bluuebunny/crossref_metadata_2025_split huggingface dataset:
Vibration of Euler-Bernoulli Beams With Arbitrary Boundaries and Intermediate Constraints
Authors: Yong Yan 
Published: April 2021

Abstract
It is an easy task to obtain the analytical solution for a simple Euler-Bernoulli beam. Difficulties, however, do arise when a beam structure has a large number of different-type intermediate constraints, such as exterior simple supports, interior hinges, rollers and other elastic supports. The purpose of this paper is to develop a systematic approach to obtain exact solutions for any kinds of complex beam configurations. The main feature of this approach is that the vibration motion is treated as the result of wave scattering around different media. The discovery of wave scattering phenomena around intermediate constraints sheds the light, for the first time, on the fact that any constraint can serve as a waveguide capable of transmitting and reflecting waves in either directions. This new finding enables us to treat a complex beam structure as a stepped beam which can be handled easily by using the wave propagation approach, previously developed by Yong and Lin (1989) for the analysis of piece-wise periodic structures.
Vibration of a Spinnng Annular Disk With Coupled Rigid Body Motion
Authors: Yang Shih-Ming 
Published: April 2021

Abstract
The vibration of a spinning annular disk with coupled translational and rotational rigid body motion is analyzed. The spinning disk, with one linear spring as transverse load, is free to translate and rotate relative to the shaft axis. The governing equation includes the rigid body translation, rigid body rotation, and flexible disk vibration. Coupling effect between rigid body motion and each annular disk vibration modes is identified. Because of the coupling effects, stable operation of the spinning disk beyond divergence (critical speed) is achieved, the disk loses its stability to flutter. This stability prediction is different from that of a spinning disk without rigid body motion where the disk is unstable at and right after divergence.
Parametric Excitation Under Multiple Excitation Parameters: Asymmetric Plates Under a Rotating Spring
Authors: Shen I. Y. , Mote C. D. 
Published: April 2021

Abstract
A perturbation method is developed to predict stability of parametrically excited dynamic systems containing multiple perturbation parameters. This method, based on the Floquet theorem and the method of successive approximations, results in a nonlinear matrix eigenvalue problem whose eigenvalues are used to predict the system stability. The method is applied to a classical circular plate, containing elastic or viscoelastic inclusions, excited by a linear transverse spring rotating at constant speed. Primary and secondary resonances are predicted. The transition to instability predicted by the perturbation analysis agrees with predictions obtained by numerical integration of the equations of motion.
Coupling Loss Factors and Coupling Damping for Flanged Cylindrical Shells
Authors: Keswick P. R. , Norton M. P. 
Published: April 2021

Abstract
This paper reports on an investigation into an experimental and theoretical evaluation of coupling loss factors and the experimental evaluation of coupling damping for statistical energy analysis of flanged cylindrical shells. It includes the following.
1. An evaluation of the power injection method and the steady state energy method for determining the coupling loss factors of conservative and non-conservatively coupled cylindrical shells. The investigation also establishes if it is necessary to use post processing or additional damping to the subsystems to obtain meaningful loss and coupling loss factors from the power injection method.
2. Establishment of a procedure for measuring coupling damping using the in-situ loss factors measured from the power injection method for non-conservatively coupled systems. The coupling damping estimates are measured for the same non-conservatively coupled cylindrical shell as used for the coupling loss factor experiments.
3. Usage of an elastic wave propagation analysis to obtain theoretical estimates of the coupling loss factors for cylindrical shells connected by a solid flange joint using the Fliigge stress equations for cylindrical shells. The flange joint arrangement is modelled as a ring connecting the two shell halves, where the Love equations are used to develop the in-plane and out-of-plane ring forces and moment. The coupling loss factor is calculated from the power transmitted across the joint and from the stored energy on the incident side.
An Approach to the Vibration Analysis of Confocal Elliptic Annular Plates
Authors: Huang Shyh-Chin , Wang Jaw-Lin 
Published: April 2021

