bluuebunny/crossref_metadata_2025 huggingface dataset:
Operation of a Torsionally-Loaded, Composite Shaft Above Two Flexural Critical Speeds
Authors: Frederick Jeffrey R. , Darlow Mark S.
Published: April 2021

A graphite/epoxy composite shaft has been successfully balanced to operate above two flexural critical speeds while subjected to a steady torsional load. This experimental investigation has been conducted as part of a research program concerning the optimal design of supercritical composite power transmission shafts for rotorcraft applications. Of particular interest is the use of composite materials in the design of tail rotor and synchronization shafts.

Rotating tests were conducted with a composite shaft that models the half length of the tail rotor drive shaft of the AH-64 helicopter. Tests were performed with magnetic and coulomb damping. It was shown in past research that an unloaded composite shaft could be balanced through and operated above two flexural critical speeds [1,2]. In this series of tests, a steady torsional load has been applied which models that of a tail rotor driveshaft. Adequate magnetic damping performance was observed up to 1000 rpm, although its effectiveness diminished at higher speeds. The remaining tests were conducted with an external coulomb damper. Results show controllable operation above two critical speeds, and smooth operation was observed at the scaled operating speed of 3500 rpm. All synchronous and nonsynchronous vibrations were easily controlled with 6% external damping applied through the entire speed range up to 5000 rpm.
Dynamic Analysis of Flexible Gear Trains/Transmissions: An Automated Approach
Authors: Amirouche F. M. L. , Shareef N. H. , Xie M.
Published: April 2021

In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of inter-connected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of 3-D isoparametric elements having six degrees of freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions together with the equations of motion using Kane’s method, strain energy concepts are presented in a matrix form suitable for computer implementation. The constraint jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.
Comparison of Analysis and Experiment for Dynamics of Low-Contact-Ratio Spur Gears
Authors: Oswald Fred B. , Rebbechi Brian , Zakrajsek James J. , Townsend Dennis P. , Lin Hsiang Hsi
Published: April 2021

Low-contact-ratio spur gears were tested in the NASA gear-noise rig to study gear dynamics including dynamic load, tooth bending stress, vibration, and noise. The experimental results were compared with a NASA gear dynamics code to validate the code as a design tool for predicting transmission vibration and noise.

Analytical predictions and experimental data for gear-tooth dynamic loads and tooth-root bending stress were compared at 28 operating conditions. Strain gage data were used to compute the normal load between meshing teeth and the bending stress at the tooth root for direct comparison with the analysis. The computed and measured waveforms for dynamic load and stress were compared for several test conditions. These are very similar in shape, which means the analysis successfully simulates the physical behavior of the test gears.

The predicted peak value of the dynamic load agrees with the measurement results within an average error of 4.9 percent except at low-torque, high-speed conditions. Predictions of peak dynamic root stress are generally within 10 to 15 percent of the measured values.
Numerical Analysis of the Transient Responses of Bladed Disks
Authors: Irretier H. , Omprakash V.
Published: April 2021

A numerical model for the dynamic analysis of a rotationally periodic structure under rotation subjected to non-stationary excitation system of forces is presented on the basis of principles of finite elements and cyclic symmetry. Based on this model, the transient response characteristics of a representative practical bladed disk system during run-up subjected to nozzle-excitation are studied taking into account many important practical aspects of the problem. Some fundamental effects concerning the response maxima and resonance shift of these responses with respect to the cantilever blade response, angular acceleration and the order of excitation are discussed.
Mixed Time Series Models for Time-Varying Metal Cutting Process
Authors: Ya Wu , Shiqiu Ke , Shuzi Yang , Shanxiang Xu , Weiguo Li , Qiang Jiang
Published: April 2021

The concept of time-varying metal cutting chatter is developed in this paper and the AR and SETAR models based on the segmented time series are introduced to describe the time-variability, which is applied in analyzing the chatter in a type Mx-4 lathe. The emphasis of this work is placed on four aspects: the AR spectrum, the chatter modal damping ratio, the eigenvalues of a time-varying system and the limit cycle for a steady chatter. It is pointed out that, for time-varying chatter, its time interval is quite short compared with ordinary chatter and it will wither away owing to the time-varying parameters of the system. It is also shown that the machine cutting system under steady chatter is still stable and its damping is not equal to zero. The results can well explain the special phenomenon of chatter in Mx-4 lathe and is helpful to the study of time-varying metal cutting chatter.
A Method of Linearized Dynamic Condensation
Authors: Bouhaddi N. , Cogan S. , Fillod R.
Published: April 2021

Three frequency domains are defined for a dynamic condensation : the GUYAN condensation domain [1], the LEUNG PETERSMANN [3,4] domain, and the intermediate domain resulting from the approach presented in this article. This definition is based on the Rayleigh Quotient.

