bluuebunny/crossref_metadata_2025 huggingface dataset:
Prediction and Elimination of Subharmonic Resonances in Mechanical Systems With Nonlinear Foundations
Authors: Natslavas Sotirios , Tratskas Petros
Published: March 2021

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.
Beam Networks Analysis by a Power Flow Method
Authors: Ichchou Mohammed Najib , Le Bot Alain , Jezequel Louis
Published: March 2021

The dynamical behaviour of systems in medium and high frequency range has become a subject of increasing interest over the last few years. Recently, an original strategy called Energy Flow Method has been developed to describe the structural/acoustical response in mid frequencies. In this paper, a review of the one dimensional Energy Flow Method is first proposed. An original propagative method based on the reflection and transmission matrix is proposed to study coupled beams with longitudinal and transversal motion. The method is applied to the junction of two beams with an arbitrary angle. The results show the efficiency of such a formulation for the mid frequency analysis of beam networks.
Characteristics of the Nonlinear Hysteresis Loop for Rotor-Bearing Instability
Authors: Guo Jenq-Shan , Adams M. L.
Published: March 2021

The nonlinear hysteresis loop of a journal-bearing supported rotordynamic system is characterized by the Hopf-bifurcation and Saddle-Node speeds. The nonlinearity of this system occurs in the journal-bearing fluid-film forces, and requires the imbedding of a solution for the Reynolds lubrication equation within a numerical integration scheme of the coupled motion equations in order to perform proper simulations. These show that under light bearing static load, the Saddle-Node and Hopf bifurcation coalesce to a single speed at essentially two times the self-excited vibration frequency (i.e., the lowest natural frequency). At higher bearing loads, the classical instability threshold speed (i.e., Hopf bifurcation) occurs at progressively higher rotor speeds. However, the disappearance speed (Saddle Node of the periodic orbit) of the nonlinear limit cycle occurs at progressively lower rotor speeds, asymptotically approaching approximately 1.725 times the lowest natural frequency. By adding a rotor unbalance force to the model, exploratory simulations have been made to determine the extent to which chaos signal processing in the normal speed-up or coast-down vibration of actual machines could be used to locate this lower speed bound of the instability hysteresis loop.
Modal Testing of Rotating Discs Using a Scanning LDV
Authors: Stanbridge Anthony B. , Ewins David J.
Published: March 2021

Modal testing of rotating structures is complicated by difficulty of access and by the fact that, if the source of excitation is fixed in space, responses occur at frequencies other than that of the excitation. This paper demonstrates the use of, and derives output equations for, a Laser Doppler Vibrometer (LDV) for response measurement.

Examples are given of measurements using the LDV beam aimed (i) at a point fixed in space, (ii) at a fixed point on the disc, and (iii) rotating at a non-synchronous speed. The third technique is perhaps the most useful, enabling the circumferential spatial disc response, expressed in terms of travelling waves or orthogonal standing modes, to be directly derived at any speed, frequency or state of disc mistuning.

The same technique, applied to a non-rotating disc, provides a simple qualitative measurement of the mode shape associated with each natural frequency. An example based on a centrifugal impeller is included.
Direct Parameter Estimation of Weak Nonlinear Systems Using Vibration Test Data
Authors: Weiland Matthias , Link Michael
Published: March 2021

A method has been developed for the identification of structural systems which exhibit influences of weak nonlinear stiffness and damping terms. It is based on a linear method for direct identification of incomplete system matrices from vibration test data. The basic identification equations are extended by additional stiffness and damping terms. Their contribution to the overall response is governed by higher powers of the individual response amplitudes. Hence, the method is a linearisation approach to the full nonlinear solution and basically derived from the well known ‘Harmonic Balance’ method which is applied to multi-degree of freedom systems.

The paper presents the basic theory of the method and illustrates its application to several test examples. First simulated test cases with nonlinear stiffness and damping terms are discussed. Then, as a practical application, the results of an automobile motor/gearbox assembly are given.
Variation of Fluid Flow Forces in Seals With Rotor Bending
Authors: Kwanka K.
Published: March 2021

Fluid-induced forces in labyrinth seals can cause unstable self-excited vibrations of the turbomachine rotor. Generally, a linear approach employing dynamic coefficients is used to describe these forces. A new procedure for the identification of the coefficients which uses two excitation sources placed on a flexible rotor is presented. The change in the stability limit and vibrational frequency caused by the investigated labyrinth gas seal contains the dynamic coefficients.

