Saturation phenomena and nonlinear resonances of rotating pretwisted laminated composite blade under subsonic air flow excitation
TL;DR: In this paper, the saturation and the jumping phenomena between the torsional vibration mode and the bending vibration mode are investigated for a rotating cantilever plate under the subsonic air flow force.
About: This article is published in Journal of Sound and Vibration.The article was published on 2020-07-21. It has received 40 citations till now. The article focuses on the topics: Plate theory & Torsional vibration.
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TL;DR: In this paper, the flutter analysis of a rotating pre-twisted GPLRC blade under supersonic airflow is investigated, and the performance of the IMLS-Ritz method for this problem is validated by comprehensive convergence studies and careful comparison studies.
Abstract: In this study, the flutter analysis of a rotating pre-twisted functionally graded graphene nanoplatelets reinforced composite (FG GPLRC) blade under supersonic airflow is investigated. The pre-twisted blade is multi-layered and reinforced with graphene nanoplatelets (GPLs) evenly distributed in each layer while the GPL weight fraction changes from layer to layer through the thickness direction. The effective Young's modulus is determined by Halpin-Tsai micromechanical model while the Poisson's ratio and mass density are predicted by Voigt's rule for GPLRC layers. According to assumptions of the first-order shear deformation theory (FSDT), the first-order piston theory and shell theory, the dynamic model of rotating pre-twisted GPLRC blades subjected to supersonic flow is developed. Meshless the improved moving least-square Ritz method (IMLS-Ritz) is used to derive the discrete dynamic equations of rotating pre-twisted GPLRC blades under aerodynamic load. The accuracy of the IMLS-Ritz method for this problem is validated by comprehensive convergence studies and careful comparison studies. A detailed parameter investigation of the effects of GPL distribution configuration, rotation velocity and geometrical parameters on flutter behavior characteristics of GPLRC blades is systematically conducted.
36 citations
TL;DR: In this article, the primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns.
Abstract: The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns The FGGP-reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet It is novel to simplify the leakage of the airflow in the tip clearance to the non-uniform axial excitation The rotating speed of the steady state adding a small periodic perturbation is considered The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation Utilizing the first-order shear deformation theory, von Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations The primary resonance and nonlinear dynamic behaviors of the FGGP-reinforced rotating pretwisted composite cantilever plate are analyzed by Runge–Kutta method The amplitude–frequency response curves, force–frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations
26 citations
TL;DR: In this article, the authors investigated the complex nonlinear vibrations and internal resonance of the rotating blade subjected to the aerodynamic force, which is simplified to a pretwisted rotating cantilever rectangular plate with the varying cross-section and varying rotating speed.
25 citations
TL;DR: In this paper, the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment were dealt with.
Abstract: This paper deals with the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment. The imperfect beam contains different modes of geometric imperfections such as sine, global, and local modes, and it is restrained by an elastic root. Three types of CNTs distributions including FG-X, UD, and FG-O distributions are considered and the material is temperature-dependent. First, bending–bending coupled governing equations are established through the Hamilton’s principle based on the Euler–Bernoulli beam theory. By setting different parameters, the governing equations can solve the problems of free vibration, buckling, and dynamic stability of the beam. Then, the differential quadrature method (DQM) is employed to get the discrete equations and numerical solutions of the natural frequency, critical buckling load, and instability region. Finally, parametric studies are carried out to present the effects of hub radius, rotating speed, material properties, geometric imperfections, and rigidity of the elastic root on the natural frequencies, critical buckling load, and instability regions. Results show that the elastic root and imperfection mode have obvious influence on the instability regions.
16 citations
TL;DR: In this article, the primary resonances of a pre-deformed rotating beam model including the quadratic and cubic nonlinearities are investigated in the presence of the 3:1 internal resonance.
