Research On Design Method And Mechanical Properties Of Negative Stiffness Metamaterials And Structures Of Ships

As more and more ships and marine structures serve at deep sea and the polar regions,the extreme loads and complex environments put forward higher requirements on the issues of their safety.The previous design methods and products are facing great challenges and innovation must be conducted.The development of new materials and design methods of structures are two important parts of the innovation.On the other hand,the lightweight,green,and intelligent trends make the new materials and structures have broad application prospects."metamaterials" with strong designability and extraordinary mechanical properties have become the focus of research in the field of naval architecture and ocean engineering.Among them,the negative stiffness metamaterials have superior impact resistance.Unlike other metamaterials,which absorb energy through plastic deformation,the negative stiffness metamaterials undergo layer-by-layer elastic buckling under external loads,thus achieving repeatable impact energy absorption.This paper focuses on the design and analysis methods of negative stiffness(NS)metamaterials and negative stiffness metamaterial structures,and explores the application of negative stiffness structures in marine engineering.First,based on the theory of periodicity in crystallography,a "Bravais lattices design method for NS metamaterials" was proposed and different multidimensional and multidirectional NS metamaterials were systematically designed.Starting from the 2D and 3D NS metamaterial configurations,the "double negative" metamaterials with negative stiffness and negative Poisson’s ratio(NPR)were designed.The NS metamaterial cell configuration is expanded to the macro scale to design metamaterial structures of beams and cylindrical cellular shells whose impact resistance and sound insulation performance were studied,respectively.New metamaterial hull structures and devices were presented for the vibration isolation and impact resisting problems of ships.The main content of this paper is as follows:(1)A "Bravais lattices design method for NS metamaterials" was proposed.The NS effect of a cosine-shaped curved beam under midpoint compression was introduced and analyzed parametrically.Taking microstructures with NS curved beams as unit cells,multidimensional and multidirectional NS metamaterials were designed by the Bravais lattices design method for NS metamaterials.The method and designed configurations enrich the research on NS metamaterials.(2)The quasi-static and dynamic characteristics of unidirectional,bi-directional orthogonal and tri-directional orthogonal NS metamaterials were studied.3D printing technology was used to manufacture metamaterial prototypes,and quasi-static and impact experiments were designed to verify the numerically calculated data.The results show that the designed unidirectional uniform NS metamaterials exhibit common mechanical properties of NS metamaterials.However,the unidirectional graded NS metamaterials show some differences due to the increasing critical buckling force.For example,the recovery order of the cell layers during unloading does not depend on the buckling order during loading,and more impact energy can be absorbed.Mechanical tests have verified the numerical results well.The bi-directional orthogonal NS metamaterial shows a coupling phenomenon in the mechanical behavior on the two axes,that is,the periodic rotation of the cells occurs.For the tri-directional orthogonal NS metamaterial,mechanical behaviors on different axes show good independence.(3)Two-dimensional and three-dimensional "double-negative" metamaterials exhibiting NS and NPR effects were designed.Taking the incremental Poisson’s ratio and incremental equivalent elastic modulus as metrics,the influence of geometric parameters on the mechanical properties was analyzed and verified via quasi-static tests.Behaviors of the NSNPR metamaterials under impact were investigated.The results show that the designed NSNPR metamaterials exhibit noticeable NS and NPR effects.The angle between the oblique curved beam and the horizontal axis determines the geometry of the metamaterial and has great influence on the Poisson’s ratio.The thickness of the curved beam can effectively adjust the stiffness of the metamaterial,which has great influence on the impact resistance.The numerical results of Poisson’s ratio when the cells are fully compressed are in good agreement with the test results.The designed 3D NSNPR metamaterial exhibits independent NPR effects on two orthogonal axes perpendicular to the compression direction.Therefore,the two Poisson’s ratios can be designed separately.(4)A macro-scale NS metamaterial beam was designed.The effects of segment lengths and plate thicknesses on the static and dynamic performance of the beam were studied.An optimization process based on surrogate models was established to seek the optimal performance of impact resistance.The results show that the force-displacement curve of the NS metamaterial beam is serrated-shaped.The thicknesses of the face sheets and interlayers and the lengths of the curved plate segments affect the local stiffness of the beam and the buckling order of the curved plate layers.Different parts of the NS beam dominate the resistance to deformation according to the impact load intensity,and the largest portion of the strain energy is stored in the four curved plate layers.When the segment near the center is shorter and the interlayers near the top face sheet are much thicker than the other three,the NS metamaterial beam shows better impact resistance.(5)A multifunctional NS metamaterial cylindrical cellular shell which can endure large deformation was proposed and designed,and its large-deformation quasi-static behavior and small-deformation sound-insulation performance were studied.The influence of the curved beam thicknesses and the mass of blocks in the cell on the sound insulation performance is investigated.The geometric parameters of the NS cylindrical shell are optimized for optimal sound transmission loss in certain frequency bands.The results show that when subjected to radial compressive load,the cylindrical shell exhibits the typical characteristics of NS structures,thus is suitable for impact cushioning.Compared with conventional honeycomb metamaterial cylindrical shells with the same size and weight,the presented shell shows higher sound transmission loss at frequencies above 200 Hz.The sound insulation can be improved by changing the thicknesses of the curved beams and inserting mass blocks in the cavities of the cells.Optimizations for specific frequency bands show great improvements in the average sound transmission loss,indicating strong designability of the NS metamaterial cylindrical shell.(6)A multi-layer NS metamaterial impact-resistant base was designed,and the structural response and impact isolation performance under impact load were analyzed.The results show that the designed NS metamaterial base exhibits excellent impact isolation performance.The acceleration isolation coefficient is in the range of 0.02 to0.04,and velocity isolation coefficient is in the range of 0.2 to 0.3.A cosine-shaped nonlinear vibration isolator was proposed.Harmonic balance method and Runge-Kutta method were used to calculate the vibration response,and the influence of geometric parameters on the vibration transmissibility was analyzed.The design of the nonlinear vibration isolator is simple,and different performance can be achieved by tuning its geometric parameters.A novel impact-resistant ship bottom protective structure was designed,which is comprised of rubber plates and steel NS metamaterials.The response of hull section members under slamming load was analyzed and compared with that of the original hull model.The maximum stresses in the bottom region are about 70% of those of the original model,when the NS metamaterial bottom protective structure is assembled.Therefore,the protective structure possesses excellent buffering and energy absorption characteristics,and is instructive for the design of protective structures of ships.