bluuebunny/crossref_metadata_2025_split huggingface dataset:
Vibration, Buckling and Dynamic Stability of a Non-Uniform Cantilever Plate With Thermal Gradient Resting on a Pasternak Foundation
Authors: Takahashi Kazuo , Furutani Hisaaki 
Published: March 2021

Abstract
The dynamic stability of a non-uniform rectangular cantilever plate on a Pasternak foundation under the action of a pulsating inplane load is reported in this paper. The small deflection theory of the thin plate is used Hamilton’s principle is used to derive the time variables while the dynamic stability is solved by the harmonic balance method.
Natural frequencies and buckling properties are presented at first. Then, regions of instability which contain simple parametric resonances and combination resonances are discussed for various parameters of a Pasternak foundation, non-uniform cross section and thermal gradient.
Prediction and Elimination of Subharmonic Resonances in Mechanical Systems With Nonlinear Foundations
Authors: Natslavas Sotirios , Tratskas Petros 
Published: March 2021

Abstract
In the first part of this work an analysis is presented on the dynamics of a two degree of freedom nonlinear mechanical oscillator. The model consists of a rigid body which rests on a foundation with nonlinear stiffness. This body can exhibit both vertical and rocking motions, which are coupled through the nonlinearities only. In the present study, attention is focused on the response of the system under external harmonic excitation of the vertical translation only, leading to conditions of subharmonic resonance of order three. Also, the model parameters are chosen so that its two linear natural frequencies are almost identical (1:1 internal resonance). For this case, the method of multiple time scales is first applied and a set of four coupled odes is derived, governing the amplitudes and phases of approximate motions of the system. Then, determination of approximate periodic steady state response of the oscillator is reduced to solving a set of four nonlinear algebraic equations. It is shown that besides linear and nonlinear single-mode response, two-mode response is also possible, due to the internal resonance. In addition, the stability of the various single- and two-mode periodic responses of the system is analyzed. In the last part of the work, the analytical findings are verified and complemented by numerical results. The main interest lies on identifying the effect of system parameters on the existence and stability of the predicted motions. The results of this study reveal patterns of appearance of these motions, which provide valuable help in the efforts to eliminate them. Finally, direct integration of the original equations of motion reveals the existence of other more complex motions, which coexist with the analytically predicted motions within the frequency ranges of interest.
Nonresonant Modal Interactions
Authors: Feng Zaichun 
Published: March 2021

Abstract
Modal interactions in nonlinear systems provide a means by which energy can be transferred between modes. This energy interchange may give rise to chaotic motions in dynamical systems. Extensive research has been focused on the resonant modal interactions when the frequencies of the interacting modes are commensurate such as one-to-one and one-to-two resonances. It is recently realized that modal interactions can also occur even if the frequencies of the interacting modes are non-commensurate. In this work, mechanism for these nonresonant modal interactions is identified and illustrated through a simple mechanical system.
Nonlinear Combination Resonances in Cantilever Composite Plates
Authors: Oh Kyoyul , Nayfeh Ali H. 
Published: March 2021

Abstract
We experimentally investigated nonlinear combination resonances in a graphite-epoxy cantilever plate having the configuration (–75/75/75/ – 75/75/ – 75)s. As a first step, we compared the natural frequencies and mode shapes obtained from the finite-element and experimental modal analyses. The largest difference in the obtained frequencies was 2.6%. Then, we transversely excited the plate and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance Ω≈12(ω2+ω5) and the internal combination resonance Ω≈ω8≈12(ω2+ω13), where the ωi are the natural frequencies of the plate and Ω is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.
Stability of Sliding in a System Excited by a Rough Moving Surface
Authors: Berger Edward J. , Krousgrill Charles M. , Sadeghi Farshid 
Published: March 2021

Abstract
A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.
Stabilization of Periodic Flap-Lag Dynamics in Rotor Blades
Authors: Schmitt John M. , Bayly Philip V. , Peters David A. 
Published: March 2021

Abstract
A method to increase the stability of periodic flap-lag dynamics in helicopter rotor blades is investigated. Instability in the flap-lag dynamics of stiff-in-plane rotors can occur as forward flight speed is increased, or if significant pitch-lag coupling is present. A method originally developed to control chaos can be applied to stabilize unstable or weakly stable periodic behavior. Stabilization is achieved using small perturbations of the mean blade pitch angle. The approach, which will be referred to as periodic active control (PAC), consists of applying discrete control to the Poincaré map associated with the nonlinear dynamical system. Control effort is applied efficiently, since it does not change, but only stabilizes underlying periodic motion. Stabilization can lead to higher safe speeds, decreased transient effects, and simplified designs in helicopters.
Slow Escapes From Resonance
Authors: Quinn D. Dane 
Published: March 2021