This definition is based on the Rayleigh This new proposed approach is based on the dynamic condensation developed by PETERSMANN [4] and accounts for the dynamic effects of the slave dof by a linearization of the mass correction term for a given frequency band.
Inverse Problem in Vibration for Generating Symmetric Coefficient Matrices
Authors: Starek Ladislav , Inman Daniel J.
Published: April 2021

This paper provides a symmetric solution to the inverse eigenvalue problem for systems defined by second order vector differential equations representing a multiple degree of freedom spring-mass damper system. Formulations are provided for calculating real symmetric coefficient matrices from spectral data. These relations are also defined for both simple and Jordan systems.
Solution of Dynamic Problems of Structural Elements Using Simple Polynomial Approximations
Authors: Laura Patricio A. A.
Published: April 2021

A survey of studies dealing with vibrating structural elements using simple polynomial approximations in connection with Rayleigh-Ritz or Galerkin-type methods is presented.

The classical use of polynomials when solving dynamic problems of deformable bodies consists of constructing a set of coordinate functions in such a way that they satisfy at least the essential boundary conditions and that they represent “reasonably well” the deformation field of the structural element under study.

An alternative and more rational procedure has been developed and used in recent years whereby orthogonal polynomials are used. A “base function” is constructed and then one generates a set of orthogonal polynomials using the Gram-Schmidt or equivalent procedure.

The present paper presents comparisons of numerical results in the case of different types of vibrating structural elements Special emphasis is placed on Rayleigh’s optimization procedure which consists of taking one of the exponents of the polynomial coordinate functions as an optimization parameter “γ”. Since the calculated eigenvalues constitute upper bounds, by minimizing them with respect to “γ” one is able to optimize the eigenvalues.
New Mode Superposition Method of Structural Dynamics in Generalized Coordinates
Authors: Shiohata K. , Hatake S. , Fujisawa F.
Published: April 2021

A new mode superposition method of structural dynamics is presented, which uses eigenmodes and modified static modes. The modified static modes matrix is obtained from the static modes and lowest eigenmodes by external loads in generalized coordinates. By using modified static modes, the load vectors corresponding to the highest modes can be set at zero.

The proposed method and the conventional method with both a limited number of eigenmodes and all eigenmodes are applied to two numerical models, and the effectiveness of the proposed method is discussed.
Efficient Numerical Solution of Multidimensional Fokker-Planck Equations Associated With Chaotic and Nonlinear Random Vibrations
Authors: Kunert A.
Published: April 2021

In the presented paper the response of nonlinear random oscillators is calculated by the numerical solution of the associated Fokker-Planck-Equation. This approach can be used to approximate the invariant probability density of chaotic nonlinear oscillators or to calculate the response of a nonlinear oscillator, driven by additive white noise. A weighted residual approach is proposed to solve the Fokker-Planck-Equations numerically. By this method the partial differential equation is transformed to a coupled set of linear ordinary differential equations. These equations can be derived easily, because the integrals associated to the Galerkin procedure can be solved analytically. Considering stationary densities the solution is given by a generalized Eigenproblem. Utilizing sparse matrix techniques the solution can be calculated very efficiently.
On the Nonlinear Behavior of Rotating Shafts
Authors: Leinonen Tatu
Published: April 2021

This paper presents a nonlinear model to describe the bending behaviour of a rotating shaft, based on the general theory of a bending bar. Justification for this theoretical model has been provided by tests, the resulting curves more closely fitting observed results than those of other models.
Non-Linear Modal Interaction in a Clamped-Clamped Beam: Part I — Deterministic Approach
Authors: Ibrahim R. A. , Afaneh A. , Lee B.
Published: April 2021

The nonstationary response characteristics of multimode interaction in a clamped beam subjected to harmonic excitation is investigated. The nonlinear coupling of the first three modes is considered and resulted in a fourth order internal resonance condition for certain values of initial static axial load. The method of multiple time scales is employed to derive five equations in amplitudes and phase angles. It is found that the beam cannot reach any stationary solution in the neighborhood of the combination internal resonance. Within a small range of internal detuning parameter the third mode, which is externally excited, is found to transfer energy to the first two modes. Outside this region, the response is governed by a unimodal response of the third mode which follows the Duffing oscillator characteristics. The boundaries that separate unimodal and mixed mode responses are obtained in terms of the excitation level, damping ratios and internal resonance detuning parameter. The domains of attraction of the two response regimes are also obtained. The experimental results and response characteristics to random excitation will be reported in parts II and III, respectively.
Self-Excited Oscillation Analysis of a Multidegree-of-Freedom System With Cubic Non-Linearities: Dynamic Problems in Rolling Mill (IV)
Authors: Chen YongDe , Xu YeYi
Published: April 2021

In nalyzing the self-excited oscillation in drive systems of a rolling mill, almost all of the scholars didn’t consider the internal resonance and zero-frequency. We indicate that these important factors couldn’t be neglected. In this paper, dynamic model is reconstructed, and self-excited oscillation is discussed in the presence of an internal resonance. Several new conclusions are drawn.

