Research On Vibration Characteristics Of A Bi-stable Cosine Beam Nonlinear Vibration Isolator

The vibration of various power equipment on the aircraft has an important impact on the life of the aircraft,the performance of precision instruments and the comfort of personnel riding.Referring to the standard ISO 2631-1,human thoracic and abdominal organs are sensitive to both vertical vibration of 4-8Hz and lateral and longitudinal vibration of 1-2Hz.Comfort is an important index to be considered in the design of civil aircraft,which has high requirements for vibration isolation performance.Traditional linear vibration isolators have good vibration isolation effect for high frequency vibration with external excitation frequency higher than its own inherent frequency,but the vibration isolation effect for low frequency vibration is not ideal due to its own limitation.Based on high static and low dynamic stiffness non-linear low frequency passive vibration isolators not only have good static load support capability but also have good low dynamic stiffness characteristics,which is of great practical significance to improve the life and reliability of equipment.In order to isolate the low frequency vibration on aircraft,this paper proposes a nonlinear low frequency passive vibration isolator with high static and low dynamic stiffness characteristics,which is composed of a linear positive stiffness spring in parallel with a bistable cosine beam negative stiffness structure.Firstly,through the static analysis of the cosine beam nonlinear vibration isolator,the conditions to be satisfied by the structural parameters of the isolator at the quasi-zero stiffness equilibrium position are given.Secondly,the dynamics model of the system under the action of harmonic forces and harmonic displacements is established,and the equilibrium point analysis of the undamped undisturbed system is used to obtain the existence of equilibrium bifurcation behavior and its static bifurcation curve as well as the conditions to satisfy the stable quasi-zero stiffness,and the phase plane method is used to analyze each equilibrium point to obtain the dynamic characteristics of the system with the transition from single trap to double trap.Furthermore,the static analysis of the cosine beam nonlinear vibration isolation system gives the structural parameter conditions that need to be satisfied for the cosine beam element of the isolator at the zero stiffness equilibrium point.The dynamic response of the system is approximated by using the averaging method,and then the stability of the solution is analyzed according to the Lypunov’s 1st approximation stability theory to obtain the instability region of the vibration response.In addition,the effects of different height-thickness ratios,damping coefficients and external excitation amplitudes on the transmission rate of the nonlinear vibration isolation system are analyzed by numerical methods,and the frequency ratio of its transmission rate less than 1 is compared with that of the linear vibration isolator,and the starting vibration isolation frequency of the cosine beam nonlinear vibration isolator is much smaller than that of the linear system.The vibration isolation performance of the system under the action of harmonic forces is analyzed by finite element software simulation,which further verifies that the starting vibration isolation frequency of the cosine beam nonlinear vibration isolator is smaller than that of the linear system.Finally,the vibration isolation experimental device is built to experimentally study the vibration isolation performance of the bistable cosine beam nonlinear vibration isolator under harmonic displacement excitation.This provides a theoretical basis for the design of low-frequency nonlinear vibration isolators.