Influence of nonlinear elastomer on isolated lag dynamics and rotor/fuselage aeromechanical stability
03 Apr 2000-
TL;DR: In this paper, the effect of nonlinearities of an elastomeric bearing on isolated lag dynamics and coupled rotor/fuselage ground resonance stability of an idealized bearingless rotor blade is studied.
Abstract: This paper presents a study on the effect of nonlinearities of an elastomeric bearing on isolated lag dynamics and coupled rotor/fuselage ground resonance stability of an idealized bearingless rotor blade. The rotor blade is modeled as an elastic beam with a nonlinear elastomer and a rigid torque tube. First, amplitudedependent natural frequency of the blade in lag mode is analyzed using numerical perturbation technique. Then the problem of amplitudedependent stability of the coupled rotor/fuselage system under ground resonance condition is investigated. The stability of the system is analyzed by two approaches, namely, 1) by eigenanalysis of the linearized equations and 2) by response of the nonlinear system to an initial disturbance by time integration. The results of the eigenanalysis indicate that the effect of amplitude seems to be more dominant on the progressive lag mode damping than on regressive lag mode damping. It is also observed that so far as the stability in ground resonance is concerned there exist optimum locations for the attachment of both the elastomer and torque tube. Results of the time-domain analysis of the nonlinear equations indicate clearly that the stability of the system is dependent on the magnitude of initial disturbance.
TL;DR: In this paper, a time domain model of linear viscoelasticity is developed based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic.
Abstract: A time domain model of linear viscoelasticity is developed based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. The anelastic displacement field is used to describe that part of the strain that is not instantaneously proportional to stress. General coupled constitutive equations for (1) the total and (2) the anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. A key feature of the model is the absence of explicit time dependence in the constitutive equations. Apparent time-dependent behavior is described instead by differential equations that govern (1) the motion of mass particles and (2) the relaxation of the anelastic displacement field. These coupled governing equations are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also treated: the anelastic displacement field is effectively an internal field, as it is driven exclusively through coupling to the total displacement, and cannot be directly affected by applied loads. In order to illustrate the use of the method, model parameters for a commonly-used high damping polymer are developed from available complex modulus data.
TL;DR: In this paper, the nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping.
Abstract: The nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping. The spring-mass system has also a cubic nonlinearity. The response is found by using two different perturbation approaches. In the first approach, the method of multiple scales is applied directly to the nonlinear partial differential equations and boundary conditions. In the second approach, the Lagrangian is averaged over the fast time scale, and then the equations governing the modulation of the amplitude and phase are obtained as the Euler-Lagrange equations of the averaged Lagrangian. It is shown that the frequency-response and force-response curves depend on the midplane stretching and the parameters of the spring-mass system. The relative importance of these effects depends on the parameters and location of the spring-mass system.
TL;DR: In this paper, a viscoelastic solid model consisting of a combination of linear and non-linear springs and dashpots is developed to represent an elastomeric damper, and a nonlinear constitutive differential equation is derived to characterize the damper behaviour in the time domain.
Abstract: A viscoelastic solid model, comprising of a combination of linear and non-linear springs and dashpots, is developed to represent an elastomeric damper. A non-linear constitutive differential equation is derived to characterize the damper behaviour in the time domain. A system identification method is presented to determine the spring - dashpot parameters (coefficients of the constitutive equation) from experimental data. The model is able to predict the non-linear amplitude-dependent behaviour of elastomeric dampers under single as well as dual-frequency excitations. A `two-level implicit - implicit' scheme is developed for the integration of the non-linear damper model into a structural dynamic analysis. With increase in amplitude of excitation, softening behaviour of the lead spring results in lesser motion in the Kelvin chain, lower damping levels, and slower decay of initial perturbations. The baseline model is augmented with additional series and parallel non-linear springs to represent the reduction in damping (G'') at very small amplitudes, and the occurrence of limit cycle oscillations.
TL;DR: In this article, the spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.
Abstract: A conventional articulated rotor blade has mechanical flap and lag hinges, a lag damper, and a pitch bearing. In connection with an interest in designs of greater mechanical simplicity and increased maintainability, hingeless and bearingless rotors have been developed. A hingeless blade lacks the hinges and is cantilevered at the hub. It does have a pitch bearing for pitch control. A bearingless design eliminates the hinges and the pitch bearing as well. In the present investigation of bearingless rotor blade characteristics, finite element analysis has been successfully applied to determine the solutions of the nonlinear trim equations and the linearized flutter equations of multiple-load-path blades. The employed formulation is based on Hamilton's principle. The spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.