scholarly journals A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Issam El Hantati ◽  
Ahmed Adri ◽  
Hatim Fakhreddine ◽  
Said Rifai ◽  
Rhali Benamar
Keyword(s):  
Approximate Method ◽  
Forced Vibration ◽  
Algebraic System ◽  
Strain Energy ◽  
Dynamic Behaviour ◽  
Forced Vibrations ◽  
Geometrical Parameters ◽  
Geometrically Nonlinear ◽  
Free And Forced Vibrations ◽  
Nonlinear Algebraic System

The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation.

The Effect of Geometry on Harmonically Varied Helix Milling Tools

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Markel Sanz ◽  
Alex Iglesias ◽  
Jokin Munoa ◽  
Zoltan Dombovari
Keyword(s):  
Algebraic System ◽  
Point Of View ◽  
Geometrical Parameters ◽  
Stability Properties ◽  
Edge Geometry ◽  
Variable Helix ◽  
Nonlinear Algebraic System ◽  
The Stability ◽  
Milling Tools ◽  
Equivalent Description

Abstract Two different kinds of descriptions for edge geometry of harmonically varied helix tools are studied in this work. The edge geometries of the so-called lag and helix variations are used in this paper, and their equivalency is established from engineering point of view. The equivalent relation is derived analytically and the nonlinear algebraic system is described, with which the numerical equivalency properties can be determined. The equivalent description can be utilized in variable helix tool production to determine an optimized set of geometrical parameters of the edge geometry. The stability properties are shown and compared for a simple one degree-of-freedom case with the nonuniform constant helix tools. The robustness of the results related to the harmonically varied tools is critically discussed in this paper showing advantages compared to the nonuniform constant helix case. The results suggest that the more extreme the edge variation is, the more stable the process performed with the corresponding harmonically varied tool becomes.

scholarly journals Geometrically nonlinear free and forced vibrations of Euler-Bernoulli multi-span beams

2018 ◽  
Vol 211 ◽  
pp. 02001 ◽  
Author(s):  
Hatim Fakhreddine ◽  
Ahmed Adri ◽  
Saïd Rifai ◽  
Rhali Benamar
Keyword(s):  
Algebraic System ◽  
Single Mode ◽  
Forced Vibrations ◽  
Nonlinear Frequency ◽  
Bending Vibration ◽  
End Conditions ◽  
Nonlinear Frequency Response ◽  
Simple Support ◽  
Beam Bending ◽  
Nonlinear Algebraic System

The objective of this paper is to establish the formulation of the problem of nonlinear transverse forced vibrations of uniform multi-span beams, with several intermediate simple supports and general end conditions, including use of translational and rotational springs at the ends. The beam bending vibration equation is first written at each span and then the continuity requirements at each simple support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. The formulation is based on the application of Hamilton’s principle and spectral analysis to the problem of nonlinear forced vibrations occurring at large displacement amplitudes, leading to the solution of a nonlinear algebraic system using numerical or analytical methods. The nonlinear algebraic system has been solved here in the case of a four span beam in the free regime using an approximate method developed previously (second formulation) leading to the amplitude dependent fundamental nonlinear mode of the multi-span beam and to the corresponding backbone curves. Considering the nonlinear regime, under a uniformly distributed excitation harmonic force, the calculation of the corresponding generalised forces has led to the conclusion that the nonlinear response involves predominately the fourth mode. Consequently, an analysis has been performed in the neighbourhood of this mode, based on the single mode approach, to obtain the multi-span beam nonlinear frequency response functions for various excitation levels.

scholarly journals Geometrically nonlinear free and forced vibrations analysis of clamped-clamped functionally graded beams with multicracks

2018 ◽  
Vol 211 ◽  
pp. 02002 ◽  
Author(s):  
Mohcine Chajdi ◽  
Ahmed Adri ◽  
Khalid El bikri ◽  
Rhali Benamar
Keyword(s):  
Volume Fraction ◽  
Geometrical Nonlinearity ◽  
Beam Theory ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Cracked Beam ◽  
Free And Forced Vibrations ◽  
Wide Range ◽  
Rotational Spring Model

Geometrically nonlinear free and forced vibrations of clampedclamped Functionally Graded beams with multi-cracks, located at different positions, based on the equivalent rotational spring model of crack and the transfer matrix method for beams is investigated. The FG beam properties are supposed to vary continuously through the thickness direction. The theoretical model is based on the Euler-Bernoulli beam theory and the Von Karman geometrical nonlinearity assumptions. A homogenization procedure, taking into account the presence of the crack, is developed to reduce the problem examined to that of an equivalent isotropic homogeneous multi-cracked beam. Upon assuming harmonic motion, the discretized expressions for the total strain and kinetic energies of the beam are derived, and through application of Hamilton’s principle and spectral analysis, the problem is reduced to a nonlinear algebraic system solved using an approximate explicit method developed previously (second formulation) to obtain numerically the FG multi-cracked beam nonlinear fundamental mode and the corresponding backbone curves for a wide range of vibration amplitudes. The numerical results presented show the effect of the number of cracks, the crack depths and locations, and the volume fraction on the beam nonlinear dynamic response.

