M.N. Hamdan

An approach to study the effects of tool geometry on the primary chatter vibration in orthogonal cutting

Abstract The effects of tool rake and flank clearance angles on the stability of self-excited primary chatter vibration in high-speed dry orthogonal turning process are experimentally and analytically investigated. The analytical study of the problem is based on the assumptions that the frictional forces on the rake and the flank faces are proportional to the tool-work interface contact area and that the physical relationships established in steady state cutting can be applied to dynamic cutting. The experimental and analytical results indicate that a larger rake angle as well as a larger flank angle increases the stability of vibration. The results also reveal that the excitation energy is provided by the friction force on the flank surface and the cutting force acting on the tool rake.

Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia

Abstract The free and forced vibrations of a uniform beam elastically restrained against rotation at one end and against translation at the other end, and carrying a lumped mass with rotary inertia and external loading at an arbitrary intermediate point, are analyzed. The analysis involves solving the exact eigenvalue problem for the base beam to obtain the exact mode shape functions which account for the effects of the elastic restraints at the beam ends. These mode shape functions are then used in conjunction with Galerkins method, with the lumped mass and rotary inertia treated as applied loads, to obtain the approximate eigenvalue parameters and resonance response of the beam-mass system. Parametric studies are carried out to investigate the effects of the stiffness of elastic restraints, and location and magnitude of the lumped mass and rotary inertia on the eigenfrequency parameters and resonance response of the beam-mass system. Partial computational results are compared with existing data: the agreement is generally good. For convenience, the results are presented in dimensionless form.

Wavelet and chaos analysis of flow induced vibration of a single cylinder in cross-flow

Abstract This paper attempts to shed some light on the characteristics of the flow induced vibration of an elastically mounted single cylinder in a cross flow using the newly developed joint time–frequency analysis techniques (JTFA) and in particular the modulated Gaussian wavelet. More specifically, the modulated Gaussian wavelet is chosen in the current work, since it was shown in [1] to be more effective than other well known wavelets in analysing the flow induced vibrations of a single cylinder similar to the one under consideration. In the current work, this wavelet shows good evidence that the flow induced vibration process, in the range of system parameters considered, is most likely to undergo nonstationary, nonlinear and chaotic dynamics. It is found that for certain values of system parameters the nonlinearity may lead the system into chaos. Phase plane portraits, Poincare maps and fractal dimensions have been used to confirm the chaotic behavior of the response of the system under investigation.

Analysis of forced non-linear undamped oscillators by a time transformation method

The recently developed time transformation method [1–3] is extended to the analysis of forced vibration of the strongly non-linear undamped oscillator, u+u+ef(u)=P(t) , where f(u) is a non-linear function of the displacement u(t) and e is not necessarily small. Two types of external loading P(t) are considered: a step input and a simple harmonic input. The frequency-amplitude relation is obtained through a slight modification of the results developed in reference [2] for the unforced oscillator. A comparison with the results of numerical and other analytic methods is made. It can be deduced that the time transformation approach offers simple and accurate approximations for the oscillators considered.

On the primary frequency response of strongly non-linear oscillators : a linearization approach

Abstract The problem considered is the primary frequency response of the class of strongly non-linear forced oscillators u + 2η u + mu + eg(u) = P cos (Ωt) , whee g(u) is an odd non-linear function of the displacement u(t), e may be arbitrarily large, and m = −1, 0 or +1. A simple approximation to the fundamental harmonic of the response is obtained by first linearizing the static terms using the frequency relations developed in reference [1] for the autonomous conservative oscillator and then using the averaging method to solve the linearized forced problem. A comparison with the numerical and other approximate analytic methods results is made, which shows the advantages of the present technique in terms of computational effort and accuracy.