Applied Mechanics and Materials Vol. 430

Abstract: In this paper an overview of the self-sustained oscillators is given. The standard van der Pol and the Rayleigh oscillators are considered as basic ones. The cubic nonlinear term of Duffing type is included. The special attention is given to the various complex systems based on the Rayleighs and van der Pols oscillator which are extended with the nonlinear oscillators of Duffing type and also excited with a periodical force. The connection is with the linear elastic force or with linear damping force. The objectives for future investigation are given in this matter.

Abstract: This work is concerned with single-degree-of-freedom conservative nonlinear oscillators that have a fixed restoring force, which comprises a linear term and an odd-powered nonlinear term with an arbitrary magnitude of the coefficient of nonlinearity. There are two cases of interest: i) non-isochronous, when the system has an amplitude-dependent frequency and ii) isochronous, when the frequency of oscillations is constant (amplitude-independent). The first case is associated with the constant coefficient of the kinetic energy, while the frequency-amplitude relationship and the solution for motion need to be found. To that end, the equation of motion is solved by introducing a new small expansion parameter and by adjusting the Lindstedt-Poincaré method. In the second case, the condition for the frequency of oscillations to be constant is derived in terms of the expression for the position-dependent coefficient of the kinetic energy. The corresponding solution for isochronous oscillations is obtained. Numerical verifications of the analytical results are also presented.

Abstract: The response of a cantilever beam with a lumped mass attached to its free end subject to harmonical excitation at the base is investigated by means of the Optimal Homotopy Asymptotic Method (OHAM). Approximate accurate analytical expressions for the solutions and for approximate frequency are determined. This method does not require any small parameter in the equation. The obtained results prove that our method is very accurate, effective and simple for investigation of such engineering problems.

Abstract: This paper is concerned with analytical treatment of nonlinear oscillation of a self-excited system. An analytic approximate technique, namely OHAM is employed for this purpose. Our procedure provides us with a convenient way to optimally control the convergence of solutions, such that the accuracy is always guaranteed. An excellent agreement of the approximate solutions with the numerical ones has been demonstrated. Three examples are given and the results reveal that the procedure is very effective and accurate, demonstrating the general validity and the great potential of the OHAM for solving strongly nonlinear problems.

Abstract: Depending on the type of systems, the resonance states are either short and without inducing structural changes, or lead to forced variations of the elasticity and damping parameters with the additional energy absorption. For the material physical systems, that simulate the dynamic behavior of equipments, industrial plants and constructions, the operation in resonance mode is unstable being characterized by pulse variations in the band-pass. In this case, the necessary energy input, from outside, when the operation state is maintained within the band-pass, inevitably leads to the modification of the elastic and damping parameters and to structural degradation processes appearance. Thus the resonance band, Δω, considered as a significant parameter of the excitation, as well as the specific relaxation duration considered as an intrinsic system parameter are in a functional correlation of the dynamic system. When the dissipation increases Δc > 0, the relaxation duration drops with Δt=m/Δc, in such a way that the relation Δω Δt = 1 is valid, similar to the Heisenberg indeterminacy formula for subatomic particles. It can be observed that for Δt tending to 0 and for very high values of Δc the resonance state can be achieved for any value of the excitation pulsation as a discrete variable parameter by the modification of the viscous component. In the ideal case, the resonance interval is reduced to a single value that corresponds to its own pulsation. The systems dynamic behavior generated by periodic functions resulting in either forced vibrations or wave propagation processes in viscoelastic media is characterized by doubtful operation and physical instability within resonance.

Abstract: In this paper we consider the propagation equation of the longitudinal elastic wave in the presence of the volume forces, taking into account the shear phenomena of a thin elastic plate. In order to find an approximate analytical solutions of the governing system we apply Optimal Homotopy Asymptotic Method (OHAM). This technique combines the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution. An excellent agreement is found between the results obtained using OHAM and numerical integration results.

Abstract: The present paper is a generalization of the problem of a rubber spring pendulum discussed by Bhattacharyya in 2000 and Stănescu in 2011, which studied the case of the neo-Hookean rod without mass. In our paper we consider that the mass of the neo-Hookean rod is not negligible and its deformation is realized such that at any moment of time the rod can be treated as a homogeneous rigid bar of variable length. Using the second order Lagrange equations we obtained the equations of motion in the most general case and we identified as particular cases the situations presented in the bibliography. We also performed a study of the equilibrium positions and their stability. A study of the small oscillations about the stable equilibrium positions is realized too. The theoretical results are finally compared to those obtained by numerical simulation.

Abstract: Our paper realizes a study of the vibrations of an engine excited by a harmonic force and sustained by four identical neo-Hookean springs of negligible masses. The considered model is one with three degrees of freedom (one translation and two rotations) and we obtain for it the equations of motion. Using these equations, we determine for the unexcited system the equilibrium positions and their stability. We also study the small oscillations about the stable equilibrium positions and we find the fundamental eigenpulsations of the system. For the case of the excited system we perform a numerical study considering the situation when the pulsation of the excitation is far away from the eigenpulsations and the situation when the pulsation of the excitation is closed to one eigenpulsation, highlighting the beat phenomenon.

Abstract: Paper addresses the implementation of feature based artificial neural networks and self-organized feature maps with the vibration analysis for the purpose of automated faults identification in rotating machinery. Unlike most of the research in this field, where a single type of fault has been treated, the research conducted in this paper deals with rotating machines with multiple faults. Combination of different roller elements bearing faults and different gearbox faults is analyzed. Experimental work has been conducted on a specially designed test rig. Frequency and time domain vibration features are used as inputs to fault classifiers. A complete set of proposed vibration features are used as inputs for self-organized feature maps and based on the results they are used as inputs for supervised artificial neural networks. The achieved results show that proposed set of vibration features enables reliable identification of developing bearing and gear faults in geared power transmission systems.