•Nonlinear oscillations of unbalanced asymmetric thin-walled composite shafts.•Simultaneous resonance due to coexisting of unbalanced force and the asymmetry.•Stability of the parametrically excited ...shafts under stretching nonlinearity.•Considering nonlinear and gyroscopic couplings using Euler's angles.•Validating results by comparing them with experimental results of previous studies.
The combined effects of asymmetry and geometrical nonlinearity have a serious effect on the stability of composite shafts. These effects, that should be given special attention in the designing of these structure, are revealed in this study. The asymmetry of the shaft is modeled with a rectangular cross-section that makes the shaft transverse stiffness in one plane to differ from the other. This in effect, manifests itself as a parametric excitation of the system. Moreover, the analysis also considers the large lateral amplitude that can produce geometric nonlinearity and stretching of the system. Parametrically excited equations of the motion are obtained by considering the Euler's angles, the anisotropic properties of the constituent material, and employing the extended Hamilton's principle. Non-classical effects such as gyroscopic moment, rotary inertia, and nonlinear couplings due to stretching are also taken into account. However, because of the thin-walled features of the system, the shear deformations and warping effects are ignored. After discretizing the resulting equations, they are solved by employing the method of multiple scales (MMS). To justify/evaluate the proposed model's accuracy, several comparisons are made with various authentic results in the literature. In addition, to verify the results of the MMS solutions, numerical analyses are used based on the Runge-Kutta method. The effects of damping, eccentricity, and asymmetry were examined on the stability of the system. The illustrated results indicated the occurrence of hardening nonlinearity in the system. It was proved that when the rotational speed was in the neighborhood of forward frequency, despite the presence of nonlinear couplings in the equations, axial and torsional vibrations would not be excited. Furthermore, although the asymmetry affected the amplitude and phase of the system, it did not change the frequency of the vibrations and the type of bifurcation. With a fairly good balance, the unstable response of the asymmetric shaft could be easily eliminated, while even an accurate balance could not eliminate the unstable response of the asymmetric one.
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Parametric resonance may occur when the composite shaft is subjected to periodic axial loads. The phenomenon will lead to the serious destruction of the dynamic system. In this study, we aim to ...investigate the parametric instability characteristics of rotating composite shafts considering internal damping, and to provide valuable theoretical guidelines for avoiding the occurrence of parametric resonance. The two dynamic models of the composite rotor in the inertial frame and rotating frame are both established using Hamilton's principle. The governing equations of the composite rotor are reduced into a system of Mathieu–Hill equations by means of the Galerkin method. Then Floquet exponent method is employed to conduct parametric stability analysis of the periodic loaded composite rotor. After performing validation of present model and method, numerical results are presented to bring out the influences of reference frame, rotation speed, internal damping and lamination angle on the parametric instability region. The results show that the selection of reference frame does not affect the determination of the size and type of the parametric instability region. However, it is more suitable to use the rotating frame from the perspective of determining the type of the unstable region. The internal damping of composites should not be ignored when analyzing the parametric stability of composite rotors, especially for the high order excitation frequency.
The composite shaft has been widely applied to many fields such as aerospace and automotive industries due to its excellent engineering properties. The accurate dynamic analysis of composite shaft, ...which is of great importance for the stable operation of high speed-rotating machine, however, is relatively complex due to the anisotropic properties of composite material. In this study, the dynamic behavior of composite shaft that considers the laminate coupling effect is investigated. At first, a simplified homogenized beam theory (SHBT) is modified so as to take account of the essential properties of composite material such as Poisson's effect and the bending-twisting coupling effect in addition to the transverse shear deformation, the gyroscopic effect and the rotational inertia. Then a homogeneous finite element-beam model with 10 degrees of freedom and without internal damping is introduced as the study object to compare the proposed method and equivalent modulus beam theory (EMBT), the modified EMBT, SHBT and ABAQUS. The results by the modified SHBT are consistent with those obtained by different theories. In conclusion, the proposed method can be effectively applied to the dynamic analysis of composite shaft.
Nonlinear geometries and cross-sectional asymmetry can be among the most critical contributing factors affecting the performance and stability of composite shafts. The influence of these factors, ...which should be devoted to particular attention in the design of these systems and have not been investigated yet, are evaluated analytically in this study. The shaft is simply supported, made of orthotropic multi-layers, and spinning at a constant speed. To express the nonlinear system’s behavior, which is due to the large amplitude of the vibrations, it is assumed that the shaft is under the stretching assumption. Moreover, a rectangular cross-section is used to model the asymmetry that results in parametric excitation in the system. To accurately investigate the behavior of composite material, an optimal lay-up is employed. The gyroscopic coupling is included because of Rayleigh beam theory, and Euler’s angles are employed to achieve the angular velocities. The analytical study of the parametrically excited system, obtained by the method of multiple scales, is performed in two categories of resonant and nonresonant cases. In the nonresonant case, the analytical investigation suggests that the asymmetric shaft behaves like a symmetric one therefore, the parametric excitations do not have a significant impact. This claim is confirmed by numerical results. Also, the presence of the gyroscopic coupling and hollowness of the shaft causes the beating phenomenon in the system. However, in the resonant case, the presence of parametric excitation plays a pivotal role. The results also show that under certain conditions and despite the presence of damping, asymmetric balanced rotors can have a nontrivial stable amplitude. This response exists as long as the parametric excitation effects dominate the damping effects. Although damping reduces the vibrations’ amplitude, it can improve the stability of the system and eliminates unstable responses. Furthermore, the time response and frequency response curve of the system is carefully evaluated for various geometric design parameters and operation speed. Depending on the operating speed, the system can experience supercritical or subcritical pitchfork bifurcation. In addition, a detailed description of the system’s Campbell’s diagram, damping effect, and bifurcation is provided. Furthermore, it is proved that internal resonance cannot occur in the system. The accuracy of the analytical responses of the resonant case is compared with numerical ones. Stability of trivial and nontrivial responses is discussed in the time response and phase portrait of the system simultaneously. Finally, in the undamped system, multi-frequency responses are appeared as homoclinic and heteroclinic closed orbits.
