Vibration Analysis Of Fibonacci Quasi-periodic Nanoplate Structure

Noise generation in engineering structures is often caused by vibration.Measurement and analysis of vibration in structures is one of the most important contents in structural design.In order to study the dynamic characteristics of simple beam and plate structures more effectively,the influence of vibration frequency response on structures,has become a hot topic in the field of structural vibration and noise control.With the development and progress of the times,it is particularly important to study the size and model construction of materials.Based on strain gradient theory and finite element method,the frequency distribution and response characteristics of nanoplates under quasi-periodic structure arrangement are studied in this paper.In this paper,the frequency response characteristics of quasi-periodic structures are introduced,the peak and band gap are systematically analyzed and summarized from the vibration models of macro-plate structure and nano-plate structure.Taking the rectangular macroplate with SSFF as an example,the mass matrix and stiffness matrix of the plate structure are calculated by using the finite element method and the MATLAB program.Through the analysis of the plate structure arrangement,two kinds of macro-materials are selected to compare the vibration frequency response according to the periodic arrangement and the Fibonacci arrangement.The selection of Fibonacci arrangement supercells and the number of supercells are changed.Vibration characteristics of the combination of Fibonacci permutation supercells and periodic permutation primitives were visually analyzed.This provides the necessary theoretical support for the vibration analysis of nanostructures.In the field of nanostructure,graphene is the main research object.Two kinds of nanoplate materials are selected to establish the finite element model of Fibonacci structure arrangement and periodic structure arrangement.Through numerical simulation,the vibration of different periodic number arrangement,different boundary conditions,different quasi-periodic supercell number,and the specific material parameters of nanomaterials,i.e.small-scale effect,are studied and analyzed.In this paper,based on the finite element method,the vibration response of the plate with Fibonacci structure arrangement is analyzed,and the vibration characteristics of the plate are obtained.Based on the second-order strain gradient finite element method,the vibration characteristics of nanoplate structure,the frequency response of nanoplate in Fibonacci arrangement,and the vibration analysis of different boundary conditions,different number of supercells and small-scale effects are obtained.