1,721,103 research outputs found
Nonlinear warping effects on the flexural-torsional behavior of a thin-walled open cross-section beam
No full textFlexural-torsional behavior of beams both in static and dynamics has been the subject of several papers in the recent past. In [1] flexural-torsional couplings in the motion of a cantilever beam was considered, limiting the model to linear warping. An approach based on the extension of the Vlasov theory to the nonlinear field is found in [2]; however, due to the complexity of the problem, several simplifying assumptions have been used. More recently in [3] the description of the mechanical behaviour of beams with open cross-sections is dealt with in a rigorous manner by extending in nonlinear field the Vlasov theory. The nonlinear effects of the torsional curvature on the elongation of the longitudinal fibers and the nonlinear warping of the section are considered. The model obtained is very complex and missing any possibility of recognizing the mechanical meaning of the different numerous terms.
With the aim to study cases in which the torsional curvature is prevailing with respect to the flexural ones, the model in [3] has been specialized to describe the behavior of a cantilever beam and in particular with a monosymmetric cross-section. The simplified equations make it possible to stress the role of the nonlinear terms due to nonlinear warping and torsional elongation of the longitudinal fibers. The attention is focused on the response to static forces and on the stability of the equilibrium branches. Analytical results are compared with results of different nonlinear FE models and mainly with experimental results. Numerical and experimental investigation confirms the importance of the new nonlinear contributions and permits to validate the model developed [3].
In particular the model furnishes values of critical loads in flexural-torsional stability that the classical nonlinear one-dimensional beam models are not able to describe correctly. From a technical point of view it has been shown that the literature results for the critical loads are very far from the results obtained by means of the refined model proposed. In one case – flexural torsional buckling along symmetry cross section axis – is almost double the correct one, i.e. not in favour of safety. In another case - flexural torsional buckling along no symmetry axis – is almost half the correct one, in favour of safety.
References
[1] Crespo da Silva, M.R.M., Glynn, C.C., 1978. Nonlinear flexural-flexural-torsional dynamics of inextensional beams. - I. Equations of motion'. J. Struct. Mech.. 6(4), 437-448.
[2] Ghobarah, A.A., Tso, W.K., 1971. A non-linear thin-walled beam theory. Int. J. Mech. Sci. 13, 1025-1033.
[3] Di Egidio, A., Luongo, A., Vestroni, F., 2003. A nonlinear model for open cross-section thin-walled beams - Part I: Formulation. Int. J. Non-Linear Mech.. 38(7), 1067-1081
Structural dynamic identification and damage detection
No full textDynamic methods are a powerful tool for studying the behaviour of existing structures and their health conditions. The practical application, however, often raises subtle questions related to the accuracy and completeness of experimental data, the complexity of the mechanical modelling and, ultimately, the inverse nature of the problems that leads to ill-conditioning and non-uniqueness. This chapter addresses some of these aspects, and presents a short overview of the topic, with particular emphasis on dynamic structural identification and damage detection
Post-critical response of an axially moving beam
No full textIn this paper the dynamic response of a simply supported traveling beam, subjected to a pointwise transversal load, is investigated. The motion is described by means of a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities obtained through the Galerkin method. The system is studied in the super-critical speed range with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability, and direct simulations of global postcritical dynamics. In the supercritical speed range a regular motion around bifurcated equilibrium position becomes chaotic for particular values of frequency and force. The bifurcation diagram for varying force intensity is shown, it can be noticed that a chaotic motion occurs in a wide range of the forcing parameter, co-existiig with a 3T periodic solution in a limited window
Mitigation of structural vibrations by hysteretic oscillators in internal resonance
No full textThe present paper deals with the dynamics of a two-degrees-of freedom system consisting of a nonlinear absorber attached to a primary linear structure under external excitations. The nonlinear attachment exhibits a hysteretic restoring force modeled with the classic Bouc–Wen law [hysteretic vibration absorber (HVA)]; furthermore, the mechanical characteristics of the nonlinear oscillator are tuned to regulate the ratio between the two natural frequencies and to lead the system near to internal resonance conditions. The steady-state periodic solutions are investigated, and particular attention is given to the study of modal interactions by means of frequency response curves for various excitation levels. A parametric investigation is performed to analytically detect the conditions for the occurrence of (n : 1) internal resonances for low and high external excitations. Finally, specific resonance conditions have been found under which the nonlinear attachment produces a notable reduction of the vibration amplitude of the primary system for a wide range of the excitation level. The aim of the paper is therefore twofold: the first purpose is to investigate the effect of the hysteretic damping on the passive mitigation of structural vibrations. The second purpose is to improve the system capacity of mitigating structural vibrations, by optimally choosing the characteristics of the HVA
Post-critical dynamics of an axially moving beam
No full textIn the present paper, the dynamic behaviour of a beam subjected to an axial transport of mass is analyzed. The Galerkin method has been used to discretize the problem; a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and supercritical speed ranges with emphasis on the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning linear subcritical behaviour, static bifurcation analysis including linear stability and direct simulation of global postcritical dynamics
The role of the hysteretic restoring force on modal interactions in nonlinear dynamics
No full textHysteretic behaviour characterizes elements of a wide class of mechanical systems: the dependence of their restoring force on the deformation history has a great influence on the dynamic response. For this reason, an increasing interest has been registered in the study of typical phenomena of nonlinear dynamics, also because hysteresis belongs to the class of strong nonlinearities. The paper is devoted to the analysis of the modification of the response of two degrees-of-freedom chain systems due to the characteristics of the restoring force of a hysteretic element; attention is given to its dissipation characteristic, comparing the cases of full and reduced hysteresis. With increasing excitation amplitude, the strong hysteretic nonlinearity modifies the nonlinear frequencies and in turn their ratio, easily leading to internal resonance conditions. For a system close to a 3:1 resonance condition, the modification of the frequency response curves (frcs) for increasing excitation intensity is illustrated and compared with the response of similar systems not in internal resonance. The general trend of the phenomena is slightly qualitatively influenced by the dissipation property, whereas the quantitative differences are notable. The only evident difference is the presence of a frequency range of coexisting solutions in the case of reduced hysteresis. In both cases, after a bifurcation a novel mode arises around the first resonance, with similar frequency and different shape. The case of reduced hysteresis makes it possible to better investigate the evolution of nonlinear modes of a system, close to the Hamiltonian system embedded by the actual dissipative one. The occurrence of this novel mode, peculiar of systems with strong nonlinearities, is responsible of a substantial transfer of energy between the two modes in internal resonance conditions. Finally, an example of quasiperiodic oscillations is presented to show one of the other possible scenarios which arise even in the presence of significant dissipation
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