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Strongly Nonlinear Effects of an Unbalanced Mass and the Supply Voltage of the Non-Ideal DC Motor on the Vibration Amplitude of a Thin Rectangular Plate  [PDF]
Lionel Merveil Anague Tabejieu, Cabrel Fotso Kamche, Vanlie Maurice Kontchou, Eric Sinclair Fongho, Joseph Nkongho Anyi
World Journal of Mechanics (WJM) , 2026, DOI: 10.4236/wjm.2026.162002
Abstract: In this paper, the strongly nonlinear effects of an unbalanced mass and the supply voltage of a non-ideal DC motor on the vibration amplitude of a thin rectangular plate are investigated. The influence of these two parameters on the occurrence of the Sommerfeld phenomenon—specifically in terms of the energy delivered by the motor—as well as on the emergence of the so-called limited energy source phenomenon related to voltage saturation, is thoroughly analyzed using analytical and numerical methods. By considering the interaction between the thin rectangular plate and the non-ideal DC motor, the governing equations of the vibration system are derived using the Lagrange formalism. A perturbation method based on averaging is then employed to obtain the steady-state response. Numerical simulations using the fourth-order Runge–Kutta method are also conducted to validate the analytical results. The effect of the non-ideal loading is strongly nonlinear, leading to a non-monotonic behavior of the vibration amplitude with respect to both the supply voltage and the unbalanced mass of the motor. Moreover, the amplitude jump phenomenon, which indicates the presence of the Sommerfeld effect, is clearly captured across a wide range of parameters. This paper provides useful insights for the design of industrial floor structures that support rotating machinery.
Investigation of Shock Waves in Non-Ideal Gas under the Action of Magnetic Field  [PDF]
Kanti Pandey, Praveen Prakash Pathak
Advances in Pure Mathematics (APM) , 2017, DOI: 10.4236/apm.2017.710035
Abstract: In present paper, certain aspect of shock wave in non-ideal gas, when magnetic field is orthogonal to the trajectories of the gas particles and electrical conductivity is taken to be infinite, is investigated. Considering one-dimensional unsteady non-planer motion, basic equations, its general solution and formation of shock-wave, conservation laws and jumps conditions, variation of area of non-uniform cross section and analytical solution of strong non planer shock is obtained.
The Non-Smooth Problem of Wheel Motion  [PDF]
Wies？aw Grzesikiewicz, Artur Zbiciak
Advances in Pure Mathematics (APM) , 2020, DOI: 10.4236/apm.2020.1011041
Abstract: Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smoothness of this problem means that its solution is determined by an absolutely continuous function having a discontinuous first derivative. For this reason, a collision problem describing abrupt changes of velocity has been formulated next to the equations of motion specifying the acceleration. The non-idealness of constraints means that the constraint reaction force includes also a component resulting from the friction between the wheel and the constraints. Differential equations specifying acceleration of the wheel making contact with the constraints and algebraic equations for determining the changes in the wheel’s velocity at the moment of collision have been formulated in the paper. The principal task in these formulations is to determine the reaction forces of the considered constraints. This task is specified by the relationships between acceleration and the constraint reaction force components. In the description of the collision, these relations refer to the post-collision velocities and reaction force impulses. For determining an approximate solution of the formulated wheel motion problem, an original numerical method and a computer program for wheel motion simulation have been developed. Selected results illustrating the changes in displacements and velocity have been presented.
Frequency-Concentration Dependence of Optical Activity of a Non-Ideal 1D-Superlattice  [PDF]
Vladimir V. Rumyantsev, Stanislav A Fedorov
Journal of Modern Physics (JMP) , 2011, DOI: 10.4236/jmp.2011.212192
Abstract: In the present work the widths of layers constituting the non-ideal superlattice are much bigger then the characteristic scales of space dispersion. In such a case the contribution of individual layers to gyrotropy can be regarded as independed. Thus the corresponding optical quantities can be expressed through the layers’ gyrotropic characteristics. This approach is applied to calculate the specific rotation angle of plane of polarization of light propagating through a nonideal 1D-superlattice, which varies in composition as well as in layers’ width. We carry out numerical calculation of the frequency dispersion of optical activity of a non-ideal superlattice, which includes impurity layers with point defects.