It is important that problems which may also occur in the real turbomachine are considered by the identification procedure. The conservative dynamic coefficients, such as the direct stiffness, influence the bending of the mode shapes and thus affect indirectly the stability limit. The magnitude of the exciting forces depends on the axial positioning of the excitation source and also on the mode shape bending. These two dependencies are investigated by experiment and considered in the identification procedure.
Excitation of Arbitrary Displacement/Velocity Conditions in Rotationally Periodic Structures
Authors: Schmiechen P. , Ewins D. J. , Bucher I.
Published: March 2021

For an investigation into the structural interaction between rotating and non-rotating rotationally periodic turbine components, it was required to be able to generate experimentally prescribed response conditions. In more descriptive terms, conditions were sought to excite wave-patterns such as travelling and standing waves, and to suppress certain modes. In the paper these conditions are derived from modal properties. Simulated data are presented to demonstrate some of the phenomena and to highlight the practical difficulties.

For rotationally periodic structures, most natural frequencies are of multiplicity two, and are sometimes called ‘double modes’. Their associated mode shapes can rotate in the plane of symmetry. The responses due to the two modes can be combined and expressed in a wave form, which can be split into travelling and standing wave components.

Theoretically, it is possible to excite a pure travelling wave in a perfectly rotationally periodic structure, but there are limits to this in practice as real structures will always exhibit some degree of imperfection. These structures are said to be mistuned, and the imperfection splits the double modes into pairs of close modes.

Simulations show the predicted vibration phenomena. In particular, the case of discrete excitations relevant to modal testing is investigated. The simulations show clearly that in this case components of other modes will generally be present.

In an experiment, the results for driving the excitations will not give the theoretically expected response due to non-linearities of the shaker-structure interaction. However, the effects can be reduced by employing a computerised search algorithm.
Three Dimensional Vibration of a Ballooning String
Authors: Hall Kevin J. , Zhu Fang , Rahn Christopher D.
Published: March 2021

In many textile manufacturing processes, yarn is rotated at high speed forming a balloon. In this paper, Hamilton’s principle is used to derive the nonlinear partial differential equations of a ballooning string. Jacobian elliptical sine functions satisfy the nonlinear steady state equations. The steady state eyelet tension is related to the string length for a constant balloon height. For high tension and low string length cases, single loop balloons occur. As the string length increases, tension decreases and multiple loop solutions are obtained. The nonlinear partial differential equations are linearized about the steady state solutions, resulting in three coupled equations with spatially varying coefficients. The equations involve a positive definite mass matrix operator, skew symmetric gyroscopic matrix operator, and symmetric stiffness matrix operator. It is shown using a Galerkin approach that only single loop balloons are stable for practical yarn elasticity. The natural frequencies of the single loop balloon increase with decreasing balloon size and increasing yam stiffness. The effect of yarn elasticity on the first three vibration modes of a single loop balloon is analyzed. The steady state and stability analyses are experimentally verified.
Modeling, Actuation, and Control of an Active Fluid Vibration Isolator
Authors: Panza Michael J. , McGuire Dennis P. , Jones Peter J.
Published: March 2021

An integrated mathematical model for the dynamics, actuation, and control of an active fluid/elastomeric tuned vibration isolator in a two mass system is presented. The derivation is based on the application of physical principles for mechanics, fluid continuity, and electromagnetic circuits. Improvement of the passive isolator performance is obtained with a feedback scheme consisting of a frequency shaped notch compensator in series with integral control of output acceleration and combined with proportional control of the fluid pressure in the isolator. The control is applied via an electromagnetic actuator for excitation of the fluid in the track connecting the two pressure chambers of the isolator. Closed loop system equations are transformed to a nondimensional state space representation and a key dimensionless parameter for isolator-actuator interaction is defined. A numerical example is presented to show the effect of actuator parameter selection on system damping, the performance improvement of the active over the passive isolator, the robustness of the control scheme to parameter variation, and the electrical power requirements for the actuator.
A Variational Formulation, a Work-Energy Relation and Damping Mechanisms of Active Constrained Layer Treatments
Authors: Shen I. Y.
Published: March 2021

