| Low-frequency vibration can cause varying degrees of damage to human health and affect the performance of high-precision instruments.Therefore,isolating low-frequency vibration is of great significance.However,it is difficult for commonly used linear vibration isolators to achieve efficient vibration isolation while maintaining the original bearing capacity of the system.Quasi-zero-stiffness vibration isolators have been studied extensively due to their high-static and low-dynamic characteristics,which can meet the needs of high loads carrying capacity and low-frequency vibration isolation.On the basis of previous studies,this paper first designed a tensile quasi-zero-stiffness vibration isolation system,considering that the quasi-zero-stiffness vibration isolator based on the parallel connection of positive and negative-stiffness components has high friction and poor low-frequency vibration isolation performance.The structure parameters are designed so that the element structure can realize the quasi-zero stiffness(compact quasi-zero-stiffness isolator)and bistable negative-stiffness characteristics(negative-stiffness meta-structure)respectively.Two quasi-zero-stiffness systems are studied from the perspectives of statics,dynamics,vibration isolation performance,and nonlinear dynamics.A multistable negative-stiffness mechanical metamaterial is designed based on the needs of vibration reduction,shock resistance and energy absorption.The main work and conclusions are as follows:(1)Design and research of a tensile quasi-zero stiffness vibration isolator.A kind of tensile quasi-zero stiffness isolator was designed using a pair of transverse tensile springs as negative-stiffness components in parallel with vertical compression springs.The structure model of the isolator was established and the physical model was equivalent to that of the isolator.The equations of restoring force,stiffness and displacement of the system were obtained,and the parameter conditions for realizing quasi-zero stiffness characteristics at the static equilibrium position were determined.In the analysis of dynamic characteristics,a nonlinear vibration differential equation of the system under the action of harmonic forces is established,the steady-state response solution of the system is solved using the harmonic balance method,and the accuracy of the approximate analytical method is verified using numerical methods.The stability of the steady-state response solution of the system is analyzed by the discriminant method of Mathieu equation due to the existence of multistate coexistence zone.The results show that compared with the equivalent linear system,the initial vibration isolation frequency ratio of the tensile quasi-zero stiffness isolation system is reduced by about 50%,and the low-frequency vibration isolation is realized.(2)Design and research of meta-structure vibration isolator.Considering that traditional quasi-zero stiffness vibration isolators were constructed based on the parallel connection of positive and negative-stiffness components,which can lead to complex manufacturing processes,high manufacturing costs,high-friction,and unsatisfactory low-frequency vibration isolation performance.A meta-structure isolator is designed which can avoid the assembly of positive and negative-stiffness components.and its structural parameters are adjusted to achieve quasi-zero stiffness using its own structural deformation.Firstly,based on the continuum theory and the deformation process of the meta-structure under loads,the relationship among elastic potential energy displacement function,force-displacement and stiffness-displacement of the meta-structure were deduced in detail,and the mechanical properties of the meta structure were obtained through theoretical derivation.Then,the finite element software ANSYS is used to simulate the deformation process.The influence of structural parameters vary on the mechanical properties of a unit cell is analyzed by symmetrically stacking the meta-structure up and down.The results show that the theoretical model of the meta-structure can quantify its mechanical properties well,which provides theoretical support for the design of a compact quasi-zero stiffness isolator and a multistable negative-stiffness mechanical metamaterial.(3)Design and research of a compact quasi-zero stiffness vibration isolator.Based on the research of meta structure vibration isolators,a compact quasi-zero-stiffness vibration isolator was designed.The mechanical properties of the system were verified by statics analysis,and the parameter conditions for realizing quasi-zero stiffness are determined.The approximate steady-state response solution of the system is obtained through dynamic characteristic analysis,and verified by numerical method(fourth-order Runge-Kutta method)and finite element method.The stability of the system is judged according to the Mathieu equation,and the saddle node bifurcation set of the system is solved;In the study of vibration isolation characteristics,the approximate analytical method is used to study the force transmission rate of the system and comprehensively evaluate the vibration isolation performance.The results show that compared with the equivalent linear system,the peak force transmission rate of the compact quasi-zero-stiffness vibration isolation system is reduced by 25.8%,the resonance frequency ratio is reduced by 27%,and the initial vibration isolation frequency ratio is reduced by 62.98%.Compared with the tensile quasi-zero stiffness isolation system,the initial isolation frequency ratio of the compact quasi-zero stiffness isolation system is reduced by 20.61%,which has better low-frequency vibration isolation performance.(4)Nonlinear dynamic characteristics analysis of a compact quasi-zero stiffness isolator.The compact quasi-zero stiffness vibration isolation system is a typical strong nonlinear system,which may produce nonlinear phenomenon such as multistable state,bifurcation and chaos in the dynamic evolution process.The periodic solution of the quasi-zero stiffness vibration isolation system is solved using the new extended target method,and the distribution of periodic motion in the parameter domain,the transition mechanism of the quasi-zero stiffness system and the multi-state coexistence rules are studied.(5)Research of mechanical properties of a multistable negative-stiffness metamaterial.Based on the derivation and analysis of the meta-structure isolator in Chapter 3,the negative-stiffness and bistable characteristics were realized by adjusting the structural parameters of the meta-structure,and the negative-stiffness unit cell were assembled with the cube support frame with high-stiffness,and then the negative-stiffness unit cell is periodically arrayed in space to design a multistable negative-stiffness mechanical metamaterial.The effects of series and parallel connection of a negative-stiffness unit cell on the force-displacement and energy absorption-displacement characteristics were analyzed by commercial finite element software ANSYS,and the mechanical properties of a multistble negative-stiffness mechanical metamaterial(2x2x2、3x3x3)were analyzed.The results show that the designed negative-stiffness mechanical metamaterial has ideal characteristics of energy-absorption、load-bearing and impact-resistance. |
PDF Full Text Request