Study On Vibration Characteristics And Optimization Of Gradient Lattice Sandwich Structure

The lattice sandwich structure is a multi-layer structure composed of a thin panel with excellent mechanical performance and a thick core layer with weak mechanical performance.Compared to traditional solid structure,the lattice sandwich structure offers several advantages,including higher specific strength and stiffness,as well as excellent thermal and acoustic insulation performance.As a result,it has found widespread use in engineering areas such as civil engineering,aerospace,and automotive engineering.Lattice sandwich structure often experiences various complex dynamic loads and may generate vibration or even resonance in many engineering applications.The vibration can cause the failure in engineering components or structures,which is endanger to the stability and durability of engineering structures.Resonance issues can affect the normal service life and performance of structures,which is an important problem that cannot be ignored in engineering structural design.The design based on structural optimization under passive control can significantly reduce the vibration of the structure to boost the engineering application and development of sandwich structure.Compared to the traditional uniform lattice sandwich structure,the gradient lattice sandwich structure exhibits superior load-bearing performance,energy absorption capacity and design flexibility,with a wider range of applications and development potential.This study investigates the equivalent parameters,natural frequencies and sensitivity to damage defects of a gradient lattice sandwich structure by theoretical analysis and numerical simulations,and conducts multi-objective optimization design to improve the fundamental frequency and reduce the mass of the structure.The main contents of this paper are as follows:(1)Firstly,with the aim of achieving a gradient variation of geometric properties in the structure,the uniform cross-section members are replaced by the variable cross-section members in the lattice sandwich structure.Then,based on the equivalent theory and continuity hypothesis,the equivalent elastic modulus and equivalent shear modulus of the gradient lattice unit cell are derived by the analysis of unit cell.The results of theoretical analysis are validated by the finite element analysis using ABAQUS.Finally,the applicability of the unit cell equivalent theory is demonstrated by finite element simulations of flat compression and shear on the gradient lattice structure.(2)The free vibration theoretical model of gradient lattice sandwich structure is established based on Allen basic hypothesis and Hamilton’ principle.The theoretical solution of the natural frequency of structure is obtained by hypothetical mode method and energy method respectively,and verified by comparison of the existing literature data and finite element simulated results.On this basis,the effects of gradient factor,structural geometric parameters and core topological configuration on the natural frequency of gradient lattice sandwich structure are studied by means of theoretical analysis and numerical simulation.The results show that through the gradient design of the lattice sandwich structure,the natural frequency of the structure can be increased or reduced purposefully,and the vibration caused by the external excitation frequency can be avoided.(3)The free vibration of the gradient lattice sandwich structure with damage defect is analyzed by numerical simulation method,and the natural frequency and corresponding vibration mode of structure are obtained.Based on the definition of evaluation parameters characterizing the influence of damage defects on natural frequency,and the effects of damage degree,damage location,damage form and boundary conditions on the natural frequency of structure are studied in detail.Therefore,influence of damage defect on the overall vibration characteristics of structure is investigated.(4)A framework of multi-objective optimization based on response surface method is proposed,which can enhance the vibration resistance of the gradient lattice sandwich structure while maintaining its lightweight properties.Firstly,the sensitivity analysis of the geometric parameters of the gradient lattice sandwich structure is carried out,and the significant influence parameters are selected as the optimization design variables.Then the optimization model based on response surface method is constructed to the diagnostic analysis and variance analysis by the optimization objectives of maximizing the fundamental frequency and minimizing the unit cell mass.Finally,the second generation nondominated sorting genetic algorithm is used to optimize the structure to obtain the Pareto optimal solution,and the finite element method is used to verify the optimization results.The optimized gradient lattice sandwich structure has higher fundamental frequency and lower weight than the original structure.