These results are useful for design of blooming mill drive systems.
Transitions Through Period Doubling Route to Chaos
Authors: Evan-lwanowski R. M. , Lu Chu-Ho
Published: April 2021

The Duffing driven, damped, “softening” oscillator has been analyzed for transition through period doubling route to chaos. The forcing frequency and amplitude have been varied in time (constant sweep). The stationary 2T, 4T… chaos regions have been determined and used as the starting conditions for nonstationary regimes, consisting of the transition along the Ω(t)=Ω0±α2t,f=const., Ω-line, and along the E-line: Ω(t)=Ω0±α2t;f(t)=f0∓α2t. The results are new, revealing, puzzling and complex. The nonstationary penetration phenomena (delay, memory) has been observed for a single and two-control nonstationary parameters. The rate of penetrations tends to zero with increasing sweeps, delaying thus the nonstationary chaos relative to the stationary chaos by a constant value. A bifurcation discontinuity has been uncovered at the stationary 2T bifurcation: the 2T bifurcation discontinuity drops from the upper branches of (a, Ω) or (a, f) curves to their lower branches. The bifurcation drops occur at the different control parameter values from the response x(t) discontinuities. The stationary bifurcation discontinuities are annihilated in the nonstationary bifurcation cascade to chaos — they reside entirely on the upper or lower nonstationary branches. A puzzling drop (jump) of the chaotic bifurcation bands has been observed for reversed sweeps. Extreme sensitivity of the nonstationary bifurcations to the starting conditions manifests itself in the flip-flop (mirror image) phenomena. The knowledge of the bifurcations allows for accurate reconstruction of the spatial system itself. The results obtained may model mathematically a number of engineering and physical systems.
A New Approach for Response Analysis of Nonlinear Systems Under Random Excitations
Authors: Orabi Ismail I. , Ahmadi Goodarz
Published: April 2021

A new technique for response analysis of nonlinear systems subjected to non-Gaussian excitations is presented. The technique is based on a Wiener-Hermite series expansion method. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite Kernel functions is described. The resulting response statistics are compared with those obtained from Gaussian closure scheme. A Monte Carlo digital simulation study is also performed. It is shown that the Gaussian closure technique and equivalent linearization method lead to identical results which are somewhat less accurate than those obtained by the non-Gaussian closure scheme. It is also shown that the Wiener-Hermite expansion method is well suited for response analysis of nonlinear systems under non-Gaussian excitations.
Unsteady Aerodynamics and Vortex Induced Aeroelastic Instability of a Structural Angle Section
Authors: Modi V. J. , Slater J. E.
Published: April 2021

Wake-body interactions for a two-dimensional structural angle member during stationary and vortex induced oscillatory conditions are studied using a conventional low turbulence wind tunnel. The response of an angle section with combined plunging and torsion indicates that the oscillations occur essentially in one of the two degrees of freedom. The measurements of frequency and phase substantiated this observation. The plunging resonance exhibits the familiar vortex capture phenomenon where the shedding frequency is controlled by the cylinder motion over a finite wind speed range. On the other hand, the torsional vibration shows a vortex control phenomenon where the vortex shedding governs the frequency of oscillation. The vortex induced torsional resonance was found to be severe even at moderate damping levels. The results should prove useful in structural designs such as high voltage transmission towers, antenna masts, bridges, etc. where angle sections are often used as secondary members.
Vibration and Stability of an Elastic Beam Subjected to a Periodic Axial Load With Time-Dependent Displacement Excitation at Both Ends
Authors: Wu Xiao-Feng , Akay Adnan
Published: April 2021

This paper concerns the transverse vibrations and stabilities of an elastic beam simultaneously subjected to a periodic axial load, a distributed transverse load, and time-dependent displacement excitations at both ends. The equation of motion derived from Bernoulli-Euler beam theory is a fourth-order partial differential equation with periodic coefficients. To obtain approximate solutions, the method of assumed-modes is used. The unknown time-dependent function in the assumed-modes method is determined by a generalized inhomogeneous Hill’s equation. The instability regions possessed by this generalized Hill’s equation are obtained by both the perturbation technique up to the second order and the harmonic balance method. The dynamic response and the corresponding spectrum of the transversely oscillating elastic beam are calculated by the weighted-residual method.
On Tool Instability During Machining
Authors: Sahay C. , Dubey R. N.
Published: April 2021

