Bilinear Systems with Initial Gaps Involving Inelastic Collision: Forced Response Experiments and Simulations

2021 ◽  
pp. 1-29
Author(s):  
Kohei Noguchi ◽  
Akira Saito ◽  
Meng-Hsuan Tien ◽  
Kiran X. D'Souza
Keyword(s):  
Inelastic Collision ◽  
Time Integration ◽  
Excitation Frequency ◽  
Forced Response ◽  
Bilinear Systems ◽  
Accurate Estimation ◽  
Base Excitation ◽  
Time Duration ◽  
Numerical Predictions ◽  
Harmonic Components

Abstract In this paper, the forced response of a two degree of freedom~(DOF) bilinear oscillator with initial gaps involving inelastic collision is discussed. In particular, a focus is placed upon the experimental verification of the generalized bilinear amplitude approximation (BAA) method, which can be used for the accurate estimation of forced responses for bilinear systems with initial gaps.Both experimental and numerical investigations on the system have been carried out. An experimental setup that is capable of representing the dynamics of a two DOF oscillator has been developed, and forced response tests have been conducted under swept-sine base excitation for different initial gap sizes. The steady-state response of the system under base excitation was computed by both traditional time integration and BAA. It is shown that the results of experiments and numerical predictions are in good agreement especially at resonance. However, slight differences in the responses obtained from both numerical methods are observed. It was found that the time duration where the DOFs are in contact with each other predicted by BAA is longer than that predicted by time integration. Spectral analyses have also been conducted on both experimental and numerical results. It was observed that in a frequency range where intermittent contact between the masses occurs, super-harmonic components of the excitation frequency are present in the spectra. Moreover, as the initial gap size increases, the frequency band where the super-harmonic components are observed decreases.

Complex Impact Response of a Beam and Rigid Body Structure to Harmonic Base Excitation

2005 ◽  
Author(s):  
Elizabeth Ervin ◽  
Jonathan Wickert
Keyword(s):  
Rigid Body ◽  
Contact Stiffness ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Forced Response ◽  
The Body ◽  
Body Structure ◽  
Base Excitation ◽  
Response Dynamics ◽  
Contact State

This paper investigates the forced response dynamics of a clamped-clamped beam to which a rigid body is attached, and in the presence of periodic or non-periodic impacts between the body and a comparatively compliant base structure. The assembly is subjected to base excitation at specified frequency and acceleration, and the potentially complex responses that occur are examined analytically. The two sets of natural frequencies and vibration modes of the beam-rigid body structure (in its in- contact state, and in its not-in-contact state), are used to treat the forced response problem through a series of algebraic mappings among those states. A modal analysis based on extended operators for the (continuous) beam and (discrete) rigid body establishes a piecewise linear state-to-state mapping for transition between the in-contact and not-in-contact conditions. The contact force, impulse, and displacement each exhibit complex response characteristics as a function of the excitation frequency. Periodic responses occurring at the excitation frequency, period-doubling bifurcations, grazing impacts, sub-harmonic regions, fractional harmonic resonances, and apparently chaotic responses each occur at various combinations of damping, excitation frequency, and contact stiffness. Parameter studies are discussed for structural asymmetry and eccentricity of contact point’s location.

Modeling and Experimental Validations of a Piezoelectric Energy Harvester Under Combined Galloping and Base Excitations

2014 ◽  
Author(s):  
Amin Bibo ◽  
Abdessattar Abdelkefi ◽  
Mohammed F. Daqaq
Keyword(s):  
Bluff Body ◽  
Energy Harvester ◽  
Constitutive Relations ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Beam Theory ◽  
Excitation Amplitude ◽  
The Body ◽  
Base Excitation ◽  
Piezoelectric Energy

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

Self-powered active control of elastic and aeroelastic oscillations using piezoelectric material