The purposes of this paper are to formulate active constrained layer (ACL) damping treatments through a variational approach, to study the work-energy relation of ACL, and to identify the damping mechanisms of ACL treatments. Application of extended Hamilton’s principle to ACL results in the equations of motion of ACL and the charge equation of electrostatics for the piezoelectric constraining layer. The work-energy equation together with the charge equation shows that the power dissipated through the active damping is the product of the electric field and the axial velocity of the piezoelectric constraining layer at the boundaries. This unique feature suggests that a self-sensing and actuating piezoelectric constraining layer may be an appropriate design in dissipating vibration energy without causing instability. To identify the damping mechanisms, a sensitivity analysis shows that the effectiveness of ACL damping primarily depends on the active and passive damping forces transmitted to the vibrating structure through the viscoelastic layer. The active damping force transmitted depends on the controller transfer function as well as a system parameter, termed active damping sensitivity factor, which is determined entirely by the dimensions and material properties of the passive constrained layer. Finally, numerical results on ACL beams are obtained to illustrate the theoretical predictions above.
Energy Flow Control of Interconnected Structures: II — Structural Subsystems
Authors: Kishimoto Yasuo , Bernstein Dennis S. , Hall Steven R.
Published: March 2021

The dissipative energy flow control technique for interconnected modal subsystems developed in a companion paper [1] is now applied to structural subsystems. In this paper two energy flow models for interconnected structures are derived, namely, the modal subsystem model, which views each mode as a subsystem, and the structural subsystem model, which views each substructure as a subsystem. These energy flow models provide alternative foundations for an energy flow control technique. Active feedback controllers based on both of these energy flow models are shown to reduce the vibration of a specified substructure.
Active Mode Localization in Distributed Parameter Systems With Consideration of Limited Actuator Placement
Authors: Shelley Franz J. , Clark William W.
Published: March 2021

The purpose of this work is to investigate the application of active mode localization to discretized models of distributed parameter systems where the number of control sensors and actuators is a limiting factor. A modified eigenvector scaling technique using singular value decomposition is developed which scales the lower-mode eigenvectors, producing localization over the range of these lower natural frequencies. An example using a simply supported beam model is provided, with mode localization achieved in at least the lower 3 modes utilizing as few as two control sensor/actuator pairs.
Finite Element Vibration Analysis of Composite Plates With Embedded Shape Memory Alloy Fibers at Elevated Temperatures
Authors: Zhong Z. W. , Mei Chuh
Published: March 2021

The present paper investigates the vibration behavior of the thermally buckled shape memory alloy (SMA) fiber-reinforced composite plates. The stress-strain relations are developed for a thin composite lamina with embedded SMA fibers. The finite element equation of motion including shape memory effect is presented. This equation can be mathematically separated into a static equation and a dynamic equation. The thermal postbuckling deflection and vibration of the thermally buckled position for SMA fiber-reinforced composite plates are determined. Due to the effects of nonlinear material properties of SMA, the vibration characteristics of thermally buckled composite plate with embedded SMA fibers are distinctly different from the one without SMA. Thermal postbuckling, natural frequencies and vibration modes for SMA reinforced composite rectangular plates are presented. Triangular plates with simply supported and clamped boundary conditions are also studied.
Controlling the Vibration Levels of Vibrating Vanes Using Viscoelastic Materials
Authors: Oyadiji S. O. , Tomlinson G. R.
Published: March 2021

