Other affiliations: University of Bologna
Bio: A.A. Al-Qaisia is an academic researcher from University of Jordan. The author has contributed to research in topics: Harmonic balance & Nonlinear system. The author has an hindex of 10, co-authored 28 publications receiving 337 citations. Previous affiliations of A.A. Al-Qaisia include University of Bologna.
TL;DR: The dynamics of a forced Duffing oscillator are studied by means of modern nonlinear, bifurcation and chaos theories to show that the system is ultimately experiencing chaos.
Abstract: In this paper, the dynamics of a forced Duffing oscillator is studied by means of modern nonlinear, bifurcation and chaos theories and shows that the system is ultimately experiencing chaos. The main objective is to characterize and control chaotic behavior. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Systematic following of a reference model is introduced. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally a discussion and conclusions are given with possible future extensions.
TL;DR: In this article, Krishnamurthy et al. derived a second-order parametric response of a vertically mounted flexible cantilever beam subjected to a vertical harmonic base motion using harmonic balance (HB) and the perturbation method of multiple time scales (MMS).
Abstract: This paper is concerned with second-order approximations to the steady-state principal parametric resonance response of a vertically mounted flexible cantilever beam subjected to a vertical harmonic base motion. The unimodal form of the nonlinear equation describing the in-plane large amplitude parametric response of the beam, derived in Krishnamurthy (Ph.D. Thesis, Department of Mechanical Engineering, Washington State University, 1986) based on the previous analysis in Crespo da Silva and Glynn (Journal of Structural Mechanics 1978; 6:437–48), is analysed using the harmonic balance (HB) and the perturbation method of multiple time scales (MMS). Single term HB, two terms HB, and second-order MMS with reconstitution version I (Nayfeh and Sanchez, Journal of Sound and Vibration 1989; 24:483–97) and version II (Rahman and Burton, Journal of Sound and Vibration 1989; 133:369–79) approximations to the steady-sate frequency–amplitude curves of the principal parametric resonance for each of the first four natural modes of the cantilever beam are compared with each other and with those obtained by numerically integrating the unimodal equation of motion. The time transformation T= Ω t is used in obtaining these approximations; also detuning is used in obtaining the square of the forcing MMS approximations. The obtained results show that, for the problem under consideration, the MMS version II is, in comparison with MMS version I, simpler to apply and leads to qualitatively more accurate second-order results. These results, however, show that the MMS version II tends to produce appreciable over corrections to the first-order results and may breakdown at relatively low response amplitudes, whereas the two terms HB solutions tend to improve the first-order results and lead to fairly accurate results even for relatively large response amplitudes.
TL;DR: Experimental results show that cascaded-P ID with PSO tuning performs better than single-PID, especially in disturbance rejection (a practical challenge in industrial pneumatic systems).
Abstract: This paper presents a cascade control methodology for pneumatic systems using Particle Swarm Optimization (PSO). First, experimental data is collected and used to identify the servo-pneumatic system where an Auto-Regressive Moving-Average (ARMA) model is formulated using PSO algorithm. Then, cascaded Proportional–Integral–Derivative (PID) controller with PSO tuning is proposed and implemented on real system using Hardware-In-the-Loop (HIL). The identified model is validated experimentally and the performance of the cascaded-PID controller is tested under various conditions of speed variation. Experimental results show that cascaded-PID with PSO tuning performs better than single-PID, especially in disturbance rejection (a practical challenge in industrial pneumatic systems). Results also show that cascaded-PID with PSO-tuning performs better than cascaded-PID with self-tuning in the transient and steady-state responses.
TL;DR: In this paper, the steady state periodic response has the same period as the excitation of strongly nonlinear oscillators, where the transformation of timeT = Ωt and detuning in the square of forcing frequency are used in the MMS with reconstitution version I and version II.
Abstract: The concern of this work is the steady state periodic response having the same period as the excitation of strongly non-linear oscillatorsu+δu+mu+ϵ1u2u+ϵ1uu2+ϵ2u3=P cos Ωt, wherem=1, 0 or −1, ϵ1and ϵ1are positive parameters which may be arbitrarily large. Single-mode and two-mode harmonic balance (HB) approximations, and second order perturbation-multiple time scales (MMS) with reconstitution version I and version II approximations to the steady state amplitude frequency response curves are compared, for the casem=1 with each other, and with those obtained by numerically integrating the equation of motion. The transformation of timeT=Ωtand detuning in the square of forcing frequency are used in the MMS with reconstitution version I and version II. The objective here is to assess the accuracy of these approximate solutions in predicting the systems response over some range of system parameters by examining their ability or failure in establishing the correct qualitative behavior of the actual (numerical) solution. The casesm=0 andm=1, are studied for selected range of system parameter, using the single and two modes harmonic balance method and compared to those obtained numerically. It was shown that MMS version II, in addition to being appreciably simpler than MMS version I, leads to more accurate qualitative and quantitative results even when the non-linearity is not necessarily small.
TL;DR: In this article, the forced vibrations of a flexible rotating blade under the excitation of shaft torsional vibration were studied and a reduced order nonlinear dynamic model was adopted, wherein the torsion vibration degree of freedom was substituted by a simple harmonic motion with a frequency that is function of the system rotating speed.
