Dynamic Analysis Of Rotating Functionally Graded Sandwich Micro-beams Based On Modified Couple Stress Theory

Micro-mechanical systems are widely studied,such as micro-turbines,micro-rotor airplanes,micro-drones,nano-engines,nano-sensors,atomic force microscopes,etc.Many of them can be simplified as central rigid body-cantilever micro-beam or cantilever micro-plate models.The size of the micro-structures is at the micrometer or nanometer level,which makes it show a strong scale effect relative to the macro-structures.Due to the size-dependence of micro-structures,the mechanical properties of them no longer be correctly described by the classic elastic-plastic theory.Furthermore,these structures are often used in extremely complex environments,such as high temperature,high pressure,electric fields,magnetic fields and so on.In order to meet the actual needs of engineering,it is extremely important to study the application of new composite materials with light weight,high strength and high temperature resistance in the system.Based on the modified couple stress theory,a rigid-flexible coupling dynamic model of large overall rotating hub-functionally gradient micro-beams is developed.Numerical verification was performed through relevant literatures and software,and numerical simulation is performed by MATLAB.The main research work and results of this article are as follows:1.A review of the research background of the strain gradient theory,the couple stress theory,porosities,functionally graded sandwich(FGS)beams as well as the flexible multibody systems is presented.The research goals and focus of this paper are proposed.2.The porosities are applied to functionally graded materials(FGMs),and then a high-order rigid-flexible coupling dynamic model of the rotating hub-FGS tapered porous micro-beams is developed based on the modified couple stress theory.The functionally graded sandwich tapered micro-beams are composed of a core with inperfect functionally graded materials sandwiched between two homogeneous face sheets,which can decline the influence of the traditional sandwich structure debonding damage caused by the mismatch of stiffness properties between their core and face sheets.Then,frequencies and mode shapes are analyzed when the system is moving at a constant speed.The response is analyzed when the system makes large overall motion.It was found that the rotational angular velocity,the power index of the functional gradient,the scale parameters,and the porosity have a great influence on the dynamic characteristics of the system.Furthermore,it is observed that interesting frequency veering and mode shift phenomena of the system are observed when the size-dependency changes.3.Considering the nonlinear temperature field,a higher-order rigid-flexible coupling dynamic model of the hub-FGS porous micro-beam is developed.First,it is assumed that the material properties of the core layer of the flexible beams change along the height direction according to a certain power function,and the value range of the porosity is obtained through the material properties volume distribution function.The boundary conditions between layers are used to solve the heat conduction equation,and the relational expression between the material properties of each layer structure and the coordinates y and temperature is obtained.Finally,according to the rigid-flexible coupling dynamic equation,the influence of temperature field on the vibration and response characteristics of the system at the microscale is analyzed.