The vibration characteristics of a carbon composite outlet guide vane (CCOGV), whose ends were embedded in a viscoelastic medium, were analysed by means of the finite element method. The elastic CCOGV and the viscoelastic material were modelled using twenty-noded solid brick elements. Both isotropic and orthotropic material models were used to characterise the elastic behaviour of the CCOGV. The Young’s modulus and loss factor data of the viscoelastic material were derived from the master curves of complex Young’s modulus of the material. These master curves were obtained via the application of the direct stiffness and master curve methodologies to a prismatic sample of the viscoelastic material. It is shown that the degree of correlation of the finite element predictions compared to the measured characteristics of the potted CCOGV depends on the accuracy of the elastic material properties of the CCOGV and of the complex modulus of the viscoelastic material.
Interpretation of Active Dampers As Variable-Parameter Passive Devices
Authors: Anderson Eric H.
Published: March 2021

This paper develops analogies between discrete devices that achieve damping by active and passive means. It describes the simplest models useful for inclusion in larger system design. Lumped-parameter models for representing passive dampers are given, and the similarity to local active feedback is shown. A model for active damper components containing piezoelectrics or similar materials is developed for force feedback compensation. This system is similar to the passive damper model when its parameters are allowed to vary. An active damper with direct feedback of the integral of measured force is represented by a model containing a single spring and a gain-dependent dashpot. Further aspects of the active damper are illustrated using a one-mode model of a vibrating structure. The effects of a feedforward modification to the system, and the analogy to changes in passive parameters, are illustrated by tracking the locus of the closed loop system poles with feedback gain.
Dynamic Analysis of the Axially Moving String Based on Wave Propagation
Authors: Ying S. , Tan C. A.
Published: March 2021

This paper presents an exact solution for the transverse response of an axially moving string under general boundary conditions. The response solution is derived in the frequency domain and interpreted in terms of wave propagation functions. The response in the time domain involves only several convolution integrals which can easily be obtained for many physical boundary conditions. The transient response of the translating string with a spring or a dashpot at a boundary is presented.
Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length
Authors: Esmailzadeh Ebrahim , Nakhaie-Jazar Gholamreza , Mehri Bahman
Published: March 2021

The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem.

The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.
Exact Perturbation for the Vibration of Almost Annular or Circular Plates
Authors: Parker R. G. , Mote C. D.
Published: March 2021

Using perturbation analysis, the eigensolutions for plate vibration problems on nearly annular or circular domains are determined. The irregular domain eigensolutions are calculated as perturbations of the corresponding annular or circular domain eigensolutions. These perturbations are determined exactly. The simplicity of these exact solutions allows the perturbation to be carried through third order for distinct unperturbed eigenvalues and through second order for degenerate unperturbed eigenvalues. Furthermore, this simplicity allows the resulting orthonormalized eigenfunctions to be readily incorporated into response, system identification, and control analyses. The clamped, nearly circular plate is studied in detail, and the exact eigensolution perturbations are derived for an arbitrary boundary shape deviation. Rules governing the splitting of degenerate unperturbed eigenvalues at both first and second orders of perturbation are presented. These rules, which apply for arbitrary shape deviation, generalize those obtained in previous works where specific, discrete asymmetries and first order splitting are examined. The eigensolution perturbations and splitting rules reduce to simple, algebraic formulae in the Fourier coefficients of the boundary shape asymmetry. Elliptical plate eigensolutions are calculated and compared to finite element analysis and, for the fundamental eigenvalue, to the exact solution given by Shibaoka (1956).
Distributed Transfer Function Analysis of Ring-Stiffened Cylindrical Shells
Authors: Zhou J. , Yang B.
Published: March 2021

A new analytical and numerical method is presented for modeling and analysis of cylindrical shells stiffened by circumferential rings. This method treats the shell and ring stiffeners as individual structural components, and considers the ring eccentricity with respect to the shell middle surface. Through use of the distributed transfer functions of the structural components, various static and dynamic problems of stiffened shells are systematically formulated. With this transfer function formulation, the static and dynamic response, natural frequencies and mode shapes, and buckling loads of general stiffened cylindrical shells under arbitrary external excitations and boundary conditions can be determined in exact and closed-form. The proposed method is illustrated on a Donnell-Mushtari shell, and compared with finite element method and two other modeling techniques.
On Line Estimation of Stiffness in Nonlinear Beam Models With Piezoceramic Actuators
Authors: Demetriou M. A. , Fitzpatrick B. G.
Published: March 2021

