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Earlier works on the smooth and discontinuous (SD) oscillator concentrated mainly on the time domain analysis using analytical, semi-analytical and numerical integration methods. In this paper, the frequency domain analysis of the SD oscillator subjected to harmonic excitation which is as important and giving further insight into the dynamics is carried out. Multi-Harmonic Balance Method (MHBM) in combination with arc length continuation is used to obtain the periodic solutions and their branches in the frequency domain for different values of the smoothing parameter α and exciting frequency ω. Stability of the periodic motions and bifurcation behavior are analyzed using the Floquet theory. For the discontinuous case, the oscillator is treated as a Filippov system and an event driven numerical integration method is used to obtain the response. For α > 1 , the dynamics of the SD oscillator is similar to that of the hardening Duffing oscillator, for α = 1 , it is like that of the Ueda oscillator and for 0 α 1 it is like that of the Duffing oscillator with double well potential. The SD oscillator exhibits period 1 solutions, higher order periodic solutions, chaotic solutions through symmetry breaking bifurcations, period doubling and boundary crises in different parameter ranges. Chaos is observed over a larger frequency range interspersed by narrow windows of higher order periodic solutions.

A flexible diaphragm coupling, connecting two rotating shafts, is investigated for its dynamic characteristics, when subjected to parallel offset misalignment. The diaphragm coupling is a constant velocity coupling which becomes asymmetric once misaligned. Asymmetry creates directional difference or spatial variation of stiffness, as shown by a quasi-static finite element (FE) analysis using ABAQUS software. As the shafts rotate, this spatial variation in stiffness makes the diaphragm coupling–rotor system model to become time-varying. The time-varying direct and cross–coupled stiffness terms of the coupling are synthesized from the FE model and used in the governing equations of motion of the coupling–rotor system. This leads to a parametrically excited system due to the time-periodic stiffness coefficients of the coupling. Using Simulink, numerical integration has been performed to find the response of the system for both mass unbalance and inclination unbalance excitations that arise due to the tilt of the principal axes of the diaphragm due to parallel misalignment. The responses obtained clearly indicate the effect of parametric excitation at one-fourth, one-third, and one-half of the principal parametric resonance. To verify this model, an experimental setup has been developed for the coupling–rotor system model with misalignment. The experimental results clearly show the asymmetry between the two lateral direction responses, as predicted by the model.

International audience; this work, the multiple absorption coefficient zonal method (MACZM) is being implemented and validated numerically. The method is demonstrated to be highly suitable for the analysis of radiative heat transfer in multidimensional inhomogeneous non-grey media. A uniform rectangular fine grid is considered and small CPU time is achieved. This makes the method of great interest for transient applications. The validity of the method is demonstrated in two steps. First, cases with simple geometry are considered and results are compared to results generated by direct numerical integration. Results are also generated by MODRAY, which is a source project based on an original method called the flux-planes approximation, and are shown to be equally accurate. Second, the case of a steel reheating furnace is considered. In a previous work, the furnace heat balance and temperature profiles were simulated using a finite difference computation approach and radiative exchange factors generated by MODRAY. Experiments were performed and results generated by the model were found to be in good agreement with experimental data. The radiative exchange factors are now recalculated with MACZM. They are shown to be very close to those generated by MODRAY. The comparison of the two methods clearly shows that MACZM is much faster for the calculation of the volume-volume radiative exchange factors on a uniform rectangular grid.

A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order rational elliptic form solutions to obtain approximate solutions of two nonlinear oscillators. At the end of the paper, we compare the numerical integration values of the angular frequencies with approximate solution results, based on the proposed rational elliptic balance method. © 2010 Elsevier Ltd. All rights reserved.

In this work, we derive approximate semi-analytical solutions of the steady, creeping, weakly compressible plane and axisymmetric Poiseuille flows of a Herschel-Bulkley fluid. Since the flow is weakly compressible, the radial velocity component is assumed to be zero and the derivatives of the axial velocity with respect to the axial direction are assumed to be much smaller than those with respect to the radial direction. The axial velocity is then given by an expression similar to that holding for the incompressible flow, the only difference being that the pressure-gradient is a function of the axial coordinate and satisfies a non-linear equation involving the density of the fluid. In the present work, a linear as well as an exponential equation of state, relating the density of the fluid to the pressure, are considered. The pressure distribution along the flow direction is calculated by means of numerical integration and the two-dimensional axial velocity can then be constructed. The effects of compressibility, the equation of state, the Bingham number and the power-law exponent on the solutions are investigated. © 2008 Elsevier B.V. All rights reserved. 158 1-3 162 169 Cited By :13

This contribution presents the kinetostatic analysis of a spatial compliant mechanism actuated by three Shape Memory Alloy (SMA) wire actuators. This mechanism exploits both shape memory and superelastic effects of SMA actuators. The moving platform of the mechanism is mounted on a pillar made of superelastic SMA and its mobility is obtained from the large deflection of the pillar by the selective actuation of any one or two wires in differential manner. The deflection expressions obtained are basically force-displacement kinematic relationships, derived after incorporating follower forces and variable moments developed by the actuators. Two sets of geometric parameters, related to deflected and undeflected conditions, have been utilized to solve the coupled relationship between the force developed by the SMA actuation and the force required for the elastica deflection. The deflection expressions are solved using Romberg integration method and the numerical results obtained have been validated by comparing them with those obtained from FEM simulation. The results show that, for the design of compliant mechanisms exhibiting large displacements the force-displacement relationships in linear form, as applicable to small deflections, are no longer valid.