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•Analytical study of parametric resonance in asymmetric gyroscopic composite shafts.•The stability of the resonant and nonresonant cases due to the parametric excitation.•The beating phenomenon due to the proximity of the forward and backward frequencies.•Supercritical and subcritical pitchfork bifurcations in the primary resonance.•Homoclinic and Heteroclinic orbits on the phase portrait of the undamped system.
Composite cylinders to be used as half shafts must satisfy several requirements, such as critical speed, critical buckling torque, and load carrying ability. This study focused on the investigation ...of carbon fiber reinforced epoxy composite cylinders produced by filament winding to be used as half shafts. A preliminary torsional test in a ±455 cylinder was performed and three other laminates were chosen for the study: ±22/±45, ±89/±45, and ±45/±45. Radial and longitudinal compression tests were performed. Mechanical analysis has been carried out using analytical and numerical approaches, and good correlation was found between them and the experimental values. The ±45/±45 cylinder showed the best performance under torsional loading, as expected, as well as radial and longitudinal compression, but not critical buckling torque.
In the aerospace and automotive applications driveshafts are manufactured using fiber reinforced composite materials. Compared to a conventional metallic driveshaft, a composite driveshaft gives ...higher natural frequencies and critical speeds, and lower vibration. They are also lightweight structures, especially when they are tapered. The design of the driveshaft is based on its fundamental natural frequency, and tapering the driveshaft can substantially improve the value of this natural frequency. In this study, the vibration analysis of the tapered composite driveshaft is carried out using the hierarchical finite element formulation, and for this purpose, the Timoshenko beam theory is used. In addition, the effects of rotary inertia, transverse shear deformation, gyroscopic force, axial load, coupling due to the lamination of composite layers, and taper angle are incorporated in the hierarchical finite element model. The potential energy and the kinetic energy of the tapered composite shaft are obtained, and then the equations of motion are developed using Lagrange’s equation. The finite element solution is validated using the approximate solution based on the Rayleigh-Ritz method. A comprehensive parametric study is conducted based on the hierarchical finite element formulation.
Long fibre-reinforced metal matrix composite materials, which are widely used in industry, have complex and diverse damage modes due to their structural characteristics. In this study, the ...progressive damage process and failure mode analysis of the SiCf/TC4 composite shafts were thoroughly investigated under single torsional loads. A bearing performance test was carried out, the damage process was monitored using acoustic emissions, and the fracture specimens were analysed using a scanning electron microscope (SME). More specifically, under reverse torque loading, the damage process was slow-varying, the interface was subjected to tensile force, and fracture occurred mostly in the form of interface cracking; further, the breaking load of the specimen was 11,812 Nm. Under forward loading, the damage process was fast-varying. The fibres were subjected to tensile forces, and the fracture form was mostly fibre fracture; the breaking load of the specimen was 10,418 Nm. Under torque loading, the first damage to the specimens appeared in the outermost layer of the composite material’s reinforced section, and the initial cracking position was at the interface, expanding from the outside to the inside. Based on the principles of macro-mechanics and micro-mechanics theory, the cross-scale models were proposed, which contain the shaft with the same dimensions as the specimen and a micro-mechanics representative volume element (RVE) model. The initial interface damage load was 6552 Nm under reverse torque loading. Under forward loading, the initial interface damage load was 9108 Nm. In comparison to the acoustic emission test results, the main goal was to calculate the progressive damage process under the same conditions as the experiment, verifying the effectiveness of the cross-scale models.
In this paper, the internal resonance phenomena of a composite shaft-disk system with multi-degrees-of-freedom are analyzed. The force caused by the unbalanced mass of the disk is considered as an ...external excitation force. The shaft is simply supported. Shear deformation and gyroscopic effects are considered. The strain–displacement relationship of the shaft element is expressed using the Timoshenko beam theory. Each node has 5 degrees of freedom. SHBT (simplified homogenized beam theory) is applied to calculate the stiffness of the composite shaft. WQEM (weak form quadrature element method) is used to construct the element matrices, and the system matrices are established using the element matrix assembly rule of the FEM (finite element method). The reduced-order model is applied to reduce the calculation time. IHB (incremental harmonic balance) method is utilized to solve the nonlinear equations of motion of the composite shaft-disk system. The nonlinear vibration characteristics of the Jeffcott rotor are analyzed using the proposed method and compared with the results of previous researches, and the results are very similar. Based on these considerations, the nonlinear vibration phenomena of the composite shaft-disk system with multi-degrees-of-freedom are considered at the several resonance points.
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