The ability to identify changes in material properties in flexible structures is of great importance in the design of compensators. In this paper we consider an online (adaptive) scheme for estimating stiffness changes of a beam undergoing persistent excitation from piezo-ceramic patches. The nonlinearity involved is a piecewise linear stiffness function meant to provide a simple model of damage. The estimation scheme identifies the time at which the system becomes nonlinear and it provides an estimate of the stiffness function.
Identification of Thermal and Hysteretic Response of SMA Embedded Flexible Rods
Authors: Kurdila Andrew J. , Webb Glenn
Published: March 2021

In this paper, the equations of motion governing the transient response of an elastomer rod with embedded shape memory alloy actuators are derived. The elastomeric flexural dynamics and elastomeric thermal dynamics are represented by a pair of parameter-dependent, coupled, partial differential equations. The response of the structural system exhibits strong hysteresis effects due to the nonlinear nature of the constitutive law of the SMA actuator. As opposed to previous work by the authors in which an explicit equation for the nonlinear constitutive law is utilized, the work herein utilizes an integral operator in a phenomenological representation of the hysteresis. Specifically, a static hysteresis operator is employed to represent the current-to-stress transformation in the SMA. The hysteresis operator consequently appears as a control influence operator in the system of governing partial differential equations. This paper presents a two-stage identification process to characterize the multivalued response associated with hysteresis. Preliminary experimental results validate the effectiveness of the method for the class of problems considered.
Updating of Dynamic Finite Element Models Based on Experimental Receptances and the Reduced Analytical Dynamic Stiffness Matrix
Authors: Lammens Stefan , Brughmans Marc , Leuridan Jan , Heylen Ward , Sas Paul
Published: March 2021

This paper presents a model updating method based on experimental receptances. The presented method minimises the so called ‘indirect receptance difference’. First, the reduced analytical dynamic stiffness matrix is expressed as an approximate, linearised function of the updating parameters. In a numerically stable, iterative procedure, this reduced analytical dynamic stiffness matrix is changed in such a way that the analytical receptances match the experimental receptances at the updating frequencies.

The updating frequencies are a set of selected frequency points in the frequency range of interest. Some considerations about an optimal selection of the updating frequencies are given.

Finally, a mixed static-dynamic reduction scheme is discussed. Dynamic reduction of the analytical dynamic stiffness matrix at each updating frequency is physically exact, but it involves a great computational effort. The presented mixed static-dynamic reduction scheme is a simple strategy to reduce the computational cost with a minor loss of accuracy.
Parallel Interval Algorithm for the Parameter Identification of Linear Elastomechanical Systems
Authors: Oeljeklaus Michael , Natke H. Günther
Published: March 2021

An interval analytical approach to parameter identification in the frequency domain of mathematical models for linear elasto-mechanical systems is described. A priori information, measurement errors and — if possible — unmeasurable degrees of freedom are modelled in terms of intervals. A parallel iterative update method — based on the interval analytical Gauss-Seidel method — is used to reduce the volume of the parameter search space initially given. The search for the global minimum of the WLS objective function using output residuals is performed on the reduced parameter space in a last step1. Subsystem identification and sub-model synthesis are used in the case of realistic models with a large number of degrees of freedom. Parallelization of the algorithm with respect to subsystems is applied in the case of large structures to reduce the amount of memory and to speed-up the computation. Test results for some simulations for a test structure are given in order to illustrate the method.
Efficient Eigenvector Sensitivities by a New Procedure Based Upon Lanczos Vectors
Authors: Ojalvo I. U. , Zhang L.-M.
Published: March 2021

A new Lanczos vector based procedure, for the efficient computation of eigenvector sensitivities to changes in system parameters, is presented in this paper. The method is based upon a matrix reduction which uses the identical Lanczos vectors as those used to obtain the original eigenvectors. Thus, the equation systems solved may be greatly reduced from the original matrix sizes. An explanation regarding why the method is most accurate, for the lowest eigenvectors’ derivatives, is offered. Numerical results for two modest sized examples are supplied, from which trends in the method’s accuracy are suggested.