bluuebunny/crossref_metadata_2025_split huggingface dataset:
Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam
Authors: Dufour Régis , Berlioz Alain , Streule Thomas 
Published: March 2021

Abstract
In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.
Nonlinear Dynamics of a Transversely Excited Flexible Cantilever Beam
Authors: Tabaddor Mahmood , Nayfeh Ali H. 
Published: March 2021

Abstract
Some experimental results concerning the nonlinear dynamics of a transversely excited beam are presented. The excitation is harmonic. A frequency sweep around the fourth natural frequency of the beam reveals some interesting modal interactions. The first phenomenon is the transfer of energy from the fourth mode, approximately 33.10 Hz, to the first mode, approximately 0.70 Hz. This interaction involves modulation of the amplitude and phase of the fourth mode. The second interaction involves the participation of the fourth mode and the second mode, approximately 5.80 Hz. The mechanism by which the second mode is activated as yet remains unidentified.
On the Parametrical Excitation of Nonlinearly Coupled Wave Equations
Authors: van der Burgh A. H. P. , Kuznetsov P. , Vavilov S. A. 
Published: March 2021

Abstract
In this paper a mathematical model for the study of the interaction of longitudinal and transversal vibrations in a stretched string is presented. The study implies an existence theory for time periodic transversal vibrations generated by a horizontal excitation of one of the end-points of the string. The conditions for the existence of this parametrically excited time periodic vibrations are evaluated in a practical application.
The innovative character of the results obtained concern the application of an operator method to a system of nonlinearly coupled wave equations modeling the dynamical behaviour of a strectched string where unite elasticity is taken into account.
It may be known that in the literature little attention has been paid to a rigorous analysis of time periodic solutions for systems of partial differential equations.
Finite Amplitude Dynamics of a Flexible Spinning Disc
Authors: Malhotra N. , Sri Namachchivaya N. , Whalen T. 
Published: March 2021

Abstract
The transverse dynamics of a high speed spinning disc which is clamped at the inner radius and rotating with a time-varying spin rate is examined in a space fixed frame of reference. The general nonlinear equations of motion governing the disc dynamics are systematically derived using displacement as well as stress function formulations. These equations of motion include the effects due to inherent bending rigidity, membrane stresses arising from centrifugal forces, non-axisymmetry of the in-plane and transverse displacements, geometric nonlinearities, aerodynamic damping arising from air stationary and moving with respect to the disc, parametric excitation due to time varying spin rate, etc. For the constant rotation case, the linearized equations of motion are solved by taking both membrane as well as flexural stiffness effects into account. This leads to a power series solution for the radial shape functions and harmonic solutions for the circumferential shape functions. The two-dimensional eigen-functions thus obtained can describe a disc mode with any number of nodal diameters and nodal circles, and the resulting eigen-frequencies match very well with the numerical results. The nonlinear and non-axisymmetric in-plane response is also determined, and a 2-DOF system of ODEs is obtained which governs the dynamic variation of the amplitudes of traveling waves associated with the dominant mode of the transverse motion.
Reduced Boring Bar Vibrations Using Damped Composite Structures
Authors: Trego Angela , Eastman Paul F. , Pratt William F. , Jensen C. G. 
Published: March 2021

Abstract
A new technology, called Stress Coupling Activated Damping (SCAD©), was applied successfully to a lathe boring bar. It reduced high frequency vibrations by up to 20 db. It can be applied to a wide range of structural designs. The geometries of the damped structures are not limited to thin plates but can be applied to tubes, I-beams, and complex structures. This allows SCAD© technology to be applied to several industry design problems, including the metrology, medical, aerospace, automotive and machine tool industries. SCAD© will also allow boring bars to: 1) be optimized for stiffness, frequency and loss factor, 2) be ‘tuned’ to a specific resonant frequency, 3) have improved damping regardless of boring bar diameter, 4) lengthen the usable tool length without a significant increase in cost, and 5) decrease cutting surface vibration induced pattern.
Nonlinear Normal Modes in the Presence of Internal Resonances: An Energy-Based Approach
Authors: King Melvin E. , Vakakis Alexander F. 
Published: March 2021

