Experimental study of impact oscillator with one-sided elastic constraint

2007 ◽  
Vol 366 (1866) ◽  
pp. 679-705 ◽  
Author(s):  
James Ing ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch ◽  
Soumitro Banerjee
Keyword(s):  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Experimental Investigations ◽  
Coexisting Attractors ◽  
Impact Oscillator ◽  
Good Correspondence ◽  
Experimental Procedure ◽  
Acceleration Signal ◽  
The Stability ◽  
Elastic Constraint

In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

COMPLEX DYNAMICS OF BILINEAR OSCILLATOR CLOSE TO GRAZING

2010 ◽  
Vol 20 (11) ◽  
pp. 3801-3817 ◽  
Author(s):  
EKATERINA PAVLOVSKAIA ◽  
JAMES ING ◽  
MARIAN WIERCIGROCH ◽  
SOUMITRO BANERJEE
Keyword(s):  
Complex Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Basins Of Attraction ◽  
Experimental Investigations ◽  
Unstable Periodic Orbits ◽  
Chaotic Oscillations ◽  
Impact Oscillator ◽  
Parameter Values ◽  
Elastic Constraint

In this work the strange behavior of an impact oscillator with a one-sided elastic constraint discovered experimentally is compared with the predictions obtained using its mathematical model. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University reveal different bifurcation scenarios under varying excitation frequency near grazing which were recorded for a number of values of the excitation amplitude. In the paper, particular attention is paid to the chaotic oscillations recorded near grazing frequency when a nonimpacting orbit becomes an impacting one under increasing excitation frequency. It was found that the evolution of the attractor is governed by a complex interplay between smooth and nonsmooth bifurcations, and the interactions between a number of coexisting orbits. The occurrence of coexisting attractors is manifested in the experimental results through discontinuous transitions from one orbit to another via boundary crisis. In some cases, the basins of attraction have a fractal structure. Detailed numerical exploration also revealed coexisting unstable periodic orbits. These stable and unstable coexisting orbits are often born far from the parameter values at which they influence the system dynamics. The very rich dynamics of the bilinear oscillator close to grazing is demonstrated and typical mechanisms of the attractors' appearance and disappearance are explained using stability analysis.

Experimental Investigations Into Nonlinear Vibro-Acoustics for Detection of Delaminations in a Composite Laminate

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Ashish Kumar Singh ◽  
Vincent B. C. Tan ◽  
Tong Earn Tay ◽  
Heow Pueh Lee
Keyword(s):  
Frequency Dependence ◽  
Composite Laminate ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Experimental Investigations ◽  
Frequency Sweep ◽  
Ultrasonic Methods ◽  
Acoustic Methods ◽  
Different Depths ◽  
Excitation Frequencies

In recent years, nonlinear vibro-acoustic methods have shown potential to identify defects which are difficult to detect using linear ultrasonic methods. However, these methods come with their own challenges such as frequency dependence, requirement for a high excitation amplitude, and difficulties in distinguishing nonlinearity from defect with nonlinearity from other sources to name a few. This paper aims to study the dependence of nonlinear vibro-acoustic methods for detection of delaminations inside a composite laminate, on the excitation methods and excitation frequencies. It is shown that nonlinear vibro-acoustic methods are highly frequency dependent and commonly used excitation signals which utilize particular values of excitation frequencies might not always lead to a clear distinction between intact and delaminated regions of the specimen. To overcome the frequency dependence, signals based on frequency sweep are used. Interpretation of output response to sweep signals to identify damage is demonstrated using an earlier available approach, and a simpler approach is proposed. It is demonstrated that the damage detection with sweep signal excitations is relatively less dependent on excitation frequency than the conventional excitation methods. The proposed interpretation technique is then applied to specimens with delamination of varying sizes and with delaminations at different depths inside the laminate to demonstrate its effectiveness.

Stochastic Stability of a Universal-Joint Driven Torsional System

1999 ◽  
Author(s):  
S. F. Asokanthan ◽  
Xiao-Hui Wang
Keyword(s):  
Lyapunov Exponent ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Angular Speed ◽  
Analytical Models ◽  
Largest Lyapunov Exponent ◽  
Deterministic Case ◽  
Speed Fluctuation ◽  
The Difference ◽  
The Stability

Abstract Torsional instabilities in a two-degree-of-freedom system driven by a Hooke’s joint due to random input angular speed fluctuation are investigated. Linearised analytical models are used for calculating the largest Lyapunov exponent. Instability behaviour is then characterised by examining the sign of this exponent. Conditions for the onset of instability via sub-harmonic parametric resonances has been shown to coincide with those for the deterministic case. However, the onset of instability via sum as well as the difference type combination resonance is found to be different from that of the deterministic case. The instability conditions for the system under input angular speed fluctuation have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predictions for the deterministic and the stochastic cases are compared. The effect of fluctuation probability density as well as that of inertia loads on the stability behaviour of the system has been examined.