Torsional Vibrations of a Multi-Rotor System Having a Non-Linear Flexible Coupling

1957 ◽  
Vol 61 (563) ◽  
pp. 779-781
Author(s):  
S. Mahalingam
Keyword(s):  
Forced Vibration ◽  
Elastic Characteristic ◽  
Approximate Solutions ◽  
Forced Vibrations ◽  
Rotor System ◽  
Torsional Vibrations ◽  
Flexible Coupling ◽  
Free And Forced Vibrations ◽  
Non Linear ◽  
Nonlinear Elastic

The free and forced vibrations of a multi-rotor system where one section of the shaft has a nonlinear elastic characteristic are considered in this paper. For any frequency of steady vibration the system is reduced to an equivalent rotor at either end of the nonlinear section. The vibrations at all points are assumed to be one-term approximate solutions and the amplitudes of steady forced vibration are determined by a method outlined by the author in an earlier paper.

Vibration Behaviour of a Disc Assembly with a Cracked Lacing Wire

2005 ◽  
Vol 293-294 ◽  
pp. 451-458
Author(s):  
Dariusz Szwedowicz ◽  
Carlos Acosta ◽  
Jorge Bedolla ◽  
Eladio Martinez
Keyword(s):  
Static Analysis ◽  
Dynamic Behaviour ◽  
Forced Vibrations ◽  
Rotating Disc ◽  
Nodal Diameter ◽  
Free And Forced Vibrations ◽  
Resonance Frequencies ◽  
Turbine Disc ◽  
Experimental Tool ◽  
Timing Measurement

In this paper, mathematical descriptions of the static and dynamic behaviour of the bladed disc with the undamaged and damaged lacing wire are briefly explained. For a steam turbine disc with 70 axial blades coupled by the lacing wire, the centrifugal static analysis is performed. Then, the free and forced vibrations are computed to find differences in vibrations of the bladed disc with and without a failure in the lacing wire. The tip timing measurement is considered as an experimental tool for identifications of possible failures. According to the obtained FE results, a failure of the lacing wire in the rotating disc assembly can be identified by monitoring the centrifugal deformations of the blade tips, resonance frequencies and response amplitudes of the whole bladed disc. The dynamic behaviours of the failure-free disc and with cracked wire connection are compared to each other to outline differences in the known nodal diameter and dispersion curve definition.

scholarly journals Linear and geometrically nonlinear free and forced vibrations of fully clamped multi-cracked beams

Diagnostyka ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Mohcine Chajdi ◽  
Ahmed Adri ◽  
Khalid El bikri ◽  
Rhali Benamar
Keyword(s):  
Forced Vibrations ◽  
Geometrically Nonlinear ◽  
Free And Forced Vibrations ◽  
Cracked Beams

Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction

2003 ◽  
Vol 56 (4) ◽  
pp. 349-381 ◽  
Author(s):  
Marco Amabili ◽  
Michael P. Paı¨doussis
Keyword(s):  
Cylindrical Shells ◽  
Fluid Structure Interaction ◽  
Harmonic Excitation ◽  
Forced Vibrations ◽  
Geometrically Nonlinear ◽  
Flowing Fluid ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Free And Forced Vibrations ◽  
Circular Cylindrical Shells

This literature review focuses mainly on geometrically nonlinear (finite amplitude) free and forced vibrations of circular cylindrical shells and panels, with and without fluid-structure interaction. Work on shells and curved panels of different geometries is but briefly discussed. In addition, studies dealing with particular dynamical problems involving finite deformations, eg, dynamic buckling, stability, and flutter of shells coupled to flowing fluids, are also discussed. This review is structured as follows: after a short introduction on some of the fundamentals of geometrically nonlinear theory of shells, vibrations of shells and panels in vacuo are discussed. Free and forced vibrations under radial harmonic excitation (Section 2.2), parametric excitation (axial tension or compression and pressure-induced excitations) (Section 2.3), and response to radial transient loads (Section 2.4) are reviewed separately. Studies on shells and panels in contact with dense fluids (liquids) follow; some of these studies present very interesting results using methods also suitable for shells and panels in vacuo. Then, in Section 4, shells and panels in contact with light fluids (gases) are treated, including the problem of stability (divergence and flutter) of circular cylindrical panels and shells coupled to flowing fluid. For shells coupled to flowing fluid, only the case of axial flow is reviewed in this paper. Finally, papers dealing with experiments are reviewed in Section 5. There are 356 references cited in this article.

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