Nonlinear Dynamical Behaviours And Designmethodology For A Class Of Solid And Liquid Mixture Vibration Isolator

In present, the low frequency vibration isolation is still one of focuses and difficulties in the field of vibration isolation. The existing passive isolation techniques mainly have deficiencies on respects of loading capacity, low frequency isolation, fatigue life and air leakage, etc. The Bellows type Solid And Liquid Mixture(B-SALi M) vibration isolator, which is a class of nonlinear isolation device is proposed for vibration isolation of heavy machines with low frequency. It consists of a multi-layers bellows container filled with SALi M working media including elastic elements and incompressible liquid. The proposed B-SALi M isolator is capable of improving the loading capacity and effectiveness of low frequency isolation for current passive vibration isolation techniques. Therefore, it is potentially suitable for vibration isolation of marine ships, heavy vehicle and rail transport, etc., as well as reduction of the line spectra in radiated underwater noise of submarines.The vibration isolation system comprising B-SALi M isolator is essentially a non-smooth dynamical system due to the discontinuity of its piecewise linear-nonlinear stiffness. In additional with common smooth dynamics phenomena(e.g. sudden jump), some typical non-smooth dynamical behaviours(e.g. grazing induced unstablility) can also occur, which increases the complexity of isolator’s dynamics analysis. Meanwhile, in engineering, one are more interested in a couple of practical problems, such as how to utlise the nonlinear characteristics to improve the isolator’s effectiveness and how to suppress the adverse dynamical behaviours.Consequently, the principal purpose of this dissertation is to study nonlinear dynamics behaviours and design principle for the piecewise smooth B-SALi M isolation system. Meanwhile, the investigation of low frequency isolation technique and active isolation strategy is explored as well. The main themes and contributions of the dissertation are stated as follows:1. The study begins with the mechanics modelling of B-SALi M isolator as well as the derivation of its stiffness property. First of all, the stiffness of the solid element under outer liquid pressure and inner air pressure is derived by respectively introducing bending beam model and plate-shell model. Second, due to the geometry nonlinearity of large deformation of bellows structure, the axial nonlinear stiffness of solid element is established by parameter perturbation method, based on which, the axial stiffness property of B-SALi M isolator is obtained. It shows that the isolator’s stiffness is piecewise linear-nonlinear, which is confirmed by the quasi-static experiment, and moreover, element quantity and bellows structure parameters can adjust the isolator’s stiffness property. This presented work is the theoretical basis for the design of B-SALi M isolator’s stiffness.2. The dynamical response and its stability of B-SALi M vibration system are presented subsequently. The study is discussed in two cases: transversal intersection and non-transversal intersection, i. e. grazing. In the former case, the single-crossing period n motion is sought by matching method first. And then, based on fixed phase Poincaré section, the stroboscopic map is constructed by introducing the discontinuity map. Following that, on the basis of the Poincaré section of discontinuity boundary, the global Poincaré map of transversal orbit is composed by sub-maps in different state spaces, and directly the Jacobi matrix is obtained. In the latter case, the discontinuity map is once more introduced to construct the global Poincaré map, based on which, the normal form for grazing bifurcation is derived. This presented work provides the theatrical support for dynamical design of B-SALi M isolator.3. The following study focuses on the nonlinear dynamics design methodology of B-SALi M isolator. The sudden jump phenomenon may bring the vibration isolation system adverse impact, and thus the bifurcation of primary resonance is classified through using singularity theory first. It can be seen that the sudden jump may be caused by saddle-node bifurcation and grazing bifurcation, and the sharp corner of frequency response curve indicates the occurrence of grazing bifurcation induced by stiffness’ s discontinuity. Then the subsequent investigation gives the design principle of avoidance of sudden jump according to the topology of frequency response curve. And as a result, the increase of element quantity can help avoiding the occurrence of sudden jump. Besides, through analyzing eigenvalue of Jacobi matrix of Poincar é map, the parameter condition of suppression of period-doubling bifurcation is presented and it shows that increase of damping level can effectively suppress the occurrence of period-doubling bifurcation.4. The subsequent study turns to vibration isolation properties of B-SALi M isolator fixed on the flexible base and the improvement design for conventional standing B-SALi M isolator. In the case that the orbit cannot exceed the stiffness’ s discontinuity point, the energy transmissibility is measured by vibration experiment and effects of excitation condition and isolator’s parameters on vibration level difference are discussed as well in the test. In the case that the orbit is able to exceed the discontinuity point, the design principle for vibration isolation of primary resonance is considered first, and then effects of B-SALi M isolator’s parameters on its vibration isolation properties are studied. Furthermore, the novel type B-SALi M with high static and low dynamical stiffness(HSLDS) is proposed to isolate low or even ultra-low frequency vibration. Comparasion result shows that the modified isolator can effectively improve the effectiveness of low frequency isolation, and if designed properly, it even can isolate the vibration of less than 2Hz.5. The active vibration isolation strategy of time-delayed cubic velocity feedback is presented finally, which parallels the active control loop to the passive B-SALi M isolator. Through the use of multi-scale perturbation method, the primary resonance of controlled system is investigated first, based on which, effects of time delay on primary resonance and its stability are explored. It is found that the proper velocity feedback can not only adjust the system’s damping but also change the system’s stiffness property. Subsequently, effects of feedback parameter on vibration isolation performance are studied via numerical simulation and it is concluded that the gain can not only reduce the whole force transmissibility level and greatly suppress vibration in the resonance region, but also can keep the transmissibility unchanged over higher frequency range where vibration isolation is required. And last, the design principle of feedback parameters is presented according to stability analysis of primary resonance.