Abstract: This paper studies the forced vibrations of a flexible rotating blade under the excitation of shaft torsional vibration. A reduced order nonlinear dynamic model is adopted, wherein the torsional vibration degree of freedom is substituted by a simple harmonic motion with a frequency that is function of the system rotating speed. The resulting system of second-order ordinary differential equation with harmonically varying coefficients is solved using the method of harmonic balance. The forced response solution is compared to the numerical integration results. Agreement is found with respect to stable and unstable regions of the blade vibrations. The solution is useful for defining dangerous operating speed ranges and for quantifying the relationship between shaft torsional and blade bending natural frequencies.
TL;DR: In this paper, the authors provide an overview of methods to detect, locate, and characterize damage in structural and mechanical systems by examining changes in measured vibration response, including frequency, mode shape, and modal damping.
Abstract: This paper provides an overview of methods to detect, locate, and characterize damage in structural and mechanical systems by examining changes in measured vibration response. Research in vibration-based damage identification has been rapidly expanding over the last few years. The basic idea behind this technology is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties will cause detectable changes in the modal properties. The motivation for the development of this technology is presented. The methods are categorized according to various criteria such as the level of damage detection provided, model-based versus non-model-based methods, and linear versus nonlinear methods. The methods are also described in general terms including difficulties associated with their implementation and their fidelity. Past, current, and future-planned applications of this technology to actual engineering systems are summarized. The paper concludes with a discussion of critical issues for future research in the area of vibration-based damage identification.
TL;DR: In this paper, a vibration isolator consisting of a vertical linear spring and two nonlinear pre-stressed oblique springs is considered, and the softening parameter leading to quasi-zero dynamic stiffness at the equilibrium position is obtained as a function of the initial geometry, pre-stress and the stiffness of the springs.
Abstract: A vibration isolator consisting of a vertical linear spring and two nonlinear pre-stressed oblique springs is considered in this paper. The system has both geometrical and physical nonlinearity. Firstly, a static analysis is carried out. The softening parameter leading to quasi-zero dynamic stiffness at the equilibrium position is obtained as a function of the initial geometry, pre-stress and the stiffness of the springs. The optimal combination of the system parameters is found that maximises the displacement from the equilibrium position when the prescribed stiffness is equal to that of the vertical spring alone. It also satisfies the condition that the dynamic stiffness only changes slightly in the neighbourhood of the static equilibrium position. For these values, a dynamical analysis of the isolator under asymmetric excitation is performed to quantify the undesirable effects of the nonlinearities. It includes considering the possibilities of the appearance of period-doubling bifurcation and its development into chaotic motion. For this purpose, approximate analytical methods and numerical simulations accompanied with qualitative methods including phase plane plots, Poincare maps and Lyapunov exponents are used. Finally, the frequency at which the first period-doubling bifurcation appears is found and the effect of damping on this frequency determined.
TL;DR: In this article, the authors evaluated the nonlinear aspects of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam, where an actual fatigue crack was introduced instead of a narrow slot.
Abstract: Experimental evaluation of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed, where an actual fatigue crack was introduced instead – as usual – of a narrow slot. The nonlinear aspects of the dynamic response of the beam under harmonic excitation were considered and the relevant quantitative parameters were evaluated, in order to relate the nonlinear resonances to the presence and size of the crack. To this end, the existence of sub- and super-harmonic components in the Fourier spectra of the acceleration signals was evidenced, and their amplitudes were quantified. In particular, the acceleration signals were measured in different positions along the beam axis and under different forcing levels at the beam tip. The remarkable relevance of the above mentioned nonlinear characteristics, and their substantial independence on force magnitude and measurement point were worthily noted in comparison with the behavior of the intact beam. Thus, a reliable method of damage detection was proposed which was based on simple tests requiring only harmonically forcing and acceleration measuring in any point non-necessarily near the crack. Then, the time-history of the acceleration recorded at the beam tip was numerically processed in order to obtain the time-histories of velocity and displacement. The nonlinear features of the forced response were described and given a physical interpretation in order to define parameters suitable for damage detection. The efficiency of such parameters was discussed with respect to the their capability of detecting damage and a procedure for damage detection was proposed which was able to detect even small cracks by using simple instruments. A finite element model of the cantilever beam was finally assembled and tuned in order to numerically simulate the results of the experimental tests.
TL;DR: In this paper, the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end is presented.
Abstract: This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions.
TL;DR: In this paper, a new modeling method for the vibration analysis of a rotating cantilever beam is proposed and compared to the other modeling methods, applying the Hamilton principle, the equations for the axial, chordwise and flapwise motions are derived.
Abstract: A new modeling method for the vibration analysis of a rotating cantilever beam is proposed and compared to the other modeling methods. Applying the Hamilton principle, the equations for the axial, chordwise and flapwise motions are derived. During the derivation of these equations, the nonlinear von Karman strain and the corresponding linear stress are used to consider the stiffening effect due to rotation. The derived equations of motion obtained from the proposed method are analytically and numerically compared to equations from the previous modeling methods. Computations of the natural frequencies and time responses show that the described equations of motion are more reliable than the equations of the other modeling methods.