulse Shaping for a Two-Link Flexible Manipulator
Authors: Cho Jung-Keun , Park Youn-sik
Published: March 2021

Input shaping is a method to reduce the motion-induced vibration in a flexible system. A kind of input shaping method (time-varying impulse shaping) has been proposed previously which is applicable to vibration reduction of time-varying systems. This paper presents experimental results of time-varying impulse shaping with a two-link flexible manipulator. The flexible manipulator has two revolute joints and moves on a vertical plane under gravity. A dynamic model was developed to provide a basis for the shaping, and the model was proved through some experiments. The reference trajectories commanded to the system are shaped by using the suggested time-varying impulse shaping. Implemented to the two-link flexible manipulator, test results demonstrate that the link vibration can be greatly suppressed during and after a point-to-point motion, and the residual vibration reduction was observed more than 90% with this shaping.
Optimum Design of Sandwich Panels With Piezoelectric and Shape Memory Alloy Actuators
Authors: Birman Victor , Simonyan Arthur
Published: March 2021

The problems of optimum distribution of stiffener-actuators manufactured from piezoelectric or shape memory alloy materials and bonded to or embedded within the facings of a sandwich plate are considered. The sandwich plate consists of thin composite or isotropic facings and a thick shear deformable core. The amplitude of forced vibrations of the plate is reduced using symmetric couples of piezoelectric actuators subjected to out-of-phase dynamic voltages. Shape memory alloy stiffener-actuators are used to reduce bending deformations. In the latter case, a desirable effect is achieved by activating the stiffeners on one side of the middle surface. Optimum design is considered based on the requirement of minimal transverse static or dynamic deflections subject to a constraint on the volume of the material of the actuators. The variables employed in the process of optimization are the ratios of the cross sectional areas of the stiffener-actuators in each direction to their respective spacings. It is shown, that, dependent on the load, materials, and geometry, optimization can significantly reduce deflections, i.e. enhance the strength, of sandwich plates.
Elasto-Plastic Analysis of Anisotropic Plates and Shells With Moderate Thickness by FEM
Authors: Zhong W. F. , Huang Y. Y.
Published: March 2021

A numerical analysis of anisotropic plates and shells with moderate thickness is dealt with in this paper by using elasto-plastic finite element method. The Huber-Mises yield surface extended by Hill and the nine-node Heterosis element are introduced into the present model. In order to increase the computational accuracy and the speed of convergence an improving arc-length iteration method for solving nonlinear increment finite element equations is presented. Numerical examples are given and compared with available solutions. It is shown that the proposed method is more efficient than existing finite element method.
The Efficacy of the Momentum Balance Method in Transverse Impact Problems
Authors: Yigit Ahmet S. , Christoforou Andreas P.
Published: March 2021

An elastic-plastic contact law that incorporates local permanent deformation in the contact zone has been used to investigate the efficacy of the momentum balance method in transverse impact problems. The momentum balance solution is compared to the numerical solution of the same equations using the contact law. It is shown that the momentum balance method gives very good results for the post impact behavior of both the impacter and the beam. In certain cases, it is also shown to yield satisfactory results for the dynamic behavior during contact. It is demonstrated that the momentum balance method with an appropriate coefficient of restitution obtained from the contact law, is physically the same as using the contact law itself, with the difference that the local deformation is neglected.
Split Vibration Modes in Acoustically-Coupled Disk Stacks
Authors: Tseng Jung-Ge , Wickert Jonathan
Published: March 2021

Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.
Green’s Function Synthesis for Layered Distributed Parameter Systems
Authors: Lueschen Gerhard G. G. , Bergman Lawrence. A.
Published: March 2021

Dynamic Green’s functions for a class of layered distributed parameter systems are derived using a new method. The resulting system Green’s function, which is comprised of the elemental Green’s function of each of the substructures, defines the dynamics of the fully coupled system. Green’s functions for sandwiched beams with both identical and different layer properties are derived. The result retains the accuracy of the constituent elemental Green’s functions. The application of the method to other layered structures is immediate as long as the elemental Green’s functions of the substructures are known.
Effects of the Electromagnetic Forces on Vibrational Behavior of the Laminated Mechanical Structure of Stator Cores
Authors: Ozturk Cuneyt
Published: March 2021

Stator laminations can have mutual excitation sources depending to the inertial forces that can excite the mechanical resonances and radial components of the electromagnetic forces that vary with the magnetic flux changes and the magnetostrictive forces.

Magnetostrictive forces can appear depending to the material properties of the plates and have mechanical and magnetic causes Mechanical properties of the lamination plates can be determined both in numerical and experimental methods.

Magnetostrictive effects of the laminations have significant contribution to the audible noise of electric motors. The combined effects of radial components of electromagnetic forces and magnetostrictive deformation can cause further amplification problems of noise.

