An Experimental Study of a Single-Degree-of-Freedom Impact Oscillator

Purpose. Impacts appear in a wide range of mechanical systems. To study the dynamical behavior introduced by impact in practical way, a single-degree-of-freedom impact oscillator rig is designed. Originality. A simple piece-wise linear system with symmetrical flexible constraints is designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piece-wise models. The new design choice is based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness as well avoidance of the delay introduced by the structure. Meanwhile, the new design provides the possibility of the applications of the complex control algorithms. Design/methodology/approach. The design process is described in detail. The initial experimental results of the rig as well as numerical simulation results are given. In this rig, the mass driven force is generated by electromagnet, which can be adjusted and control easily. Also, most of the physical parameters can be varied in a certain range to enhance flexibility of the system allowing to observe subtle phenomena. Findings. Compared with the simulation results, the designed rig is proved to be validated. Then, the initial experimental results demonstrate potentials of this rig to study fundamental impact phenomena, which have been observed in various engineering systems. They also indicate that this rig can be a good platform for investigating nonlinear control methods.

Stochastic Bifurcations of a Fractional-Order Vibro-Impact Oscillator Subjected to Colored Noise Excitation

A stochastic vibro-impact system has triggered a consistent body of research work aimed at understanding its complex dynamics involving noise and nonsmoothness. Among these works, most focus is on integer-order systems with Gaussian white noise. There is no report yet on response analysis for fractional-order vibro-impact systems subject to colored noise, which is presented in this paper. The biggest challenge for analyzing such systems is how to deal with the fractional derivative of absolute value functions after applying nonsmooth transformation. This problem is solved by introducing the Fourier transformation and deriving the approximate probabilistic solution of the fractional-order vibro-impact oscillator subject to colored noise. The reliability of the developed technique is assessed by numerical solutions. Based on the theoretical result, we also present the critical conditions of stochastic bifurcation induced by system parameters and show bifurcation diagrams in two-parameter planes. In addition, we provide a stochastic bifurcation with respect to joint probability density functions. We find that fractional order, coefficient of restitution factor and correlation time of colored noise excitation can induce stochastic bifurcations.

A Solution Procedure Combining Analytical and Numerical Approaches to Investigate a Two-Degree-of-Freedom Vibro-Impact Oscillator

In this paper, a new approach is proposed to analyze the behavior of a nonlinear two-degree-of-freedom vibro-impact oscillator subject to a harmonic perturbing force, based on a combination of analytical and numerical approaches. The nonlinear governing equations are analytically solved by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM), which provided highly accurate explicit analytical solutions. Benefiting from these results, the application of Schur principle made it possible to analyze the stability conditions for the considered system. Various types of possible motions were emphasized, taking into account possible initial conditions and different parameters, and the explicit analytical solutions were found to be very useful to analyze the kinetic energy loss, the contact force, and the stability of periodic motions.

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

It 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.

Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints

The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.

Power spectrum of hydraulic fractures with constricted opening

<p>Propagation of hydraulic fractures in rocks is often a non-smooth process, which leaves behind a number of rock bridges distributed all over the fracture. The bridges constrict the fracture opening and thus affect the determination of hydraulic fracture dimensions from the volume of pump-in fracturing fluid. This makes it necessary to detect the emergence of bridges and their concentration over the fracture surface.</p><p>Opening of hydraulic fractures in rocks is determined by a balance of pressure from the fracturing fluid and the normal component of the in-situ compressive stress. If an external excitation is applied (e.g. by a seismic wave), closure of the fracture is additionally resisted by the stiffness of fracturing fluid. Subsequently, a simple model of hydraulic fracture is presented by a bilinear spring with a certain stiffness in tension and a very high stiffness in compression. This constitutes so-called bilinear oscillator [1, 2] in which the compressive stiffness considerably exceeds the tensile one. The presence of bridges increases stiffness in tension thus reducing bilinearity of the modelling spring. Therefore the determination of the bilinearity is a first step in the reconstructing the effective stiffness of the bridges.  </p><p>We use the model of bilinear oscillator, identify multiple resonances and determine the first two harmonics (or first two peaks of in the power spectrum). The ratio of their amplitudes directly depends upon the bilinearity (ratio of compressive to tensile stiffnesses), hence the bilinearity is determinable from the amplitude ratio. Then the effective bridge stiffness can be estimated.</p><p>1. Dyskin, A.V., E. Pasternak and E. Pelinovsky, 2012. Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration 331(12) 2856-2873. ISBN/ISSN 0022-460X, 04/06/2012.</p><p>2. Pasternak, E., A. Dyskin<sup></sup>and Ch. Qi, 2020. Impact oscillator with non-zero bouncing point. International Journal of Engineering Science, 103203.</p><p><strong>Acknowledgement</strong>. The authors acknowledge support from the Australian Research Council through project DP190103260.</p>