Abstract
We study a Hamiltonian system of coupled oscillators that approximate two forced pendulums, connected with a torsional spring. The uncoupled limit is described by two identical oscillators, each possessing a homoclinic trajectory separating bounded from unbounded motion. Unlike previous work by Rand and Quinn on a dissipative system of coupled homoclinic oscillators [11], the coupling preserves the Hamiltonian structure of this system. However, integrability is destroyed and we resort to analytic and numerical techniques to describe the motion of the system.
We focus on intermediate energy levels which lead to detained motions, defined as trajectories that, though unbounded, oscillate within the region defined by the homoclinic orbit of the unperturbed system for a long but finite time. These detained motions coexist with truly bounded trajectories that are contained within isolating first integrals.
We analyze the existence and behavior of these motions in terms of equipotential surfaces. These curves represent bounds on the motion of the system and are shown to be closed for low energies. However, above some critical energy level the equipotential curves become open. The detained trajectories are shown to be a result of these open curves and the stochasticity of near-integrable Hamiltonian systems.
A Quasiperiodic Mathieu Equation
Authors: Rand Richard , Hastings Rachel 
Published: March 2021

Abstract
In this work we investigate the following quasiperiodic Mathieu equation:
x ¨ + ( δ + ϵ cos ⁡ t + ϵ cos ⁡ ω t ) x = 0
We use numerical integration to determine regions of stability in the δ–ω plane for fixed ϵ. Graphs of these stability regions are presented, based on extensive computation. In addition, we use perturbations to obtain approximations for the stability regions near δ=14 for small ω, and we compare the results with those of direct numerical integration.
Decoupling the Free Axial-Transverse Motions of a Nonlinear Plate: An Invariant Manifold Approach
Authors: Georgiou Ioannis T. , Schwartz Ira B. 
Published: March 2021

Abstract
We approximate the nonlinearly coupled transverse-axial motions of an isotropic elastic plate with three nonlinearly coupled fundamental oscillators, and show that transverse motions can be decoupled from in-plane motions. We demonstrate this decoupling by showing analytically and numerically the existence of a global two-dimensional nonlinear invariant manifold. The invariant manifold carries a continuum of slow, periodic motions. In particular, for any motion on the slow invariant manifold, the transverse oscillator executes a periodic motion and it slaves the in-plane oscillators into periodic motions of half its period. The spectrum of the in-plane slaved motions consists of two distinct harmonics with frequencies twice and quadruple than that of the dominant harmonic of the transverse motion. Furthermore, as the energy level of motion on the slow manifold increases the frequency of the largest harmonic of the in-plane motions approaches the in-plane natural frequencies. This causes the in-plane oscillators to oscillate in pure compression.
Non-Linear Ship Rolling in Random Seas by the Statistical Non-Linearization Technique
Authors: To C. W. S. 
Published: March 2021

Abstract
The study of motion of ships or similar slender offshore structures in irregular seas has, in recent years, gathered sufficient interest due to the fact that experimental data and various approximate techniques are readily available, and that ship safety is a much more expensive issue. Central to the study is the problem of predicting ship rolling motion due to random waves.
In this paper a method, employing the statistical non-linearization technique that was developed by the author, is applied to evaluate the joint stationary probability density of response of a model proposed by Roberts and associates for the analysis of nonlinear ship rolling in random seas. For small nonlinear damping and small intensity of excitation the result is identical to that obtained with the generalized stochastic averaging method of energy envelope presented earlier by the author.
Monte Carlo Verification of Multivariate Delta Method Variance Estimation of Harmonic Dynamic Response Coefficients
Authors: Montgomery David E. , Lindholm Brian E. , West Robert L. 
Published: March 2021

Abstract
Time series response data from harmonic tests can be resolved into real and imaginary components. In comparing two signals, one phased relative to the other, the real and imaginary model coefficients of the relative signal represent components that are in phase with the reference signal and 90° out-of-phase, respectively. Obtaining these real and imaginary components is a well understood process. However, determining the quality of the component estimates requires the use of a statistical technique known at the multiple multivariate delta method. In this paper, the delta method is described in the context of estimating real and imaginary components to response signals. This development includes a brief review of the multiple linear regression techniques used to analyze the excitation and response signals individually. Additionally, the delta method is verified by comparing estimated variances with variances obtained in a Monte Carlo simulation. The results of this analysis can be applied to experimental structural dynamics modeling and to the problem of updating finite element models. In both of these cases, use of the delta method provides statistically optimal weightings to the least-squares formulations used in these modeling techniques.
Multi-Objecitve Control of Dynamical Systems
Authors: Voulgaris Petros 
Published: March 2021