The present paper describes the role of the tool in vibrations of a machining system. The cutting force has been assumed to be constant. The shear deformation of the tool is considered. The quasi-static analysis of the situation yields a maximum allowable uncut chip thickness, which shows how the frictional interaction at the tool face and the ratio of the components of cutting forces alter this value. The relationship also expresses the effect of tool dimensions and work material on the vibration of the tool.
Stability of Perfect Viscoelastic Columns Subjected to Periodic Axial Loading
Authors: Shirahatti Uday S. , Sinha S. C.
Published: April 2021

The stability problem associated with an Euler-Bernoulli beam made of an arbitrary linear viscoelastic material is formulated. The three parameter solid and the Kelvin-Voigt models are analyzed in the presence of constant as well as periodic loads. The application of a finite time stability concept is shown for the constant loading case when the traditional stability criterion fails to make sense. For the case of a periodic loading, the stability diagrams are obtained through an application of Floquet theory. It is found that the addition of periodic loads may significantly alter the stability behavior of a column which is originally subjected to a constant load only.
Stability Analysis of Turbomachinery From the Viewpoint of Seal
Authors: Iwatsubo T. , Sheng B. C.
Published: April 2021

The stability of the typical rotating fluid machineries such as the single-stage and multi-stage pumps which consist of impellers, bearings and noncontacting seals is evaluated from the viewpoint of seals. The individual contribution of the impeller, bearing as well as seal to the stability, and the dynamic interactions of these fluid elements are investigated. In the investigation, some types of bearings, and seals such as annular smooth seals, parallel grooved seals and damper seals are compared to seek the better ones for the rotor stability. The effect of working conditions on the stability is also investigated. The results show that the rotor stability is strongly affected by the characteristics of these fluid elements, and the stability can be improved by changing the unstable fluid element.
Application of the Boundary Element Method to Predict the Acoustic Field in a Two-Dimensional Duct
Authors: Pates Carl S. , Shirahatti Uday S.
Published: April 2021

In the development of the newer supersonic and hypersonic flight vehicles, an increased need for the analysis of acoustic fields and the response of structures to acoustic loads in the presence of high temperature and large mean flow velocities have become necessary. A major concern has been in the area of pressure fields associated with ducts. Such acoustic ducts are frequently used to test the response of various structural elements of flight vehicles. Many new methods have been created and used to approximate the sound fields in ducts. Since the region or boundary of an acoustic problem can extend to infinity, some approximating methods require much time and effort to solve the problem. Many ways have been examined to simplify the acoustic problem and still obtain reasonable results. In the past thirty years, the boundary element method (BEM) has been researched and proven to be an extremely simplified and accurate method for solving acoustic problems. Since BEM only discretizes the boundary, the dimensionality of the problem is reduced by one.

This paper presents a boundary element formulation to predict the pressure field in a two-dimensional acoustic duct. The boundary conditions basically consist of two types: known pressure or known normal derivative of pressure. In order to examine the boundary element method, a 2-D rectangular duct problem will be investigated. The example problem will consist of a duct with rigid walls and a specified pressure distribution at the entrance. Pressure values will be calculated for boundary nodes using the boundary element method. These values will be compared with the available classical solutions.
Enhanced Vibration Control of Ultrasonic Tooling Using Finite Element Analysis
Authors: O’Shea Kevin
Published: April 2021

The use of finite element analysis (FEA) in high frequency (20–40 kHz), high power ultrasonics to date has been limited. Of paramount importance to the performance of ultrasonic tooling (horns) is the accurate identification of pertinent modeshapes and frequencies. Ideally, the ultrasonic horn will vibrate in a purely axial mode with a uniform amplitude of vibration. However, spurious resonances can couple with this fundamental resonance and alter the axial vibration. This effect becomes more pronounced for ultrasonic tools with larger cross-sections.

The current study examines a 4.5″ × 6″ cross-section titanium horn which is designed to resonate axially at 20 kHz. Modeshapes and frequencies from 17–23 kHz are examined experimentally and using finite element analysis. The effect of design variables — slot length, slot width, and number of slots — on modeshapes and frequency spacing is shown. An optimum configuration based on the finite element results is prescribed. The computed results are compared with actual prototype data. Excellent correlation between analytical and experimental data is found.
Boundary Element Method Used in Random Response Calculation of the Plate-Beam Structure
Authors: Zhu J. M. , Huang L.
Published: April 2021

The furnace walls of the large boilers in power plants are combined structures consisting of orthotopic plate and equally spaced beams, which are usually submitted to random vibration under the excitation of the pressure fluctuation induced by combustion in the furnace. In this paper, a numerical method based on BEM to compute the random response of the structure is offered. The agreement between the computing results and the measured data in a practical example verifies the effectiveness of the method.
Coupled Axial-Lateral Dynamic Analysis Using 3-D Riccati-Finite Element Method
Authors: Subbiah Rajagopal
Published: April 2021