Abstract
An approach is presented for the vibration analysis of annular, confocal, elliptic plate. The approach employs the separation of variables, finite difference, and receptance concept. This method is then expanded to square plate with center crack, or with more complex geometries. The basic idea of this paper is: split the plate into several strips and get the strips’ characteristic values, then compose these strips by the receptance method to get the characteristics value of the plate. Numerical results for certain cases are compared to known data, and precise agreement is met.
Dynamic Continuum Models of Large Platelike Lattice Structures
Authors: Lee Usik 
Published: April 2021

Abstract
A rational and straightforward method is introduced for developing continuum models of large platelike periodic lattice structures based on energy equivalence. The procedure for developing continuum plate models involves the use of existing well-defined finite element matrices for the easy calculation of strain and kinetic energies of a repeating cell, from which the reduced stiffness and mass matrices are obtained in terms of continuum degrees-of-freedom defined in this paper. The equivalent continuum plate properties are obtained from the direct comparison of the reduced matrices for continuum plate with those for lattice plate. Free vibration analyses for the continuum and lattice plates are conducted to evaluate the continuum method proposed in this paper. Numerical results show that the present continuum method gives very reliable structural and dynamic properties compared to other well-recognized methods.
Frequency Spectra of Laminated Piezoelectric Cylinders
Authors: Siao J. C.-T. , Dong S. B. , Song J. 
Published: April 2021

Abstract
A method is given for determining the entire frequency spectra of a cylinder with cylindrical piezoelectric properties for both propagating modes and edge vibrations. Finite element modeling occurs in the radial direction so that layered profiles can be accommodated. In the vector of displacements and electric potential q(r)exp{iξz + nθ + ωt)}, quadratic polynomials are taken for q(r). Two algebraic eigenvalue problems can be deduced from this finite element formulation depending on whether the axial wave number ξ or the frequency ω acts as the eigenvalue. When real wave number ξ are assigned, an eigenvalue problem results for the natural frequency ω. When ω is assigned, then an eigenvalue problem for ξ emerges, where the values for ξ may be real (for propagating waves) or complex conjugate pairs (for edge vibrations in a semi-infinitely long cylinder). Two examples are given to illustrate the method of analysis, viz., a solid piezoelectric cylinder of PZT-4 ceramic material and a two-layer cylinder of PZT-4 covering an isotropic material.
A 3-D Laminated Plate Theory and Nonlinear Impact Modal Analysis
Authors: Chao C. C. , Tung T. P. , Sheu C. C. , Chern H. J. 
Published: April 2021

Abstract
A three-dimensional theory of cross-ply laminated thick plates is developed via an elasticity approach for nonlinear impact modal analysis. The simply supported plate is strictly stress free over all four edges and both lateral surfaces, in addition to stress-loading equilibrium over the patch loading area. The 3-D dynamic displacement fields are expressed in a mixed mode of double Fourier series and cubic polynomials. A system of modified Lagrange’s equations is derived incorporating all surface conditions and interface displacement and stress continuities. Validity of the present 3-D theory is proved in comparison to the only existing exact solutions in the basic cases of statics and free vibration. The nonlinear impact modal analysis is performed using the Hertz contact law in patch loading and Green’s function for small time linearization. The 3-D displacements and stresses are found to predict a tensile crack at the unimpacted side and probably, a delamination at the interface. They are always unsymmetric with respect to the mid-plane in all cases of unidirectional, symmetric and antisymmetric cross-ply laminates due to the one-sided loading.
Operation of a Torsionally-Loaded, Composite Shaft Above Two Flexural Critical Speeds
Authors: Frederick Jeffrey R. , Darlow Mark S. 
Published: April 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Non-Linear Modal Interaction in a Clamped-Clamped Beam: Part I — Deterministic Approach
Authors: Ibrahim R. A. , Afaneh A. , Lee B. 
Published: April 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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.