Stochastic Dynamics of a Variable Inertia System via Lyapunov Exponents

2008 ◽  
Author(s):  
S. F. Asokanthan ◽  
X. H. Wang ◽  
W. V. Wedig ◽  
S. T. Ariaratnam
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Stochastic Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Excitation ◽  
The Stability

Torsional instabilities in a single-degree-of-freedom system having variable inertia are investigated by means of Lyapunov exponents. Linearised analytical model is used for the purpose of stability analysis. Numerical schemes for simulating the top Lyapunov exponent for both deterministic and stochastic systems are established. Instabilities associated with the primary and the secondary sub-harmonic resonances have been identified by studying the sign of the top Lyapunov exponent. Predictions for the deterministic and the stochastic cases are compared. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. The effects of fluctuation density as well as that of damping on the stability behaviour of the system have been examined. Predicted instability conditions are adequate for the design of a variable-inertia system so that a range of critical speeds of operation may be avoided.

On the Stability and Nonlinear Dynamics of a Horizontally Base-Excited Shaker/Mould Structure With Unsymmetric End Stiffnesses

1991 ◽  
Author(s):  
John K. H. Cheng ◽  
K. W. Wang
Keyword(s):  
Rotational Motion ◽  
Excitation Frequency ◽  
Mechanical Systems ◽  
Excitation Amplitude ◽  
Governing Equations ◽  
System Parameters ◽  
The Past ◽  
Transverse Vibrations ◽  
Time Varying Parameter ◽  
The Stability

Abstract This paper presents a dynamic analysis of a horizontally base -excited shaker/ mould structure with unsymmetric gripper stiffnesses. The study explains the large rotational and transverse vibrations of the mould at specific operating frequencies observed in the experiments. The governing equations consist of a time-dependent coefficient which indicates the existence of parametric excitation effects. It is concluded that differences between the gripper stiffnesses are responsible for this phenomenon and could destabilize the system. The value of the time-varying parameter is related to the horizontal vibration amplitude of the mould and hence is a function of the system parameters and excitation frequency. The mould’s rotational motion is directly parametrically excited while its transverse vibration is excited indirectly through coupling with the rotational motion. A thorough analysis of this class of mechanical systems has not been performed in the past. In this research, studies are conducted to identify the contributions of various system parameters, such as gripper stiffness, damping, mould inertia, and excitation amplitude to the system dynamic characteristics. The results provide new insight and guidelines toward optimizing such mechanical systems.

scholarly journals Bifurcation Analysis of a Rigid Impact Oscillator with Bilinear Damping

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liping Zhang ◽  
Haibo Jiang ◽  
Yang Liu
Keyword(s):  
Mechanical Model ◽  
Period Doubling ◽  
External Excitation ◽  
Coexisting Attractors ◽  
Impact Oscillator ◽  
Grazing Period ◽  
The Stability ◽  
Complex Phenomena ◽  
Impulsive Switched System ◽  
The Impact

This paper studies a rigid impact oscillator with bilinear damping developed as the mechanical model of an impulsive switched system. The stability and the bifurcation of periodic orbits in the impact oscillator are determined by using the mapping methods. One-parameter bifurcation analyses under variation of forcing frequency and amplitude of external excitation are carried out. Coexisting attractors and various types of bifurcations, such as grazing, period-doubling, and saddle-node, are observed, which show the complex phenomena inhered in this impact oscillator.

