Applied Mathematics and Mechanics >
Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams
Received date: 2023-11-28
Online published: 2024-06-01
Supported by
the National Natural Science Foundation of China(Nos. 11602204);the National Natural Science Foundation of China(Nos. 12102373);the Fundamental Research Funds for the Central Universities of China(Nos. 2682022ZTPY081);the Fundamental Research Funds for the Central Universities of China(Nos. 2682022CX056);the Natural Science Foundation of Sichuan Province of China(Nos. 2023NSFSC0849);the Natural Science Foundation of Sichuan Province of China(Nos. 2023NSFSC1300);the Natural Science Foundation of Sichuan Province of China(Nos. 2022NSFSC1938);the Natural Science Foundation of Sichuan Province of China(Nos. 2022NSFSC2003);Project supported by the National Natural Science Foundation of China (Nos. 11602204 and 12102373), the Fundamental Research Funds for the Central Universities of China (Nos. 2682022ZTPY081 and 2682022CX056), and the Natural Science Foundation of Sichuan Province of China (Nos. 2023NSFSC0849, 2023NSFSC1300, 2022NSFSC1938, and 2022NSFSC2003)
Copyright
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).
Songye JIN, Bo ZHANG, Wuyuan ZHANG, Yuxing WANG, Huoming SHEN, Jing WANG, Juan LIU . Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams[J]. Applied Mathematics and Mechanics, 2024 , 45(6) : 1015 -1032 . DOI: 10.1007/s10483-024-3121-8
| 1 | KANE,T. R.,RYAN,R. R., andBANERJEE,A. K.Dynamic of a cantilever beam attached to a moving base.Journal of Guidance Control & Dynamics,10(2),139-151(1987) |
| 2 | HUANG,C. L.,LIN,W. Y., andHSIAO,K. M.Free vibration analysis of rotating Euler beams at high angular velocity.Computers and Structures,88(17-18),991-1001(2010) |
| 3 | LIN,S. C., andHSIAO,K. M.Vibration analysis of a rotating Timoshenko beam.Journal of Sound and Vibration,240(2),303-322(2001) |
| 4 | YANG,J. B.,JIANG,L. J., andCHEN,D. C.Dynamic modelling and control of a rotating Euler-Bernoulli beam.Journal of Sound and Vibration,274(3-5),863-875(2004) |
| 5 | LI,L.,ZHANG,D. G., andZHU,W. D.Free vibration analysis of a rotating hub-functionally graded material beam system with the dynamic stiffening effect.Journal of Sound and Vibration,333(5),1526-1541(2014) |
| 6 | FANG,J. S.,ZHOU,D., andDONG,Y.Three-dimensional vibration of rotating functionally graded beams.Journal of Vibration and Control,24(15),3292-3306(2017) |
| 7 | DU,X. K.,CHEN,Y. Z.,ZHANG,J.,GUO,X.,LI,L., andZHANG,D. G.Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect.Applied Mathematics and Mechanics (English Edition),44(1),125-140(2023) |
| 8 | ZENG,J.,MA,H.,YU,K.,XU,Z. T., andWEN,B. C.Coupled flapwise-chordwise-axial-torsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation.Applied Mathematics and Mechanics (English Edition),40(8),1053-1082(2019) |
| 9 | WANG,L. S.,SU,Z., andWANG,L. F.Flutter analysis of rotating beams with elastic restraints.Applied Mathematics and Mechanics (English Edition),43(5),761-776(2022) |
| 10 | LI,L.,LUO,Z.,LIU,K. N., andZHOU,J. L.Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies.Applied Mathematics and Mechanics (English Edition),44(2),221-236(2023) |
| 11 | JAFFERIS,N. T.,HELBLING,E. F.,KARPELSON,M., andWOOD,R. J.Untethered flight of an insect-sized flapping-wing microscale aerial vehicle.nature,570(7762),491-495(2019) |