This study investigates the effects of magnetostrictive forces on the laminated mechanical structure of stator core by referring to the changes of the plate materials depending to applicable heat treatments, magnetic properties and silicon alloying that were all considered as factors to modify the effects of magnetostriction.
Analysis of the Equations of Linear Controlled Structures
Authors: Ma F. , Lee W. C.
Published: March 2021

The coefficients of the equation of a linear controlled structure are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to structures with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.
An Operator-Adjoint Approach to Electrical Impedance Tomography
Authors: Wade J. G.
Published: March 2021

Electrical impedance tomography (EIT) is a nondestructive imaging technique whereby spatial variations in the electrical conductivity of a medium can be determined from measurements of the electric current and potential on the boundary of the medium. The EIT problem is naturally viewed as a distributed parameter inverse problem, and in this paper it is formulated as a least-squares minimization problem for the unknown conductivity function. The main focus is on a mathematical and numerical “adjoint” approach whereby the the derivatives of least-squares function may be computed efficiently when the number of degrees of freedom in the conductivity is large. Numerical examples are provided.
On the Local Regularization of Inverse Problems of Volterra Type
Authors: Lamm Patricia K.
Published: March 2021

We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include the standard Tikhonov parameter, as well as a parameter that represents the length of the local regularization interval. We present a convergence theory for the infinite-dimensional regularization problem and show that the regularized solutions converge to the true solution as the regularization parameters go to zero (in a prescribed way). In addition, we show how numerical implementation of the ideas of local regularization can lead to the notion of “sequential Tikhonov regularization” for Volterra problems; this approach has been shown in (Lamm and Eldén, 1995) to be just as effective as Tikhonov regularization, but to be much more efficient computationally.
Parameter Estimation for an Imperfectly Clamped Plate: Numerical Examples
Authors: Banks H. T. , Smith R. C. , Wang Yun
Published: March 2021

The problems associated with maintaining truly fixed (zero displacement and slope) or simple (zero displacement and moment) boundary conditions in applications involving vibrating structures have led to the development of models which admit slight rotation and displacement at the boundaries. In this paper, numerical examples demonstrating the dynamics of a model for a circular plate with imperfectly clamped boundary conditions are presented. The latitude gained when using the model for estimating parameters through fit-to-data techniques is also demonstrated. Through these examples, the manner in which the model accounts for the physical manifestation of imperfectly clamped edges is illustrated, and issues regarding the use of the model in physical experiments are defined.
A Numerical Algorithm for Determining a Coefficient in an Elliptic Equation
Authors: Lowe Bruce D. , Rundell William
Published: March 2021

We consider the question of recovering coefficients such as q or k from the equation −∇.(k∇uj) + q(x)uj = fj(x) in a domain Ω ⊂ Rn where uj(x) is subject to Dirichlet boundary conditions. The non-homogeneous source terms {fj(x)}j=1∞ form a basis for L2(Ω). We will prove that a unique determination is possible from data measurements consisting of the average flux leaving a fixed subset of the boundary of the region for each input source. The particular aplication we have in mind is the recovery of interior parameters in heat conduction problems given that we can only make measurements on the boundary, but are able to generate a sequence of internal heat sources. An algorithm that allows efficient numerical reconstruction of the coefficients from finite data will be given.
An Optimization Based Approach to Flow Matching for Burger’s Equation With a Forcing Term
Authors: Herdman Terry L. , Kang Kyehong
Published: March 2021

We consider the use of a numerical optimization technique to solve an inverse problem for Burger’s equation with a periodic forcing term. The solution depends on the initial data profile. The goal is to obtain an optimal continuous linear initial profile which generates the fixed target solution using a numerical optimization technique. Because Burger’s equation is time dependent, the cost function measures the difference between the target and the computed solution at a fixed final time. The optimization algorithm utilizes BFGS updates without computing Hessians and a line search is applied as a globalization. Burger’s equation is solved by a generalized Lax-Friedrichs scheme. This problem is motivated by flow matching problems in optimal design of nozzles and 1-dimensional ducts (see [1]).
On the Inverse Multiplicative Eigenvalue Problem With an Engineering Application
Authors: Sivan Dmitri D. , Ram Yitshak M.
Published: March 2021

The problem of determining the masses of a mass-spring system is an inverse multiplicative eigenvalue problem. Generally, the solutions of this problem are not yet fully characterised. Since all known methods of solution follow an iterative approach, the possibility of developing a closed-form algorithm is examined. Although such method is found for the two and three degree-of-freedom systems, it appears to be impractical for higher order systems. Two well known existing algorithms are then examined numerically. Both converge locally at a quadratic rate. However, for practical applications, a globally converging algorithm may be more effective. In this paper a new, linearly converging algorithm is advised. The three methods are then tested on some selected numerical examples, and their performances compared.
New Approaches for Identifying Structural Models
Authors: Cogan Scott , Lallement Gérard , Sanseigne Laetitia
Published: March 2021

