A New Finite Element Formulation for Nonlinear Vibration Analysis of the Hard-Coating Cylindrical Shell

Abstract

Abstract:In this paper, a four-node composite cylindrical shell finite element model based on Love's first approximation theory is proposed to solve the nonlinear vibration of the hard-coating cylindrical shell efficiently. The developed model may have great significance for vibration reduction of the cylindrical shell structures of the aero engine or aircraft. The influence of the strain dependence of the coating material on the complex stiffness matrix is considered in this model. Nonlinear iterative solution formulas with a unified iterative method are theoretically derived for solving the resonant frequency and response of the composite cylindrical shell. Then, a cylindrical shell coated with a thin layer of NiCoCrAlY + yttria-stabilized zirconia (YSZ) is chosen to demonstrate the proposed formulation, and the rationality is validated by comparing with the finite element iteration method (FEIM). Results show that the developed finite element method is more efficient, and the hard-coating cylindrical shell has the characteristics of soft nonlinearity due to the strain dependence of the coating material.

Free vibration analysis of rotating thin-walled cylindrical shells with hard coating based on Rayleigh-Ritz method

“…By using Rayleigh-Ritz method and Love's first approximation theory, Sun et al 11 studied the free vibration of the non-rotating cantilever cylindrical shell with hard coating and evaluated the influences of the parameters of hard coating, including Young's modulus, loss factor and thickness, on the vibration behaviors of the hard-coating shell. Considering the effect of the strain dependence of hard coating, Zhang et al developed analytical methods 12,13 and finite element methods 14,15 to study the nonlinear vibration characteristics of the static hard-coating cylindrical shell under base excitation and reveal the mechanism of soft nonlinear vibration caused by the hard coating. In addition, circumferential variable stiffness springs were proposed to simulate actual elastic constraints.…”

Passive Vibration Reduction Analysis of the Mistuned Blisk Deposited Hard Coating Using Modified Reduced-Order Model

“…In recent years, the significant mechanical damping capacities of hard coating generated by the friction energy dissipation of internal particles of coating materials [22] have been found by a number of researchers. Subsequently, hard coating was used widely as the vibration dampers to reduce the resonant stress of vibrating structures for its nicer stability and high damping capacities in high temperature [23], such as the titanium plates [24][25][26][27], the cantilever beams [28,29], the cylindrical thin shells [30][31][32] and the individual blades [33][34][35], etc. Moreover, another great advantage of hard coating was that the resonant peaks of the forced response of vibrating structures can be suppressed remarkably without influencing the structural mass and stiffness significantly because of its thin thickness.…”

Application of the hard-coating damper on the mistuned blisk for passive vibration reduction

“…[21][22][23] In recent years, the significant damping capacities of hard coating produced by internal particles friction have been found by some scholars. 24 Subsequently, the vibration reduction technology by the hard-coating dampers was widely applied to reduce the resonant stress of vibrating structures, such as the titanium plates, [25][26][27] cantilever beams, 28 cylindrical thin shells, 29,30 individual blades 31,32 and highly simplified blisk, 33,34 for its nicer stability than viscoelastic materials under high temperature and pressure. 35 Another great advantage of the hard-coating dampers was that the resonant peaks of vibrating structures can be suppressed remarkably without alerting structural mass and stiffness significantly because of its thin thickness.…”