An improved algorithmic procedure is discussed to obtain the dynamical characteristics of rotating systems applicable to both 2-D and 3-D models. The beam structure has been modeled in 3 dimension representing five degrees of freedom at each node (three translations and two rotations) using the Riccatifinite element method and solved by an iterative technique. This method provides another convenient way of solving a variety of rotating structural problems using personal computers.
The Method of Modal Parameters to Determine the Boundary Condition of Finite Element Model
Authors: Shiyu Chen , Fengquan Wang
Published: April 2021

In this paper, a method used to determine the boundary condition of Finite Element Model with structure modal parameters is presented. On deriving the method, the theory of Finite Element Model for dynamic calculating is used. Combined with the modal parameters got from experiment, a FEM-Modal Parameter equation to determine the boundary condition is put forward. For solving the equation, three methods are given. The first is the accurate method. The second is the full mode computation method by means of generlized inverse matrix. The third is the interpolation method of frequency. An applied example is given and the results of calculation fully verify the effectiveness of the method offered.
A Nonlinear Analysis of the Whirling Motions of Slender Beams Under Various Resonant Excitations
Authors: Shyu In-Ming K. , Mook Dean T. , Plaut Raymond H.
Published: April 2021

The response of a slender, elastic, cantilevered beam to a simple harmonic excitation is investigated. The nonlinear equations governing the motion of the beam are essentially those derived earlier by Crespo da Silva and Glynn (1978). In the current study, the governing equations are extended to include static deflection. These equations not only include nonlinear curvature, nonlinear inertia, inextensionality and static deflection, but also include torsional displacement. In all cases, the torsional displacement is written in terms of lateral displacements and eliminated from the governing equations. Previous derivations of equations of motion contain only the linear and cubic terms without consideration of the static displacement produced by the weight of the beam. As a result of this static deflection, there are quadratic terms in the governing equations, which introduce the possibility of superharmonic and subharmonic resonances of order two.

The partial-differential equations of motion are converted into a system of coupled ordinary-differential equations in time by the application of Galerkin’s procedure. Approximate solutions of the temporal equations are determined by the method of multiple scales. The analysis reveals that only the in-plane modes directly excited by a primary or secondary resonance and the out-of-plane modes excited by an internal resonance are involved in the first approximation of the response. The amplitudes of the other modes decay. Under some circumstances, there is no steady-state (constant amplitude, constant phase) response. Instead, the amplitude and phase are slowly modulated. Under some circumstances, the modulations are harmonic and produce discrete side bands around the fundamental frequency. For other circumstances, the modulations are chaotic.

Both stable and unstable whirling motions are found in every resonance when the principal moments of inertia of the cross-section are approximately equal. The longer the beam is, the more prominent the whirling motion becomes. The accuracy of some of the approximate solutions is verified by numerical integration. The analysis reveals some interesting possibilities: For example, in a subharmonic resonance of order two, it is possible for the out of plane motion to have a frequency that is exactly one half that of the in-plane motion, which has a frequency equal to that of the excitation. It is also possible for the frequency of the in-plane motion to be equal to that of the out-of-plane motion, which is the one half frequency of the excitation.
Characterization of a Nonlinear Mechanical System by Experimental Attractors
Authors: Kesaraju R. , Noah S. T.
Published: April 2021

Response cycles (periodic orbits) provide a detailed invariant characterization for low dimensional deterministic dynamical systems (Gunaratne and Procaccia, 1987). One can extract all the periodic orbits of order n, for n not too large, directly from the chaotic attractor and calculate their stabilities (Lyapunov exponents), Lathrop and Kostelich, 1989. This information is crucial for asserting whether two experimental attractors are the same or that a theoretical model faithfully reproduces an experimental attractor. Moreover, the periodic orbits can provide a useful characterization of the structure and dynamics of the attractor as parameters vary. This could prove to be a useful tool in failure prediction or parameter identification.
Chaotic Response of an Impulsively Loaded Two Degree of Freedom Beam Model
Authors: Symonds P. S. , Lee J.-Y.
Published: April 2021

The paper shows some recent results for a two-degree of freedom beam model, with lumped parameters of elastic and plastic behavior, as a tool for interpreting anomalous response behaviors of structural elements (beams and plates) subjected to transverse impulsive loading [1]. Such behaviors may occur when the structure has fully fixed edges and the transverse loading leads to extensional permanent strains. The 2DoF model predicts behaviors like those from numerical solutions of discretized beams and plates, but facilitates more extensive calculations. A single DoF model also provides important insights [2, 3], but the 2DoF model [4, 5] reveals the complexity, including chaos, not shown by a SDoF model.
Structural Damage Configurations Subject to Modal Oscillations
Authors: Lu Yaw-Min , Ju Frederick D.
Published: April 2021

