J. Warminski
Lublin University of Technology, Applied Mechanics, Faculty Member
An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam... more
An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of ...
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The analysis of the shape memory prosthesis (SMP) of the middle ear is presented in this paper. The shape memory prosthesis permits the adjustment of its length to individual patient needs, but sometimes the prosthesis cannot be properly... more
The analysis of the shape memory prosthesis (SMP) of the middle ear is presented in this paper. The shape memory prosthesis permits the adjustment of its length to individual patient needs, but sometimes the prosthesis cannot be properly fixed to the stapes. In this case, the impact between the prosthesis and stapes is important. Therefore, the reconstructed middle ear is modeled as a two degree-of-freedom system with a nonlinear shape memory element and soft impact to represent its behavior when the prosthesis is not properly placed or fixed. The properties of the shape memory prosthesis, in the form of a helical spring, are represented by a polynomial function. The system exhibits advisable periodic and undesirable aperiodic and irregular behavior depending on the excitation amplitude, the frequency, and the prosthesis length. The prosthesis length can change, resulting in a modification of the distance between the prosthesis and the stapes. The results of this study provide an an...
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ABSTRACT
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ABSTRACT The paper presents classical regenerative one degree of freedom model of cutting. The model is enriched in an additional friction phenomenon which generates frictional chatter. A mutual interaction between regeneration and... more
ABSTRACT The paper presents classical regenerative one degree of freedom model of cutting. The model is enriched in an additional friction phenomenon which generates frictional chatter. A mutual interaction between regeneration and frictional effects is analysed to find stability regions. In the second part of the paper a spindle speed variation method is applied for chatter suppression both for classical regenerative model and also for regenerative model with the friction effect. Finally, the map of spindle speed variation parameters is drawn.
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Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and... more
Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It has been found that the motion of the oscillator, forced by an external harmonic force, has been dynamically eliminated by the pendulum oscillations. Influence of a nonlinear spring on the vibration absorption near the main parametric resonance region has been carried out analytically, whereas the transition from regular to chaotic vibrations has been presented by using numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.
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In this paper, a model of the milling process of fibre reinforced composite material is shown. This classical one degree of freedom model of the milling process is adjusted for composite materials by variable specific cutting forces,... more
In this paper, a model of the milling process of fibre reinforced composite material is shown. This classical one degree of freedom model of the milling process is adjusted for composite materials by variable specific cutting forces, which describe the fibre resistance. The stability lobe diagrams are determined numerically. Additionally, to eliminate the chatter vibration, small relative oscillations between the
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Motion of self-excited Froude pendulum under external forcing were analyzed. Differential equation of motion includes the nonlinear damping term of Rayleigh's type. Using multiple time scale method and Lyapunov theory, vibrations,... more
Motion of self-excited Froude pendulum under external forcing were analyzed. Differential equation of motion includes the nonlinear damping term of Rayleigh's type. Using multiple time scale method and Lyapunov theory, vibrations, synchronization and stability of the system were examined. Chaotic motion was analyzed here by means of Lyapunov exponent and Melnikov approach.
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Cutting forces and the combined residual flexibility of the machine–workpiece–tool system adversely affect machining accuracy. While reducing the cutting speed, feedrate and depth of cut, on a very stiff machine tool, would alleviate the... more
Cutting forces and the combined residual flexibility of the machine–workpiece–tool system adversely affect machining accuracy. While reducing the cutting speed, feedrate and depth of cut, on a very stiff machine tool, would alleviate the problem, such a practice would be uneconomical [5]. In principle, real-time error-compensation techniques offer a more cost-effective alternative that does not call for a reduction of the material removal rate [5]. Hence, these techniques have received wide attention in recent years, complementing ...
In the present paper, the inlluence of initial conditions on the occurrence of regular and chaotic vibrations of the system with backlash, descri-bed by a non—linear diIIei'ential equation with a periodic coelTicient, was... more
In the present paper, the inlluence of initial conditions on the occurrence of regular and chaotic vibrations of the system with backlash, descri-bed by a non—linear diIIei'ential equation with a periodic coelTicient, was investigated. For specified parameters, using the Lyapunov exponent, intervals of the initial conditions leading to chaotic motion were determined. The effect of external excitation amplitude on the character of motion was analysed. For the initial conditions determining regular and chaotic motion, Poincare ...
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Vibrations of a self-excited oscillator under parametric excitation with nonlinear stiffness were investigated in this paper. Differential equation of motion includes van der Pol, Mathieu and Duffing terms. Vibrations synchronization,... more
Vibrations of a self-excited oscillator under parametric excitation with nonlinear stiffness were investigated in this paper. Differential equation of motion includes van der Pol, Mathieu and Duffing terms. Vibrations synchronization, stability of solutions were examined by means of the multiple time scale method and Floquet theory. Chaotic solutions were found by means of Lyapunov exponent.
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Vibration analysis of a non-linear parametrically andself-excited system of two degrees of freedom was carried out. The modelcontains two van der Pol oscillators coupled by a linear spring with a aperiodically changing stiffness of the... more
Vibration analysis of a non-linear parametrically andself-excited system of two degrees of freedom was carried out. The modelcontains two van der Pol oscillators coupled by a linear spring with a aperiodically changing stiffness of the Mathieu type. By means of amultiple-scales method, the existence and stability of periodicsolutions close to the main parametric resonances have beeninvestigated. Bifurcations of the system and regions of chaoticsolutions have been found. The possibility of the appearance ofhyperchaos has ...