Abstract
In this work, modifications to existing energy-based nonlinear normal mode (NNM) methodologies are developed in order to investigate internal resonances. A formulation for computing resonant NNMs is developed for discrete, or discretized for continuous systems, sets of weakly nonlinear equations with uncoupled linear terms (i.e systems in modal, or canonical, form). By considering a canonical framework, internal resonance conditions are immediately recognized by identifying commensurable linearized natural frequencies. Additionally, the canonical formulation allows for a single (linearized modal) coordinate to parameterize all other (modal) coordinates during a resonant modal response. Energy-based NNM methodologies are then applied to the canonical equations and asymptotic solutions are sought. In order to account for the resonant modal interactions, it will be shown that high-order terms in the O(1) solutions must be considered. Two applications (‘3:1’ resonances in a two-degree-of-freedom system and ‘3:1’ resonance in a hinged-clamped beam) are then considered by which to demonstrate the application of the resonant NNM methodology. Resonant normal mode solutions are obtained and the stability characteristics of these computed modes are considered. It is shown that for some responses, nonlinear modal relations do not exist in the context of physical coordinates and thus the transformation to canonical coordinates is necessary in order to define appropriate NNM relations.
An Experimental Study of the Forced Response of Pre- and Post-Critical Plates
Authors: Murphy Kevin D. , Virgin Lawrence N. , Rizzi Stephen A. 
Published: March 2021

Abstract
Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-correlation functions, small amplitude vibrations are considered about both the pre- and post-critical states. These techniques are then employed to investigate the snap-through response. The results for snap-through suggest that the motion is temporally complex and a Lyapunov exponent calculation confirms that the motion is chaotic. Finally, a snap-through boundary is mapped in the (ω, SPL) parameter space separating the regions of snap-through and no snap-through.
Random Response to Periodic Excitation With Correlated Disturbances
Authors: Hou Zhikun , Zhou Yunshen , Dimentberg Mikhail F. , Noori Mohammad N. 
Published: March 2021

Abstract
The paper addresses non-Gaussian stationary response of linear single-degree-of-freedom (SDOF) systems subject to a periodic excitation with correlated random amplitude and phase disturbances which are modeled as correlated Gaussian white noise processes. Correlation between amplitude and phase modulation is specified by the cross-correlation coefficient. Numerical results for the second and fourth moment responses are presented. The probability density function of the response is calculated based on the cumulant-neglect closure method. Non-Gaussianity of the response is discussed in terms of the excess factor. The results show that the moment responses generally increase with larger random amplitude disturbance and decrease with larger random phase modulation. The cross-correlation between amplitude and phase disturbances tend to reduce the system moment response. Large relative detuning results in smaller system moment responses. The response may become Gaussian in the sense of up to the fourth moment for sufficiently large relative detuning or random phase disturbances.
Phase-Space Reconstructions of Stick-Slip Systems
Authors: Feeny B. F. , Liang J. W. 
Published: March 2021

Abstract
Nonsmooth processes such as stick-slip may introduce problems with phase-space reconstructions. We examine chaotic single-degree-of-freedom stick-slip friction models and use the method of delays to reconstruct the phase space. We illustrate that this reconstruction process can cause pseudo trajectories to collapse in a way that is unlike, yet related to, the dimensional collapse in the original phase-space. As a result, the reconstructed attractor is not topologically similar to the real attractor. Standard dimensioning tools are applied in effort to recognize this situation. The use of additional observables is examined as a possible remedy for the problem.
Diagnosis of the Joint Backlash of a Mechanism: Wigner-Ville Distribution Combined With Correlation Techniques
Authors: Pan M.-C. , Verbeure B. , Van Brussel H. , Sas P. 
Published: March 2021

Abstract
The aim of this paper is to develop appropriate techniques to detect and classify the joint backlash of a robot by monitoring its vibration response during normal operating conditions. In this investigation, Wigner-Ville distributions combined with two-dimensional correlation techniques have been employed to diagnose various degrees of single-joint backlash. The method also allows to detect and to single out backlash present in two joints of a multi-link mechanism.
In the work reported here, the Wigner-Ville distribution based signal detection and the generalized symmetrical Itakura distance were proposed as tools for pattern differentiation. Initially the proposed methods have been applied to quantify the backlash of a single joint. Consecutively, the detection problem has been generalized to diagnose faults in two joints simultaneously. Due to the extra degree of freedom given by the 2D nature of the WVD’s, certain time-frequency regions were chosen as reference signatures in the case of single-joint backlash, and the signatures, spanning over two impact transients at the reverses of motion, were chosen in the cases of double-joint backlash. The proposed techniques have been successfully implemented on a two-link mechanism.
Finite Element Methods for the Interaction of Acoustic Fluids With Elastic Solids
Authors: Harari Isaac , Blejer Gabriel 
Published: March 2021