The present investigation aims to develop a general probabilistic approach for the prediction of potential damage configurations of structure under modal oscillations. The multiple-crack distribution of the as-predicted damage configurations were characterized by the associated probability measure in terms of crack patterns, crack locations and crack depths. It is postulated that the structure is damaged at a prevailing modal response and the cracking process is sequential. The first passage probability of critical structural parameter exceeding the characteristic material allowable was evaluated to predict the mean time to failure, crack initiation, and crack propagation. In conjunction with the multiple-crack interactive stress relief effects, the probabilistic distributions of damage configuration were established for some representative modal shapes. The analysis results indicate that the damage configurations are highly affected by the modal shape wherein modal stress peak regions provide the most probable locations for cracking. Multiple-crack configuration is more likely to occur at higher mode of vibration. A single crack pattern is dominant at lower mode of vibration.
Modal Analysis of Mini-Small Object: Dental Drill
Authors: Zhang P. Q. , Huang T. C. , Wang Q. M. , Tang X. L.
Published: April 2021

In this paper, we analyze theoretically the use of correlation statistical properties in the random speckle field, in the non-contact recording of free response information of vibrating object, and in terms of time domain signals collected simultaneously at the multiple points, and we conduct system identification techniques in the frequency and time domains to identify the dynamic parameters. The vibration of the bending arm of the dental drill is measured and analyzed. The lower-order natural frequencies and mode shapes are obtained.
Multiple Excitation Sine Testing: An Integrated Approach
Authors: Van der Auweraer H. , Otte D. , Leuridan J. , Bakkers W.
Published: April 2021

Current modal test techniques based on multiple sinusoidal excitation are reviewed. Multiple input stepped sine testing is a phase separation technique. It consists of two steps: the estimation of Frequency Response Functions, followed by modal parameter estimation.

Multiple exiter normal mode testing is a phase resonance technique, where the structure is actually forced to vibrate as a pure normal mode.

The current paper aims to review and investigate the forcing requirements for both approaches from a global point of view, and to present a new, unifying approach combining several of the advantages of both.
Complex Modal Testing Methods for Rotating Machinery
Authors: Lee Chong-Won , Joh Young-Don
Published: April 2021

Various modal testing methods are proposed for the effective use of complex modal testing for rotating machinery, focusing on excitations and measurements. The proposed methods are developed, based on the input/output relationships for complex signals, for the direct or indirect assessment of frequency response and coherence functions between complex inputs and outputs. The proposed testing methods and the classical modal testing method are compared in consideration of required number of frequency response functions (FRFs) and testing efforts.
Parametric Identification of a Vibratory System With a Clearance
Authors: Alexander Richard M. , Noah Sherif T. , Franck Charles G.
Published: April 2021

An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single degree of freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model.

The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multidegree of freedom systems.
Modeling and Dynamic Analysis of a Slider-Crank Mechanism With Flexible Coupler and Joint
Authors: Lieh Junghsen , Haque Imtiaz
Published: April 2021

Modeling and dynamic analysis of a slider-crank mechanism with flexible joint and coupler is presented. The equations of motion of the mechanism model are formulated using a virtual work multibody formalism and cast in terms of a minimum set of generalized coordinates through a Jacobian matrix expansion. Numerical results show the influence of time-varying coefficients on the mechanism dynamic behavior due to a repeated task. The results illustrate that the joint motion and coupler deformation are highly coupled. The joint response is dominated by double frequency of input, however, the coupler deformation is influenced by the same frequency as that of excitation. Increase in joint stiffness tends to decrease the variations in coupler deformation.
Modal Control by Modal Force Technique
Authors: Tsai C. D. , Ju M. S. , Tsuei Y. G.
Published: April 2021

Modal control of structure requires the estimation of the modal states variables for feedback. One approach that does not require modal states variables estimation is the direct feedback control. Recent developments in modal control for direct feedback are mainly time domain methods. In this paper, an efficient method based on frequency domain approach named Modal Force Technique is developed. The method not only allows one to modify the global dynamic behavior of the synthesized structure but also can be utilized for modal control problem if the acceleration, velocity and displacement feedbacks are used.
Approximate Linear Theories for the Dynamics of Slack Cables Supporting a Discrete Mass
Authors: Cheng S.-P. , Perkins N. C.
Published: April 2021