Abstract
In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.
Complex Eigenvalue Analysis Applied to an Aircraft Brake Vibration Problem
Authors: Feld Denis J. , Fehr Dana J. 
Published: March 2021

Abstract
A conventional finite element model of an aircraft wheel and brake is extended to include forces responsible for friction-induced noise. Responses of aircraft brake vibration modes change the normal force across the brake friction interfaces, and consequently the friction forces. The resulting friction force variations are assembled in the form of a supplemental stiffness matrix and added to the finite element model. Complex eigenvalue analysis that includes the friction force variations provides frequency and mode shape information, as well as an assessment of the predicted mode stability. A predicted unstable vibration mode compares very well to operating mode shape data determined from instrumented tests. Hardware modifications to reduce a brake noise in an aircraft cabin were based on beneficial trends found from exercising the model. Implementation of the hardware modifications on the aircraft successfully suppressed the noise.
Realistic Evaluation of Airplane Brake Vibration by Laboratory Test and Analysis
Authors: Black Raymond J. 
Published: March 2021

Abstract
An important part of the design of airplane brakes is the laboratory verification of their capability to absorb the kinetic energy of the airplane under various operating conditions ranging from normal service energy levels to the very high energy of a rejected takeoff (RTO). These “stops”, as dynamometer brake applications are called, must demonstrate acceptable temperature levels for the wheel and tire, the ability of the brake to carry out numerous taxi and service type stops without any servicing, and acceptable wear rates for the friction material so as to make the brake economically feasible for use by the airlines.
These laboratory tests are typically carried out on an adjustable inertia roadwheel dynamometer. The wheel and tire are “landed” against the flywheel of the dynamometer until the correct radial load is developed on the tire. The brakes are then applied to decelerate the dynamometer to a low taxi speed or stop it completely. With such a system various spectrums of landing and multiple taxi stops can be programmed to yield a simulation of actual airplane operation.
An attempt has been made to extend this type of dynamometer testing to examine the vibrational characteristics of the brake as part of the total landing gear system, in addition to its performance as an energy absorber. Since these total-system vibrations can be destructive to both the brake and the landing gear structure, this type of vibrational evaluation is as important as the energy evaluation of the brake.
For many transport aircraft, particularly those with four or more wheels per landing gear, it is impossible to incorporate the entire landing gear into the dynamometer testing. The nature of the testing extension has therefore been to simulate the behavior of the gear with simpler devices called simulators.
In order to duplicate as nearly as possible the vibrational characteristics that will be experienced on the airplane, various types of landing gear simulators have been used in conjunction with dynamometer testing. This paper discusses the pros and cons of landing gear simulators and a proposed approach that would utilize the simulator in a program to more accurately predict actual airplane landing gear vibrational characteristics.
Monitoring Offshore Pipelines Using Forced Transverse Vibration: Data Analysis
Authors: Hunt Hugh E. M. 
Published: March 2021

Abstract
Vibration methods are used to identify faults, such as spanning and loss of cover, in long off-shore pipelines. A pipeline ‘pig’, propelled by fluid flow, generates transverse vibration in the pipeline and the measured vibration amplitude reflects the nature of the support condition. Large quantities of vibration data are collected and analysed by Fourier and wavelet methods.
A Tutorial on Soize’s Method for Stochastic Modeling in Structural Acoustics (Fuzzy Structures Analysis)
Authors: Ruckman Christopher E. , Feit David 
Published: March 2021

Abstract
Fuzzy structures analysis (FSA) is a stochastic approach for vibro-acoustic modeling of structures whose details cannot be modeled precisely. Pioneered by C. Soize, FSA provides a new tool that may lead to more realistic models of damping mechanisms in complex structures. This paper summarizes Soize’s method in simplified form, emphasizing the solution and post-processing procedures needed to implement FSA in computer programs. Input data needed for implementing FSA with a numerical method such as finite-element analysis are summarized. Stochastic modeling of fuzzy structures is outlined, with Newmann series expressions truncated explicitly after the second-order term. Selected post-processing formulas are given for first-order and second-order solutions.
Active Cancellation of Sound in a Submerged Pipe
Authors: Ng Kam W. 
Published: March 2021

