Design Theory And Methods Of Arbitrary Poisson's Ratio Metamaterials And Application In Hull Vibration Reduction

The "Technical Roadmap for Key Areas Made-in-China 2025" points out that the design of novel materials for ships and hulls is regarded as the key to the development of high-tech ships.With the implementation of latest international regulations and standards,the requirements for structural vibration problems of ships have become more and more stringent,moreover,the trend of large-scale ships and high power of diesel engines is also making the problems of hull structure vibration increasingly prominent.Researches on conventional vibration reduction structures,vibration reduction methods and structural materials have made it difficult to make breakthroughs,but the introduction of novel design concepts and novel structures/materials provides a greater prospect for hull structural vibration reduction design.In this dessertation,the theoretical methods of the arbitrary Poisson's ratio metamaterials design and the application of the lightweight metamaterials in the hull structure are studied.Firstly,a functional element topology optimization method(FETO method)for metamaterials is proposed,where three modelling types of the FETO method are studied,and four mathematical formulas of the topology optimization problem are clarified.Secondly,using the above FETO method,the metamaterials' lightweight design and the metamaterials' optimization design with in-plane and out-plane bearing characteristics are studied.Then,the phenomenon of "load ill-conditioned,discontinuity of the compliance objective function" in multiple load cases structural topology optimization are studied.And the introduction of the compromise programming approach provides a guidance for dynamic optimization of metamaterials.Based on the concept of mechanical impedance and the compromise programming approach,a metamaterials' design method with specified vibration reduction performance is provided.Next,the phononic crystal is introduced,and the vibration reduction performance of the phononic crystal metamaterials mount is designed and studied,where the mechanism of vibration reduction is revealed and used for the vibration reduction optimization of the mount in low frequency range.In the end,based on the research of lightweight metamaterials,a novel metamaterials marine mount with vibration reduction properties is designed and applied to the vibration reduction performance analysis of the double-bottom structure of the engine room.The main works and innovations are summarized as follows:(1)This dessertation introduces a structural topology optimization theory to propose a functional element topology optimization design method(FETO method),and three models of metamaterials' optimization are established to provide different types of design requirements.Among them,the model with maximum compliance as the objective function is beneficial to the vibration reduction and energy absorption,while the model with the minimum compliance as the objective function can improve the bearing or deformation resistance,and the model with the objective function of minimizing the mass can realize the lightweighting of metamaterials.The numerical simulation shows that the proposed FETO method is suitable for designing novel metamaterials with various initial design domain shapes and arbitrary specified Poisson's ratios,that is,by designing the Poisson's ratio of a single functional element,a specified macro Poisson's ratio effect of the overall structure of the metamaterials can be achieved.In addition,the FETO method is used to design and analyze the metamaterials with the optimal in-plane and out-plane stiffness.The experimental results show that the Poisson's ratio of the design values,simulation values and test values are consistent with each other;that is,the metamaterials overall structure with the specified macro Poisson's ratio effect can be achieved by designing the Poisson's ratio of a single functional element.In addition,based on the FEDO method,the metamaterials with the optimal characteristics of in-plane and out-of-plane stiffness are designed and analyzed.(2)A series of lightweight metamaterials with specified Poisson's ratios,which are optimized for weight reduction,are designed by the FETO method,and the effects of Poisson's ratio on the static stiffness and vibration reduction of metamaterials are investigated.It shows that with the increase of the absolute value of Poisson's ratio,the vibration reduction performance is gradually improved.Moreover,under the premise that the absolute values of the positive Poisson's ratio and the negative Poisson's ratio are equal,the vibration reduction performance of the Poisson's ratio metamaterials are better.(3)The structure topology optimization model under multiple load cases is established by using the compromise programming approach,and the influence of load ratio and weight coefficient on the structural topology optimization is analyzed by examples.It provides a solution to solve "load ill-conditioned,discontinuity of the compliance objective function" in multiple load cases topology optimization,and the research of the compromise programming approach are applicable to the multiple load cases dynamic topology optimization.Then,based on the concept of origin mechanical impedance,a metamaterials vibration reduction design method is proposed,where the origin impedance value corresponding to each frequency is numerically synthesized and used as an objective function to implement the optimization problem.The frequency response shows that the metamaterials' vibration reduction design method that maximizes the mechanical impedance as the objective function can realize the design of improving vibration reduction,which optimized metamaterials has improved by at least 12% in vibration reduction performance compared to honeycomb metamaterials.(4)A metamaterials marine mount with vibration reduction performance is designed by referring to the auxetic honeycomb metamaterials,and the optimizaton is applied to maximize the vibration reduction.Next,the phononic crystal is introduced to solve the low-frequency vibration of the hull structure,and the vibration reduction characteristics of the phononic crystal metamaterials mount are studied according to the local resonance mechanism.By establishing a simplified dynamic model to analyze the influence of dynamics parameters on the vibration reduction performance of the phononic crystal metamaterials mount.Moreover,the vibration reduction mechanism of the phononic crystal metamaterials' mount is revealed,and it is applied to the vibration reduction optimization model of the phononic crystal metamaterials mout.The above researched indicate that when the natural frequency values of the phononic crystal and the honeycomb mount are close,the vibration response peak of the novel mount can be effectively reduced;in addition,by optimizing the natural frequency of the phononic crystal,the resonance phenomenon of the honeycomb mount can be suppressed.(5)The application of metamaterials in ships is intended to improve the lightweight and vibration reduction performance of the hull structure.Firstly,the frequency response of the original design of the hull structure is carried out,then the optimization method is introduced to imptove the reduction of vibration response.According to the influence of Poisson's ratios on the vibration reduction in previous research,a metamaterials mount with characteristics of vibration reduction is designed to further reduce the vibration response of the inner and outer plates of the hull structure.