A continuum model is presented that describes the three-dimensional response of an elastic cable that supports a single attached mass. Two asymptotic forms of this model are analyzed for the free, linear response of slack suspensions having small equilibrium curvature (sag) and level supports. The first model, which is valid for relatively small attached masses, assumes that the cable stretches quasi-statically and results in uniform dynamic cable tension. The quasi-static stretching assumption is partially relaxed in the second model which accounts for spatially varying dynamic tension in an approximate manner. The eigen-solutions associated with free response are compared for the two models. Results indicate that the “small mass model” provides excellent approximations to the natural frequency spectrum and vibration mode shapes for most cables and modes of technical interest. A simple criterion is presented which governs the range of validity of the small mass model.
Modeling and Dynamic Behaviors of a Rotor Suspended in Electromagnetic Bearings
Authors: Xu Jiankang , Xie Youbai , Mao Junhong
Published: April 2021

A closed loop system composed of a rotor in electromagnetic bearings and a PID (proportion-integration-differentiation) controller is developed. With the active electromagnetic forces the rotor 50 millimeters in diameter can be fully suspended in two radial electromagnetic bearings and can be driven from zero up to 3000 rpm. This closed loop system is modeled and its dynamic behaviors are analized by digital simulation. The influence of controller parameters on motion of the rotor and the relation between controller parameters and dynamic stiffness of the electromagnetic bearings are presented.
On the Optimal Correction of Structural Dynamic Models
Authors: Mottershead John E.
Published: April 2021

It is well known that a discrete analytical model cannot accurately represent the dynamics of a continuous physical system over the frequency range of the model. Methods have been presented with the intention of improving analytical models (finite element models in particular) by the use of either (a) measured modal data or (b) measured frequency responses. In this paper we consider in particular the selection of weighting terms and the physical significance of the estimates. In both cases the discussion is illustrated by means of example problems.
An Analysis of Sensitivity of Multidimensional Electromechanical System
Authors: Jasińska-Choromańska Danuta
Published: April 2021

Subject of this paper in connected with problems reffering to analysis of parametrical sensitivity of mathematical model of static properties of complex multidimensional mechanical and electromechanical systems. A full definition of an analysis requires analysis of sensitivity’s invariants and preliminary selection of tolerances of the model. This paper presents application of the above method in order to a mathematical model of an inductive transducer for the measurement of displacements.
Structural Modification Simulation: Sensitivity Analysis and the Reanalysis of Modified Structure
Authors: Li Debao , Li Fangze , Xu Peiming
Published: April 2021

This paper deals with the dynamic modification simulation of the structure. The expressions of sensitivity analysis of the system with non-proportional damping and proportional damping are derived at first. As for the reanalysis of modified structure, here we deal with the system to which the modification do not cause any change of the degrees of freedom. Transfer function analysis method and the method of twice coordinate transformation are expounded. As a successful example, the modification simulation of the frame of a dump truck is explained.
Structure Damage Detection via the Behavior of Substructure
Authors: Wang J. H. , Liou C. S.
Published: April 2021

A mechanical system generally consists of many substructures. However, it is impossible to observe the dynamic behavior of any substructure directly when the whole structure is in operation. A method was proposed in this work to determine the FRFs of a substructure by using the measured FRFs of the whole structure and the priorly known FRFs of another substructure With this method, one can detect the structural damage more easily by observing the change of the FRFs of the damaged substructure.
Recognition of Bearing Faults of the Same Kind
Authors: Bao Ming , Zhao Chun-sheng
Published: April 2021

Condition monitoring has gained much acceptance because of the reduction of maintenance expenses and the increase of rate of equipment utilization. It is very important that the serious degrees of machinery faults is correctly predicted. Two faults in a bearing part is, of course, more serious than the single fault is. If the features of bearing faults of the same kind are not recognized, faults of the same kind are, then, mistaken for a single fault, the serious consequences may be caused. The features of bearing faults of the same kind are presented and the illustrations are given in the paper. Meanwhile, the correct equation of roller’ s fault characteristic frequency is expounded conveniently.
A New Diagnosis Method Based on State Spectrum and its Applications
Authors: Zhao Zhen-Ying , Cha Jian-Zhong , Zhu Meng-Zhou , Tang He
Published: April 2021

Based on the time series, a new concept of spectrum representing the system state, called State Spectrum, is developed through the analysis of the varying principles of self-regression coefficients in this paper. The physical explanation of the spectrum, the meanings of the spectrum’s longitudinal and transverse coordinate and the way to use them in the state recognition and fault diagnosis of mechanical devices have been discussed in details. some experiments have carried out and the results indicate that the proposed new approach is very promising in fault diagnosis of mechanical devices.
The Application of Principal-Component Analysis in Gear Fault Diagnosis
Authors: Zhao Zhen-Ying , Cha Jian-Zhong , Tang He , Zhu Meng-Zhou
Published: April 2021