EXPERIMENTAL BIFURCATIONS OF AN IMPACT OSCILLATOR WITH SMA CONSTRAINT

2012 ◽  
Vol 22 (05) ◽  
pp. 1230017 ◽  
Author(s):  
ELENA SITNIKOVA ◽  
EKATERINA PAVLOVSKAIA ◽  
JAMES ING ◽  
MARIAN WIERCIGROCH
Keyword(s):  
Excitation Frequency ◽  
Dynamic Responses ◽  
Hysteretic Behavior ◽  
Resonance Structure ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Impact Oscillator ◽  
Restoring Force ◽  
Chaotic Motions ◽  
Highly Nonlinear

In this paper we study bifurcations of an impact oscillator with one sided SMA motion constraint. The excitation frequency is used as a bifurcation parameter and two different values of the excitation amplitude are considered. It is shown that as frequency varies, the system exhibits highly nonlinear behavior. A typical bifurcation diagram has a number of resonance regions separated by chaotic motions with additional windows of periodic responses. The evolution of chaotic attractors is recorded experimentally, and changes in the structure of the attractors are shown. A mathematical model is developed and the results of the simulations are compared with the experimental findings. It is shown that the model is capable of accurately predicting not only the resonance structure but also the shape of the periodic and chaotic attractors. Numerical investigations also reveal a number of coexisting attractors at some frequency values. In particular, three attractors are found numerically for A = 0.2 mm and f = 29.474 Hz and their basins of attraction are presented. For A = 0.2 mm and f = 33.463 Hz , four coexisting attractors are found. For both parameter sets, one of the numerically detected attractors was validated experimentally. The undertaken analysis has shown that the hysteretic behavior of the restraint affected the dynamic responses only at the resonances, when the displacements are sufficiently large to trigger phase transformations in the SMA restraint. In nonresonant frequency ranges the restoring force in the SMA constraint is elastic. These findings are consistent with the numerical analysis carried out in [Sitnikova et al., 2008] for a similar system, which showed that the hysteretic behavior of the SMA affects resonant responses and provides a substantial vibration reduction in those regions.

scholarly journals Complex response analysis of a non-smooth oscillator under harmonic and random excitations

2021 ◽  
Vol 42 (5) ◽  
pp. 641-648
Author(s):  
Shichao Ma ◽  
Xin Ning ◽  
Liang Wang ◽  
Wantao Jia ◽  
Wei Xu
Keyword(s):  
Excitation Frequency ◽  
System Stability ◽  
Response Analysis ◽  
External Excitation ◽  
Stochastic Response ◽  
Impact Oscillator ◽  
Nonlinear Parameters ◽  
Bifurcation Phenomena ◽  
Mc Simulation ◽  
Smooth System

AbstractIt is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Effects of Acoustic Excitation on a Swirling Diffusion Flame

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Michael E. Loretero ◽  
Rong F. Huang
Keyword(s):  
Flow Field ◽  
Bluff Body ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Mie Scattering ◽  
Flame Length ◽  
Laser Doppler Velocimeter ◽  
Scattering Method ◽  
Acoustic Excitation ◽  
Characteristic Modes

A swirling double concentric jet is commonly used for nonpremixed gas burner application for safety reasons and to improve the combustion performance. Fuel is generally spurted at the central jet while the annular coflowing air is swirled. They are normally separated by a blockage disk where the bluff-body effects further enhance the recirculation of hot gas at the reaction zone. This paper aims to experimentally investigate the behavior of flame and flow in a double concentric jet combustor when the fuel supply is acoustically driven. Laser-light sheet assisted Mie scattering method has been used to visualize the flow, while the flame lengths were measured by a conventional photography technique. The fluctuating velocity at the jet exit was measured by a two-component laser Doppler velocimeter. Flammability and stability at first fuel tube resonant frequency are reported and discussed. The evolution of flame profile with excitation level is presented and discussed, together with the reduction in flame length. The flame in the unforced reacting axisymmetric wake is classified into three characteristic modes, which are weak swirling flame, lifted flame, and transitional reattached flame. These terms reflect their primary features of flame appearances, and when the acoustic excitation is applied, the flame behaviors change with the excitation frequency and amplitude. Four additional characteristic modes are identified; e.g., at low excitation amplitudes, wrinkling flame with a blue annular film is observed because the excitation induces vortices in the central fuel jet and hence gives rise to the wrinkling of flame. The central jet vortices become larger with the increase in excitation amplitude and thus lead to a wider and shorter flame. If the excitation amplitude is increased above a certain value, the central jet vortices change the rotation direction and pacing with the annular jet vortices. These changes in the flow field induce large turbulent intensity and mixing and therefore make the flame looks blue and short. Further increase in the excitation amplitude would lift the flame because the flow field would be dramatically modified.

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.

Sign in / Sign up

Export Citation Format

Share Document