Abstract
Computation is essential to the solution of many problems of structural acoustics, particularly when wavelengths are of the same order as characteristic length scales. The development of finite element methods for large-scale computation of solutions to these problems should be preceded by a thorough analytical understanding of their performance in simplified settings in order to validate application to general configurations. Coupling such an analysis with the design of numerical methods that is based on understanding the underlying mathematical framework leads to the development of robust methods in which stability properties are enhanced while maintaining higher-order accuracy.
In this work we develop finite element methods for exterior problems of time-harmonic acoustic-structure interaction. Exterior boundary conditions are derived from an exact relation between the solution and its derivatives on an artificial boundary by the DtN method, yielding an equivalent problem in a bounded region that is suitable for domain-based computation. Solutions to the equivalent problem are unique, precluding singular behavior in finite element models.
Galerkin/least-squares technology is specialized to these problems in order to counter the numerical difficulties that result from employing traditional Galerkin methods. This is achieved by appending terms in least-squares form containing residuals of the Euler-Lagrange equations to the standard Galerkin formulation. The Galerkin/least-squares method is designed to yield dispersion-free finite element solutions to model problems, leading to superior performance on general, multi-dimensional configurations. Two one-dimensional model problems are investigated over a wide range of combinations of material properties of both media. In the first an exterior acoustic problem with impedance boundary conditions is analyzed, in order to study the influence of the elastic body on the acoustic medium. In the second, an elastic rod with an exterior acoustic medium is investigated in order to examine propagation from the solid to the fluid. The resulting method exhibits superior performance for fluid-solid interaction in multi-dimensional configurations. One version of the method offers particularly good representation of interface values.
A Slender-Body Theory in Acoustics
Authors: Van Nhieu Michel Tran 
Published: March 2021

Abstract
A new approach has been proposed to calculate the sound pressure field radiated or scattered from slender bodies. The theoretical analysis is based upon mathematical singular perturbation methods leading to the so-called slender-body approximation. The theory provides a practical method to compute the sound field as it allows a great simplification in the geometrical representation of the body surface and a reduced computation load. This paper summarizes the main results obtained with this approximation at the present state of investigation.
Main Principles of Vibrodamped Structure Scale Models for the Whole Sound Frequency Range
Authors: Ionov Alexei V. 
Published: March 2021

Abstract
At low and middle sound frequencies the physical modelling of vibro-absorbing constructions is interpreted as a reconstruction of a frequency dependence of an imaginary part of a full-scale construction dynamic rigidity which is shifted in frequency according to a scale factor. For the high sound frequency range there is a dimensionless form of a matrix energy equation. It allows the task of physical scale modeling to be formulated as a reconstruction of a vibration energy difference between structure elements excited by an external vibration load and the others its elements as in a full-scale object. The analysis is fulfilled in the specially selected frequency bands when the geometrical similarity between scale and full-scale constructions and a number of demands to their material and the loss factors are observed.
The Use of Radiation Resistance Measurements to Assess the Noise Characteristics of Machines
Authors: Paddock Everett H. , Koopmann Gary H. 
Published: March 2021

Abstract
An experimental method for assessing the noise characteristics of machines is developed. The method is based on a computation of the radiated sound power of a vibrating structure in terms of its acoustic surface radiation resistance and surface volume velocity. To measure acoustic surface radiation resistance, a probe is developed which consists of a low profile loudspeaker and a small microphone, both of which are moveable over the surface of the structure. As an application of the the method, the sound power produced by two valve covers of a 3.3L V6 internal combustion engine, a current production model and the prototype of a new design, is computed and compared. Based on the probe measurements made on a quiescent engine, a surface resistance matrix was generated for the two valve covers. Measurements of the volume velocity of the valve covers were made at two engine operating conditions: 1800 and 5300 RPM. After combining each of the velocity measurements with the resistance matrix, the results indicate that the prototype valve cover radiates significantly less sound power than the production cover at both operating conditions.
Structural Modification Software Development for Design Optimization
Authors: Gu Xiaoye , Flatau Alison B. 
Published: March 2021