2017 ◽  
Vol 28 (15) ◽  
pp. 2023-2035 ◽  
Author(s):  
Tarcísio Marinelli Pereira Silva ◽  
Carlos De Marqui
Keyword(s):  
Finite Element ◽  
Energy Harvesting ◽  
Vibration Control ◽  
The Self ◽  
Base Excitation ◽  
Sensors And Actuators ◽  
Multilayered Structures ◽  
Numerical Predictions ◽  
Active Vibration ◽  
Self Powered

Piezoelectric materials have been used as sensors and actuators in vibration control problems. Recently, the use of piezoelectric transduction in vibration-based energy harvesting has received great attention. In this article, the self-powered active vibration control of multilayered structures that contain both power generation and actuation capabilities with one piezoceramic layer for scavenging energy and sensing, another one for actuation, and a central substructure is investigated. The piezoaeroelastic finite element modeling is presented as a combination of an electromechanically coupled finite element model and an unsteady aerodynamic model. An electrical circuit that calculates the control signal based on the electrical output of the sensing piezoelectric layer and simultaneously energy harvesting capabilities is presented. The actuation energy is fully supplied by the harvested energy, which also powers active elements of the circuit. First, the numerical predictions for the self-powered active vibration attenuation of an electromechanically coupled beam under harmonic base excitation are experimentally verified. Then, the performance of the self-powered active controller is compared to the performance of a conventional active controller in another base excitation problem. Later, the self-powered active system is employed to damp flutter oscillations of a plate-like wing.

On the Experimental Dynamic Force Performance of a Squeeze Film Damper Supplied Through a Check Valve and Sealed With O-Rings

2021 ◽  
Author(s):  
Luis San Andrés ◽  
Bryan Rodríguez
Keyword(s):  
Dynamic Pressure ◽  
Excitation Frequency ◽  
Check Valve ◽  
Forced Response ◽  
Single Frequency ◽  
Squeeze Film ◽  
Dynamic Force ◽  
Viscous Damping ◽  
Test Rig ◽  
Force Coefficients

Abstract In rotor-bearing systems, squeeze film dampers (SFDs) assist to reduce vibration amplitudes while traversing a critical speed and also offer a means to suppress rotor instabilities. Along with an elastic support element, SFDs are effective means to isolate a rotor from its casing. O-rings (ORs), piston rings (PRs) and side plates as end seals reduce leakage and air ingestion while amplifying the viscous damping in configurations with limited physical space. ORs also add a centering stiffness and damping to a SFD. The paper presents experiments to quantify the dynamic forced response of an O-rings sealed ends SFD (OR-SFD) lubricated with ISO VG2 oil supplied at a low pressure (0.7 bar(g)). The damper is 127 mm in diameter (D), short in axial length L = 0.2D, and the film clearance c = 0.279 mm. The lubricant flows into the film land through a mechanical check valve and exits through a single port. Upstream of the check valve, a large plenum filled with oil serves to attenuate dynamic pressure disturbances. Multiple sets of single-frequency dynamic loads, 10 Hz to 120 Hz, produce circular centered orbits with amplitudes r = 0.1c, 0.15c and 0.2c. The experimental results identify the test rig structure, ORs and SFD force coefficients; namely stiffness (K), mass (M) and viscous damping (C). The ORs coefficients are frequency independent and show a sizeable direct stiffness, KOR ∼ 50% of the test rig structure stiffness, along with a quadrature stiffness, K0∼0.26 KOR, demonstrative of material damping. The lubricated system damping coefficient equals CL = (CSFD + COR); the ORs contributing 10% to the total. The experimental SFD damping and inertia coefficients are large in physical magnitude; CSFD slightly grows with orbit size whereas MSFD is relatively constant. The added mass (MSFD) is approximately four-fold the bearing cartridge mass; hence, the test rig natural frequency drops by ∼50% once lubricated. A computational physics model predicts force coefficients that are just 10% lower than those estimated from experiments. The amplitude of measured dynamic pressures upstream of the plenum increases with excitation frequency. Unsuspectedly, during dynamic load operation, the check valve did allow for lubricant backflow into the plenum. Post-tests verification demonstrates that, under static pressure conditions, the check valve does work since it allows fluid flow in just one direction.