The present synthesis highlights the recent developments in the research work at the R.C.A.M.L. concerning the difficulties encountered at various stages of the correcting process of linear elastodynamics finite element models and some of the solutions suggested to reduce them : optimizing test preparation, combining the principle of selective sensitivity with the concept of pseudo-tests, utilizing additional information coming from base excitations, quantifying the quality of the updated model for applications such as structural modifications or dynamic sub-structuring.
Application of a FRF Based Model Updating Technique for the Validation of Finite Element Models of Components of the Automotive Industry
Authors: Lammens Stefan , Brughmans Marc , Leuridan Jan , Heylen Ward , Sas Paul
Published: March 2021

This paper presents two applications of the RADSER model updating technique (Lammens et al. (1995) and Larsson (1992)). The RADSER technique updates finite element model parameters by solution of a linearised set of equations that optimise the Reduced Analytical Dynamic Stiffness matrix based on Experimental Receptances.

The first application deals with the identification of the dynamic characteristics of rubber mounts.

The second application validates a coarse finite element model of a subframe of a Volvo 480.
Selective Sensitivity for Model Updating With Modal Data
Authors: Gola Muzio M. , Somà Aurelio
Published: March 2021

In the present work a criterion for the minimum measured data set (modes and degree of freedom) required for a successful updating is established in the case of the inverse sensitivity method. The finite element model is used as a tool for the pre-analysis in order to plan the modal experiments, the selection of modes and degree of freedom to put into play in the updating procedure are obtained though the evaluation covariance matrix of the estimated parameters.

A two stage procedure is proposed, in the first part of the work the modal sensitivity problem is reviewed in order to illustrate a systematic procedure capable of enucleating the set of modes that effectively contributes to the updating procedure. Then the procedure is extended to the determination of the minimum number of degrees of freedom to be measured in relation to a desired upper limit for the standard deviation of the structural parameters which are to be updated.

Simple frame structures with different parameter locations are used as examples, the convergence on two parameters maps is used as demonstration of the powerful of the selection procedure to predict the chances of the successful updating.
Mode Shape Expansion Techniques for Model Error Localization and Damage Detection
Authors: Levine-West Marie B. , Milman Mark H.
Published: March 2021

Several methods for mode shape expansion are investigated. The most popular methods use the dynamic equations of motions to obtain direct solutions, or use orthogonal projections. Both approaches can also be formulated as constrained optimization problems. To account for uncertainties in the measurements and in the prediction, a new expansion technique based on least squares minimization with quadratic inequality constraints (LSQI) is proposed. Each modal expansion technique is evaluated with experimental data obtained on the Micro-Precision Interferometer testbed, using both the pre-test and updated analytical models. The robustness of these methods is verified with respect to measurement noise and model error. It is shown that the proposed LSQI method has the best performance and can reliably predict mode shapes, and can be used to locate damage elements, even in very adverse situations. A new LSQI algorithm is also proposed which significantly decreases the solution time.
Model Updating of Evolutionary Structures
Authors: Levine-West Marie B. , Melody James W.
Published: March 2021

A methodology is proposed for dynamic testing, modal identification and model correlation of structures which are assembled in an evolutionary manner. The methodology prescribes initial testing of the base structure without any attached components. As components are added onto the base structure, additional tests are performed. Three testing options are proposed, all of which enable to update the physical parameters of the components only using a Bayesian Estimation Technique (BET). Improvements to former BET implementations have been made, all of which contribute to higher fidelity models and more efficient computational times. These improvements include an optimal modal expansion technique, an error localization technique based on element modal strain energy errors, a model reduction option with component mode synthesis, and a line search algorithm to accelerate convergence. The proposed methodology has been successfully tested on an actual evolutionary structure, and significant improvement from the updated pre-test model are demonstrated.
The Dynamic Effects of Robotic Grasping Considering Flexible Joints
Authors: Kövecses J. , Fenton R. G. , Cleghorn W. L.
Published: March 2021

In this paper the dynamics of an important and frequently used robotic working process is investigated. The robot manipulator approaches, suddenly grasps and lifts a three dimensional object which is travelling on a conveyor. The spatial robot manipulator has two rigid links, rigid rotors and flexible joints. In order to model the joint flexibility, one-degree of freedom torsional springs have been used. The effects of continuous and discontinuous constraint equations are analysed. Simulation results are presented.
Stroboscope Phase Shifting Shearography for Automated Vibration Measurement
Authors: Chen Frank , Griffen Christopher T. , Hung Yau Y.
Published: March 2021

A new method for measurement and visualization of structural dynamic vibration characteristics is presented. Using digital shearography as an imaging tool combined with a stroboscopic phase shifting technique for quantitative fringe pattern interpretation, the fullfield modeshape amplitude and phase distribution is calculated. Theory together with experimental verification is discussed.