Abstract
This paper presents a method for obtaining structural matrices from experimental frequency response function (FRF) data and using these structural matrices to predict the response of the structure to modifications at various locations. The approach taken is designed for subsequent use in optimizing structural modifications to efficiently reduce radiated acoustic power. A series of programs were written for identifying the structural matrices (mass matrices, stiffness matrices and damping matrices) from the measured FRF data. These matrices are used to obtain the modified response of the structure resulting from adding linear springs at different locations on the structure. Experimental results from a beam are presented to verify these programs. Work is in progress on extending this method to incorporate modifications to the structure produced by constrained-layer damping materials.
The programs for obtaining the structural matrices and the structural response are composed of approaches used by several prior authors. Potter and Richardson’s [1,2] method is used for obtaining the relative modal parameters (modal mass, modal stiffness and modal damping). Luk and Mitchell’s [3,4] pseudo-inverse method is employed to obtain the structural matrices for cases when the number of modes measured is much less than the number of test points. A method for deriving the absolute value of modal parameters from the measured FRF data is also developed using modal analysis theory. Linear springs are added at various positions to modify the structure. The structural matrices are used to predict the modified structural responses scaled to displacement per unit force. A series of linear spring modifications are modeled and implemented experimentally to verify these programs.
Physical Properties of Transfer Function Zeros for Collocated Control in Flexible Structure System
Authors: Chung Chingyei , Lin Chin-yuh 
Published: March 2021

Abstract
In this paper, the physical meaning of transfer function zeros for collocated control in a general flexible structure system is discussed. For a flexible structure system, we propose the “Zero Dynamic Theorem”. The theorem states that in a flexible structure system, the flexible structure can be a circulatory system (non-sysmetric stiffness matrix) with viscous and gyroscopic damping (non-symmetric damping matrix), if the sensor output (generalized displacement) and the actuator input (generalized force) are “dual type” and the transfer function is strict proper and coprime (no pole/zero cancellation); then, the transfer function zeros are the natural frequencies of constrained structure. Furthermore, with this theorem, the interlacing pole/zero property for the gyroscopic systems is presented.
Development of an Engine System Model for Predicting Structural Vibration
Authors: Sung S. H. , Nefske D. J. 
Published: March 2021

Abstract
A finite-element based engine system model is developed for predicting the structural vibration of the engine. The engine system model combines modal models of the major bolted-together sub-structures of the engine, with non-structural mass models of the remaining engine components added to bring the inertial properties to those of the running engine. The model is developed and experimentally evaluated with impact and shaker excitation tests. Comparisons are made of the predicted and measured vibration response for various partially assembled engine configurations, as well as for the fully assembled engine. The comparisons illustrate the accuracy of the model in predicting the narrow-band and one-third octave-band vibration response for excitation frequencies up to 2 kHz.
Chaos of a Flexible Rotor in Journal Bearings
Authors: Brown R. D. , Drummond G. 
Published: March 2021

Abstract
Nonlinear systems can give rise to chaotic behaviour, essentially unpredictable. Oil film forces arising from hydrodynamic bearings in rotating machinery can be extremely nonlinear under conditions of large unbalance. Chaotic response has been demonstrated in theoretical models of rigid rotors supported in hydrodynamic bearings.
The behaviour of a rigid rotor can be extended by looking at a flexible rotor model supported on journal bearings and subject to large unbalance levels. The introduction of a flexible shaft yields chaotic regions which are less extensive than those obtained from a rigid rotor model. This is not surprising as the nonlinearity in the model is confined to the oil films at the end of the shaft. However if this level of unbalance is experienced in service then shaft fatigue could occur because of the sustained nature of the non-synchronous response and the effect of the resulting stress reversals.
A New Approach to Machinery Monitoring and Diagnostics Using Self-Organizing Maps
Authors: Zhang Siyu , Ganesan R. , Sankar T. S. 
Published: March 2021

Abstract
The problem of estimating an unknown multivariate function from on-line vibration measurements, for determining the conditions of a machine system and for estimating its service life is considered. This problem is formulated into a multiple-index based trend analysis problem and the corresponding indices for trend analysis are extracted from the on-line vibration data. Selection of these indices is based on the simultaneous consideration of commonly-observed faults or malfunctions in the machine system being monitored. A neural network algorithm that has been developed by the present authors for multiple-index based regression is adapted to perform the trend analysis of a machine system. Applications of this neural network algorithm to the condition monitoring and life estimation of both a bearing system as well as a gearbox are fully demonstrated. The efficiency and computational supremacy of the new algorithm are established through comparing with the performance of Self-Organizing Mapping (SOM) and Constrained Topological Mapping (CTM) algorithms. Further, the usefulness of multiple-index based trend analysis in precisely predicting the condition and service life of a machine system is clearly demonstrated. Using on-line vibration signal to constitute the set of variables for trend analysis, and employing the newly-developed self-organizing neural algorithm for performing the trend analysis, a new approach is developed for machinery monitoring and diagnostics.