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• A comprehensive stiffness model of intermediate bearing is presented. • A reduced model of dual rotor-bearing-casing coupling system is developed. • The effects of typical parameters on the vibration of the system are discussed. • The mechanism of the comprehensive stiffness and system vibration is revealed. This paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark- β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity. [ABSTRACT FROM AUTHOR]

In this paper, an exact analytical solution is proposed to investigate the free in-plane vibration of sector plates. The highly complex and coupled differential equations of in-plane vibration motion are decoupled by invoking Helmholtz decomposition. The method of separation of variables is used to solve the resulting uncoupled Helmholtz equations. Applying the boundary conditions at both radial edges, the compatible eigenvalue problems for sector plates are obtained. Then, applying the boundary conditions at inner and outer circumferential edges, the corresponding characteristic equations can be solved to obtain the natural frequencies and the associated mode shapes. The results from the proposed method agree very well with the results from the available literature and the FEM. Significant influence of the boundary conditions and the geometric parameters on the free in-plane vibration characteristics of sector plates is investigated and addressed. The superficial frequency veering "aberration" between neighboring modes is discussed and found in fact to be an eigenvalue crossing phenomenon. It is proved that for a sector plate, only with simply supported radial edges, there exists an exact analytical solution. The proposed exact analytical solution can provide not only the detailed characteristics of the free in-plane vibration of sector plates but also the benchmark for further study. [ABSTRACT FROM AUTHOR]

This paper proposes a unified semi-analytical method for the free in-plane and out-of-plane vibrations of arbitrarily shaped plates with clamped edges. The method is derived using boundary conformal mapping (BCM). The BCM is first proposed here to overcome the mathematical difficulty in describing the clamped boundary conditions of complex or/and irregular shaped plates. Elliptical, rectangular and horseshoe plates with clamped edges are studied to demonstrate the proposed method. After that, another two groups of arbitrarily shaped plates including three polygonal plates and three curve-edged plates are studied. The efficiency of the proposed method is checked through a convergence study. Results from the proposed method agree well with the available results in the literature and with finite element results. All the case studies demonstrate that the proposed method is versatile and gives good accuracy for both the in-plane and out-of-plane vibrations of arbitrarily shaped plates with clamped edges. New results from the proposed method can serve as benchmarks for further study on the vibration of plates, especially of irregular shaped plates. • Free in-plane and out-of-plane vibration solutions for clamped plates are proposed. • Solutions are semi-analytical, generalized and apply to arbitrarily shaped plates. • Boundary conformal mapping (BCM) is introduced to obtain the solutions. • BCM overcomes mathematical difficulty in describing irregular shaped boundary conditions. • BCM method is versatile and has excellent accuracy. [ABSTRACT FROM AUTHOR]