Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

ODS & Modal Testing Using a Transmissibility Chain

In this paper, we show how Operating Deflection Shapes (ODS’s) andmode shapes can be obtained experimentally from measurements thatare made using only two sensors and two short wires to connect them to amulti-channel acquisition system. This new test procedure is depicted inFigure 1. Not only is the equipment required to do a test much more costeffective, but this method can be used to test any sized test article, especiallylarge ones.

Optimal sensor placement in health monitoring of suspension bridge

Structural health monitoring(SHM) provides an effective approach to ensure the safety of structures.However,with the restriction of the cost of sensor system and data processing,only a small number of sensors could be available in the health monitoring system(HMS).In order to obtain the best identification of structural characteristics,optimal sensor placement(OSP) becomes an inevitable task in the design of HMS.This paper introduces the process for determining the OSP in HMS of a suspension bridge,in which four different OSP methods have been investigated,including the effective independence(EI) method,the effective independence driving-point residue(EFI-DPR) method,the minimized modal assurance criterion(minMAC) method and the principal subset selection-based extended EI(PSS-EI) method.Then,three criteria,which are modal assurance matrix(MAC),condition number(CN) of mode shape matrix and determinant of Fisher information matrix(FIM),were employed to evaluate the effect of the OSP methods respectively.The result showed that the PSS-EI method developed has the ability to guarantee the highest determinant of FIM,a relatively small off-diagonal term of MAC and agreeable CN,as well as the deployment of sensors in a uniform and symmetric fashion for the studied bridge.Finally,the scheme obtained by PSS-EI was adopted in the HMS.

Mode shape description of an aero-engine casing structure using Zernike moment descriptors

Vibration mode shape description of an aero-engine casing structure using Zernike moment descriptor(ZMD) was introduced in this paper.The mode shapes of the aero-engine casing structure can be decomposed as a linear combination of a series of Zernike polynomials,with the feature of each Zernike polynomial reflecting a part of characteristic of mode shapes,based on Zernike moment transformation.Meanwhile,the reconstruction of mode shapes with ZMD was explored and its ability to filtering the noise contaminated in the mode shapes was studied.Simulation of the aero-engine casing structure indicated the advantage of this method to depict the mode shapes of a symmetric structure.Results demonstrate that the Zernike moment description of the mode shapes can effectively describe the double modes in the symmetric structure and also has the ability to remove or significantly reduce the influence of noise in the mode shapes.Such feature shows great practical value for further research on the correlation,model updating and model validation of the symmetric structure's finite element model.

Mode Tracking Scheme Among Remeshed Models for Structural Optimization

Mode tracking is required in the structural optimization when the frequencies of certain specified modes must be maintained within a suitable range.A simple tracking method employing the mode number is invalid or misleading when local modes appear or disappear during mesh updating.In this work,a mode tracking scheme combining the nearest neighbor method(NNM)with the modal assurance criterion(MAC)is proposed.Several NNM algorithms are compared,and the k-dimensional tree(kd-tree)NNM is used to transform eigenvectors(mode shapes)from different scales to identical one.A threshold determination method is implemented for the MAC to assess the similarities in all the calculated modes.On the basis of the mode tracking scheme,specified modes can be tracked between different finite element method(FEM)models which have different meshes and optimized shapes.The effectiveness is verified through an example of shape optimization using an electric motor structure.