In this paper, the application of the principal-component analysis method in fault diagnosis is explored. Characterized as fast and precise, this method can be directly used for analyzing gear noise and vibration signals in time domain. The principal component method and its1 error occur-ring in the calculation are theoretically discussed in detail. A program for implementing this method has been developed and the experiments for gear fault diagnosis have been carried out with satisfactory results.
Dynamic Detection of Damage in Structure
Authors: Mao Qinghua , Shen Xiaofeng
Published: April 2021

When a damage exists in a structure, the dynamic characteristics of the structure are changed. A great deal of effort has been elaborated to determine the position and the amount of the damage by using the natural frequencies and the mode shapes. In this paper, a theoretical method is given to detect the damage in a structure based on the changes of its natural frequencies and the mode shapes. After determining the location of the damage, a correcting factor describing a reduction in stiffness of damaged element gives the amount of the damage. This method is proved on two examples of beam structures.
Effect of Operating Speed in Diagnosis of Gear Faults
Authors: Özgüven H. Nevzat , Yalçintaş Melek
Published: April 2021

This paper presents the effect of the operational speed of gears on the vibration signals measured at bearings for gear fault diagnosis purposes.The information available in literature is usually for relatively low speeds of gears. As it is very difficult to study experimentally the vibration of high speed gears with controlled specific gear faults, computer simulation is used in this work. Nonlinear dynamic analysis program developed in an earlier study is used in simulating the dynamic behavior of spur gears with several different gear faults, and an FFT algorithm is used to generate the frequency spectrum of bearing vibrations. Three types of gear faults are discussed in this paper: uniform profile error, eccentricity, and local faults on a single gear tooth. The model used in the analysis is nonlinear and includes several important effects such as variable mesh stiffness, backlash, separation of teeth, shaft and bearing dynamics. Spectra of the bearing vibrations for gears with well known faults are used to verify the computer simulation approach employed. Then the effect of the operating speed of gears on the diagnosis of these faults are studied by obtaining bearing vibration spectra at different gear speeds. It is concluded that some frequendy used and well known diagnostic rules may not apply at high speeds.
Control and Optimization of Structures Using Spectrum Analysis
Authors: Drakatos P. A. , Drakatos S. P.
Published: April 2021

In this paper diagnostic methods are applied is order to study the behaviour of the structure as they are being excited and response to the exciting reasons.

For this purpose, measurements are taken on the field of time and form the, using spectrum analysis., spectra of frequency are taken for studying to the amplitude of the frequencies or to the position of each frequencies or to the position of each frequency of the field of frequencies. It is obvious there is a connection between the condition of stress and strain of the structure between the condition of stress and strain of the. structure and the position and the amplitude of frequencies that are taken form the analysis of the measurements.

So controlling the frequencies for some kind of measurments it is easy to control the condition of the structure.

Otherwise using simulation and optimization methods it is possible first to build a model and after to examine this model for several types of fatigue.

Taking always the spectra of measurements and comparing them by themselves it is possible to find the optimal model and taken to apply the conclusions to the structure.

Finally it could be said that this work can be applied during the stage of design of the structures as it helps by control. The simulating models in order to find the optimal structure.
Optimal Design of Vibration Absorber Systems Supported by Elastic Base
Authors: Ashrafiuon Hashem
Published: April 2021

This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.
Control of Asymmetric Systems Using Complex Modes
Authors: Fan G. W. , Nelson H. D.
Published: April 2021

The complex modal approach is introduced for the optimal vibration control (Linear Quadratic Regulator) of high-order nonsymmetric discrete systems. An LQ regulator is designed based on a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex coordinates are derived. A 52 degree-of-freedom finite element based rotordynamic system is used for illustration. Simulation results show that an LQ regulator based on a reduced-order system obtained by using normal modes of a high-order system with asymmetric models can possibly destabilize the original system i.e., the spill-over problem (Ulsoy, 1984), however, this problem might be avoided by applying complex modes which provides a more accurate reduced-order model than obtained by normal modes. Comparison of the reduced-order models using normal modes and complex modes is presented. Frequency, time transient and steady state responses of the controlled and uncontrolled systems are also shown.
Digital Control Algorithms for Microgravity Isolation Systems
Authors: Sinha A. , Wang Y.-P.
Published: April 2021

New digital control algorithms have been developed to achieve the desired transmissibility function for a microgravity isolation system. Two approaches have been presented for the controller design in the context of a single degree of freedom system for which an electromagnet is used as the actuator. The relative displacement and the absolute acceleration of the mass have been used as feedback signals. The results from numerical studies are presented. It has been found that the resulting transmissibility is quite close to the desired function. Also, the maximum coil currents required by new algorithms are smaller than the maximum current demanded by the previously proposed phase lead/lag method.