Experimental and Numerical Quantification of the Aerodynamic Damping of a Turbine Blisk

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Christopher E. Meinzer ◽  
Joerg R. Seume
Keyword(s):  
Cfd Simulation ◽  
Excitation Frequency ◽  
Sweep Rate ◽  
Accurate Estimate ◽  
Rotational Frequency ◽  
Forced Response ◽  
Operating Conditions ◽  
Friction Damping ◽  
Aerodynamic Damping ◽  
Turbine Blisk

Abstract Aerodynamic damping is the key parameter to determine the stability of vibrating blade rows in turbomachinery design. Both, the assessments of flutter and forced response vibrations need an accurate estimate of the aerodynamic damping to reduce the risk of high cycle fatigue that may result in blade loss. However, only very few attempts have been made to measure the aerodynamic damping of rotating blade rows experimentally under realistic operating conditions, but always with friction damping being present. This study closes the gap by providing an experiment in which a turbine blisk is used to eliminate friction damping at the blade roots and thereby isolate aerodynamic damping. The blades are excited acoustically and the resulting nodal diameter modes are measured using an optical tip-timing system in order to realize a fully non-intrusive setup. The measured vibration data are fitted to a single degree-of-freedom model (SDOF) to determine the aerodynamic damping. The results are in good accordance with the time-linearized CFD simulation. It is observed, however, that not only the sweep rate of the acoustic excitation but also the variation of the rotational frequency during the sweep excitation, and the excitation frequency influence the apparent damping.

Plain and Full Floating Bearing Simulations With Rigid Shaft Dynamics

2007 ◽  
Author(s):  
Ian McLuckie ◽  
Scott Barrett
Keyword(s):  
System Development ◽  
Equations Of Motion ◽  
Time Integration ◽  
Forced Response ◽  
Design Parameters ◽  
Integration Scheme ◽  
Damping Coefficients ◽  
Time Integration Scheme ◽  
Combined Solution ◽  
Stiffness And Damping

This paper shows a promising predictive bearing model that can be used to reduce turbocharger bearing system development times. Turbocharger development is normally done by varying design parameters such as bearing geometry in a very time consuming experimentation process. Full Floating Bearings (FFB) are used in most automotive turbochargers and, due to emissions regulations, there has been a push towards downsizing engines and applying turbo charging to generate optimized engine solutions for both gasoline and diesel applications. In this paper the turbocharger rotor is regarded as being rigid, and the equations of motion are solved using the Bulirsch Stoer time integration scheme. These equations are solved simultaneously with the bearing model which is used also to determine nonlinear stiffness and damping coefficients. The bearings are solved using a Rigid Hydro Dynamic (RHD) Finite Difference Successive Over Relaxation (SOR) scheme of Reynolds equation that includes both rotational and squeeze velocity terms. However the solver can also consider bearing and rotor elasticity in a Multi-Body Dynamic (MBD) and Elasto-Hydro Dynamic (EHD) combined solution. Two bearing types have been studied, a plain grooved (PGB) and a full floating bearing (FFB) for comparative purposes. The mathematical models used are generic and suitable for whole engine bearing studies. The results in this paper show they are suitable for determining the onset of turbocharger bearing instability, and also the means by which bearing instability may be suppressed. The current study has investigated forced response with the combined effects of gravity and unbalance. It is worth noting that the effects of both housing excitation and aerodynamic excitation from the compressor and turbine can be easily accommodated, and will be the subject of a future paper. Other topics introduced here that will be explored further in the future include the effect of bearing and rotor flexibility in the MBD and EHD solution and the use of automatically generated stiffness and damping coefficients for any bearing geometry.

Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

2020 ◽  
Author(s):  
Akira Saito ◽  
Junta Umemoto ◽  
Kohei Noguchi ◽  
Meng-Hsuan Tien ◽  
Kiran D’Souza
Keyword(s):  
Piecewise Linear ◽  
Excitation Frequency ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Phase Portraits ◽  
Response Analysis ◽  
Experimental Setup ◽  
The Masses ◽  
Two Degree Of Freedom

Abstract In this paper, an experimental forced response analysis for a two degree of freedom piecewise-linear oscillator is discussed. First, a mathematical model of the piecewise linear oscillator is presented. Second, the experimental setup developed for the forced response study is presented. The experimental setup is capable of investigating a two degree of freedom piecewise linear oscillator model. The piecewise linearity is achieved by attaching mechanical stops between two masses that move along common shafts. Forced response tests have been conducted, and the results are presented. Discussion of characteristics of the oscillators are provided based on frequency response, spectrogram, time histories, phase portraits, and Poincaré sections. Period doubling bifurcation has been observed when the excitation frequency changes from a frequency with multiple contacts between the masses to a frequency with single contact between the masses occurs.

Adapting Dynamic Braking of AC Motors to Varying Wheel/Rail Adhesion Condition

2013 ◽  
Author(s):  
Husain Ahmad ◽  
Mehdi Ahmadian
Keyword(s):  
Reference Model ◽  
Excitation Frequency ◽  
Adaptive Controller ◽  
Rolling Stock ◽  
Accurate Estimation ◽  
Model Reference ◽  
Braking Distance ◽  
Estimation And Control ◽  
Dynamic Braking ◽  
Model Reference Adaptive

Model reference adaptive control (MRAC) is developed to control the electrical excitation frequency of AC traction motors under various wheel/rail adhesion conditions during dynamic braking. More accurate estimation and control of train braking distance can allow more efficient braking of rolling stock, as well as spacing trains closer together for Positive Train Control (PTC). In order to minimize the braking distance of a train, dynamic braking forces need to be maximized for varying wheel/rail adhesion. The wheel/rail adhesion coefficient plays an important role in safe train braking. Excessively large dynamic braking can cause wheel lockup that can damage the wheels and rail, or may lead to large coupler forces, possibly causing derailment or broken components. In this study, a multibody formulation of a locomotive and three railcars is used to develop a model reference adaptive controller for adjusting the voltage excitation frequency of an AC motor such that the maximum dynamic braking is achieved, without locking up the wheels. A relationship between creep forces, creepages, and motor braking torque is established. This relationship is used to control the motor excitation frequency in order to closely follow the reference model that aims at achieving maximum allowable adhesion during dynamic braking. The results indicate that MRAC significantly improves braking distance while maintaining better wheel/rail adhesion and coupler dynamics during dynamic braking.

Forced Response of a Squeeze Film Damper and Identification of Force Coefficients From Large Orbital Motions

2004 ◽  
Vol 126 (2) ◽  
pp. 292-300 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar De Santiago
Keyword(s):  
Excitation Frequency ◽  
Air Entrainment ◽  
Forced Response ◽  
Effective Length ◽  
Single Frequency ◽  
Squeeze Film ◽  
Inertia Force ◽  
Damping Force ◽  
Squeeze Film Damper ◽  
Force Coefficients

Experimentally derived damping and inertia force coefficients from a test squeeze film damper for various dynamic load conditions are reported. Shakers exert single frequency loads and induce circular and elliptical orbits of increasing amplitudes. Measurements of the applied loads, bearing displacements and accelerations permit the identification of force coefficients for operation at three whirl frequencies (40, 50, and 60 Hz) and increasing lubricant temperatures. Measurements of film pressures reveal an early onset of air ingestion. Identified damping force coefficients agree well with predictions based on the short length bearing model only if an effective damper length is used. A published two-phase flow model for air entrainment allows the prediction of the effective damper length, and which ranges from 82% to 78% of the damper physical length as the whirl excitation frequency increases. Justifications for the effective length or reduced (flow) viscosity follow from the small through flow rate, not large enough to offset the dynamic volume changes. The measurements and analysis thus show the pervasiveness of air entrainment, whose effect increases with the amplitude and frequency of the dynamic journal motions. Identified inertia coefficients are approximately twice as large as those derived from classical theory.

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