Abstract: The primary resonances of a pre-deformed rotating beam model including the quadratic and cubic nonlinearities are investigated in the presence of the 3:1 internal resonance. The steady state responses of the beam are analyzed in two cases of the primary resonance with the method of multiple scales. The original dynamic equation is integrated numerically in two frequency sweep directions. The theoretical results are consistent with those obtained in the numerical simulation. The contributions of quadratic nonlinearities and cubic nonlinearities to the primary resonances behavior of the rotating beam are clarified. The frequency response curves are discussed by considering different model parameters such as the thermal gradient, the rotating speed, the damping coefficient and the gas pressure. The stability regions of coupled mode solutions are compared between the models with different nonlinearities in the case of the primary resonance of the second mode. A series of interesting findings are presented.
13 citations
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TL;DR: In this paper, an analysis is presented for the nonlinear coupling of the pitch and roll modes of ship motions in regular seas when their frequencies are in the ratio of two to one.
Abstract: An analysis is presented for the nonlinear coupling of the pitch (heave) and roll modes of ship motions in regular seas when their frequencies are in the ratio of two to one. When the frequency of encounter (excitation frequency) is near the pitch frequency, the pitch mode is excited if the encountered wave amplitude (excitation amplitude) is small. As the excitation amplitude increases, the amplitude of the pitch mode increases until it reaches a critical small value. As the excitation amplitude increases further, the pitch amplitude does not change from the critical value (i.e., the pitch mode is saturated), and all of the extra energy is transferred to the roll mode. Thus, for large excitation amplitudes, the amplitude of the roll mode is very much larger than that of the pitch mode. When the excitation frequency is near the roll frequency, there is no saturation phenomenon and at close to perfect resonance, there is no steady state response in some cases. The present results indicate that large roll amplitudes are likely in this case also.
254 citations
TL;DR: In this article, an analysis on the nonlinear dynamics and chaos of a simply supported orthotropic functionally graded material (FGM) rectangular plate in thermal environment and subjected to parametric and external excitations is presented.
Abstract: In this paper, an analysis on the nonlinear dynamics and chaos of a simply supported orthotropic functionally graded material (FGM) rectangular plate in thermal environment and subjected to parametric and external excitations is presented. Heat conduction and temperature-dependent material properties are both taken into account. The material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on the Reddy’s third-order share deformation plate theory, the governing equations of motion for the orthotropic FGM rectangular plate are derived by using the Hamilton’s principle. The Galerkin procedure is applied to the partial differential governing equations of motion to obtain a three-degree-of-freedom nonlinear system. The resonant case considered here is 1:2:4 internal resonance, principal parametric resonance-subharmonic resonance of order 1/2. Based on the averaged equation obtained by the method of multiple scales, the phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the orthotropic FGM rectangular plate. It is found that the motions of the orthotropic FGM plate are chaotic under certain conditions.
154 citations
TL;DR: In this paper, the authors investigated the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs).
144 citations
TL;DR: In this article, a comprehensive review of articles about rotating composite beams and blades is presented, which addresses analytical, semi-analytical and numerical studies dealing with dynamical problems involving adaptive/smart/intelligent materials (e.g., piezoelectric materials, electrorheological fluids, shape memory alloys, etc.), damping and vibration control, advanced composite materials, complicating effects and loadings, and experimental methods.
Abstract: Rotating composite beams and blades have a wide range of applications in various engineering structures such as wind turbines, industrial fans, and steam turbines. Therefore, proper understanding of such structures is of a great importance. As a result, the behavior of rotating composite beam structures has received a lot of attention. This paper presents a comprehensive review of scholarly articles about rotating composite beams as published in the past decades. The review addresses analytical, semi-analytical and numerical studies dealing with dynamical problems involving adaptive/smart/intelligent materials (e.g. piezoelectric materials, electrorheological fluids, shape memory alloys, etc.), damping and vibration control, advanced composite materials (e.g. functionally graded materials and nanocomposites), complicating effects and loadings (e.g. added mass, tapered beams, initial curve and twist, etc.), and experimental methods. Moreover, the influence of Vlasov or restrained warping, out-of-plane warping, transverse shear, arbitrary cross-sectional geometry, trapeze phenomena, swept tip, size-dependent effect, as well as other areas that have been considered in research, are reviewed in depth. The review concludes with a presentation of the remaining challenges and future research needs.
136 citations