Modeling and Simulation of Non-ideal Buck Converter in DCM
Sheng-yu Gong,,Lin Chen, Chang-hu Yu, Guang-jun Xie*
International Journal of Computer Technology and Electronics Engineering , 2012,
Abstract: The modeling method is exemplified by Buckconverter operating in the discontinuous conduction mode(DCM), taking into account all parasitic resistances, thresholdvoltage of diode and inductor current ripples existing in actualconverters. Based on the theory of switch average model, timeaverage method of equivalent circuit, the theory of energyconservation, a circuit averaging method is studied to modelnon-ideal Buck converters operating in DCM, and a duty ratioconstraint which leads to a full order model is introduced. Onthe basis of DC circuit model and large and small-signalequivalent circuit model, the modeling and simulation analysisof non-ideal Buck converters are presented. Therefore, thederived models are convenient for modeling and designing ofDC-DC converter and its control system.
Bridging Ideal and Non
Alexandru Volacu
- , 2018, DOI: 10.1177/0032321717730297
Abstract: Many of the recent methodological debates within political theory have focused on the ideal/non-ideal theory distinction. While ideal theorists recognise the need to develop an account of the transition between the two levels of theorising, no general proposal has been advanced thus far. In this article, I aim to bridge this conceptual gap. Towards this end, I first reconstruct the ideal/non-ideal theory distinction within a simplified two-dimensional framework, which captures the primary meanings usually attributed to it. Subsequently, I use this framework to provide an algorithm for the bidirectional transition between ideal and non-ideal theory, based on the incremental derivation of normative models. The approach outlined illuminates the various ways in which principles derived under highly idealised assumptions might be distorted by the circumstances of our current world and illustrates the various paths which we can pursue in moving from our current state of the world to an ideal one
Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem
Souza, S. L. T. de;Caldas, I. L.;Balthazar, J. M.;Brasil, R. M. L. R. F.;
Journal of the Brazilian Society of Mechanical Sciences , 2002, DOI: 10.1590/S0100-73862002000200005
Abstract: this paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. the subject has being analyzed by a number of authors such as karagiannis and pfeiffer (1991), for the ideal excitation case. an interesting model of the same problem by moon (1992) has been recently used by souza and caldas (1999) to detect chaotic behavior. we consider two spur gears with different diameters and gaps between the teeth. suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. in the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. in this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. thus an extra degree of freedom is introduced in the problem. the equations of motion are obtained via a lagrangian approach with some assumed characteristic torque curves. next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.
Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem
Souza S. L. T. de,Caldas I. L.,Balthazar J. M.,Brasil R. M. L. R. F.
Journal of the Brazilian Society of Mechanical Sciences , 2002,
Abstract: This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.
Vibrations of a parametrically and self-Excited system with ideal and non-ideal energy sources
Warminski, J.;Balthazar, J. M.;
Journal of the Brazilian Society of Mechanical Sciences and Engineering , 2003, DOI: 10.1590/S1678-58782003000400014
Abstract: interactions between parametric, self-, and externally excited vibrations are analysed in this paper. the physical model of the vibrating system consists of a non-linear spring with periodically changing stiffness of mathieu type and a non-linear damping described by rayleigh's term. this system is additionally forced by a harmonic force (ideal system), or by a non-ideal energy source represented by a direct current motor with limited power supply. the model of dc motor is considered in two variants, as a classical, in kononenko's sense model, and a complete electro-mechanical system. quantitative and qualitative differences of the considered models are compared and discussed in the paper.
Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study
Fenili, A.;Balthazar, J. M.;Mook, D. T.;Weber, H. I.;
Journal of the Brazilian Society of Mechanical Sciences , 2002, DOI: 10.1590/S0100-73862002000300014
Abstract: in this paper is analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. the dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. in this critical point, a hopf bifurcation occurs. in this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). this local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.
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