Abstract
Active noise control (ANC) technique was demonstrated to reduce fluidborne noise in a submerged pipe. Specifically, the technique was applied to the flow-induced noise caused by a confined jet under both steady-state and transient conditions. A hybrid controller, which combined both feedforward and feedbackward control, was used to speed up the response of the ANC system. A preliminary test was conducted in air to test the hybrid controller with simulated confined jet. A 10-dB reduction was observed for broadband jet noise. To quantify the noise reduction potential of the ANC system in water, a two-phase test program was demonstrated. Phase 1 testing focused on the design and development of the controller and optimized the overall ANC system performance; the test was conducted in an acoustic tank. Phase 2, the actual test and evaluation of the ANC system for the submerged pipe with confined jet noise, was conducted in a lake with underwater acoustic measurement capability. Nearfield and farfield noise measurements, including directivity patterns, were obtained for a confined jet with and without active control. Without active control, the submerged pipe directivity depicted a two-lobe pattern similar to a dipole source. With active control, a 10-dB noise reduction was observed in the pipe downstream direction, whereas in the upstream direction the noise level remained the same.
Optimal Design of Acoustical Foam Treatments
Authors: Kang Yeon June , Bolton J. Stuart 
Published: March 2021

Abstract
A finite element model for elastic porous materials is presented that allows for interfaces with adjacent acoustical media that are arbitrarily oriented with respect to the global coordinate system. The foam finite element is based on a complete elastic porous material theory that can account for all the three wave types known to be significant in foams. Example problems are used to illustrate the application of foam finite elements to the optimal design of a foam wedge terminating a waveguide. The wedge angle is used as a design parameter (while the wedge volume is held constant) and the performance measure is the frequency-averaged absorption coefficient.
Analytical, Numerical and Experimental Study of the Vibro-Acoustic Behaviour of a Stiffened Shell Structure
Authors: Charron François , Panneton Raymond , Champoux Yvan , Guérin J.-M. , Boily Sylvain 
Published: March 2021

Abstract
The main objectives of this study are a better understanding of the vibro-acoustic behaviour of an airplane fuselage type structure including stiffeners and a better comprehension of the measuring techniques and the modelization approaches for this type of problem. In order to meet the above objectives, three different models were developed. The first one is an experimental model where the measured accelerations and acoustic pressures are used as a reference for the validation of predicted results. The second model is based on a semi-analytical approach. This model is derived from variational and integral approaches and solved, approximately using a Rayleigh-Ritz method. Finally, the last model is based on the finite element method. Several iterations have been necessary before reaching an excellent agreement between all three approaches, especially regarding acoustic responses. From the initial correlation between the measured and predicted results, two major problems were identified. The first one is related to convergence problem associated with the semi-analytical model when stiffeners are incorporated in the model. The second problem is associated with the proper definition of the fluid-structure intermodal coupling in the numerical and analytical approaches. This paper will present the various approaches and models. Furthermore, the investigation on the previous problems will be discussed in detail. In conclusion, new modelization limitations were identified and new modelization criteria for the intermodal coupling were developed from the present study. These results will be used for an in-depth study on the vibro-acoustic behaviour of 1/3 scale model of airplane fuselage.
Acoustic Control of Disk Drives
Authors: Chin Raymond , Wong Donald , Kumano Akihiko 
Published: March 2021

Abstract
In the present effort, a series of experimental investigations was conducted to ascertain noise generation mechanisms involved in 3.5 inch and 5.25 inch disk drives with the ultimate objective to improve the acoustic performance. The acoustic performance of selected samples was characterized in terms of sound pressure and power in a frequency range of up to 8 KHz. The acoustic and structural response of the disk drive were examined using an impact hammer and sinusoidal excitation at the spindle motor. In addition, motor torque characteristics data was collected. A sound intensity measurement technique was employed for the delineation of the acoustic directionality. Two major contributors were identified through the acoustic characterization measurement: (1) broad band noise and (2) prominent discrete tone (PDT). It was shown that the major feature extant in the disk drive acoustic frequency spectrum can be reconstructed from the data obtained from sinusoidal excitation and acoustic response data. Based on the data collected, a series of modifications were evaluated including changes to the spindle motor design, application of dampers, and introduction of vibration isolators. These modifications yielded an acoustic level reduction of 3 to 5dB. Additionally, the parts, process, and operating condition tolerances were found to have a measurable effect on the acoustic performance of disk drive.