| 12 | KOIZUMI,M.The concept of FGM..Ceramic Transactions,34,3-10(1993) |
| 13 | WANG,Y. L.,YANG,C. F.,ZHANG,Y. X.,DONG,S. P., andLI,L.Dynamics of a rotating hollow FGM beam in the temperature field.Reviews on Advanced Materials Science,60,643-662(2021) |
| 14 | ARVIN,H.,HOSSEINI,S. M. H., andKIANI,Y.Free vibration analysis of pre/post buckled rotating functionally graded beams subjected to uniform temperature rise.Thin-Walled Structures,158,107187(2021) |
| 15 | KHOSRAVI,S.,ARVIN,H., andKIANI,Y.Vibration analysis of rotating composite beams reinforced with carbon nanotubes in thermal environment.International Journal of Mechanical Sciences,164,105187(2019) |
| 16 | SHENAS,A. G.,ZIAEE,S., andMALEKZADEH,P.Post-buckling and vibration of post-buckled rotating pre-twisted FG microbeams in thermal environment.Thin-Walled Structures,138,335-360(2019) |
| 17 | LAM,D. C. C.,YANG,F.,CHONG,A. C. M.,WANG,J., andTONG,P.Experiments and theory in strain gradient elasticity.Journal of the Mechanics and Physics of Solids,51(8),1477-1508(2003) |
| 18 | XIE,Y.,LEI,J.,GUO,S.,HAN,S. H.,RUAN,J., andHE,Y. M.Size-dependent vibration of multi-scale sandwich micro-beams: an experimental study and theoretical analysis.Thin-Walled Structures,15(175),109115(2022) |
| 19 | FLECK,N. A.,MULLER,G. M.,ASHBY,M. F., andHUTCHINSON,J. W.Strain gradient plasticity: theory and experiment.Acta Metallurgica et Materialia,42(2),475-487(1994) |
| 20 | MINDLIN,R. D., andTIERSTEN,H. F.Effects of couple-stresses in linear elasticity.Archive for Rational Mechanics and Analysis,11(1),415-448(1962) |
| 21 | TOUPIN,R. A.Theories of elasticity with couple-stress.Archive for Rational Mechanics and Analysis,17(2),85-112(1964) |
| 22 | YANG,F.,CHONG,A. C. M.,LAM,D. C. C., andTONG,P.Couple stress based strain gradient theory for elasticity.International Journal of Solids and Structures,39(10),2731-2743(2002) |
| 23 | CORDERO,N. M.,FOREST,S., andBUSSO,E. P.Second strain gradient elasticity of nano-objects.Journal of the Mechanics and Physics of Solids,97,92-124(2016) |
| 24 | FU,G. Y.,ZHOU,S. J., andQI,L.On the strain gradient elasticity theory for isotropic materials.International Journal of Engineering Science,154,103348(2020) |
| 25 | LIM,C. W.,ZHANG,G., andREDDY,J. N.A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation.Journal of the Mechanics and Physics of Solids,78,298-313(2015) |
| 26 | MINDLIN,R. D., andESHEL,N. N.On first strain-gradient theories in linear elasticity.International Journal of Solids and Structures,4(1),109-124(1968) |
| 27 | ZHOU,S.,LI,A., andWANG,B.A reformulation of constitutive relations in the strain gradient elasticity theory for isotropic materials.International Journal of Solids and Structures,80,28-37(2016) |
| 28 | ZUO,D. Q.,SAFAEI,B.,SAHMANI,S., andMA,G. L.Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors.Applied Mathematics and Mechanics (English Edition),43(6),825-844(2022) |
| 29 | LU,L.,WANG,S.,LI,M., andGUO,X. M.Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets.Composite Structures,272,114231(2021) |
| 30 | LU,L.,SHE,G. L., andGUO,X. M.Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection.International Journal of Mechanical Sciences,199,106428(2021) |
| 31 | KONG,S. L.A review on the size-dependent models of micro-beam and micro-plate based on the modified couple stress theory.Archives of Computational Methods in Engineering,29(1),1-31(2021) |
| 32 | FANG,J. S.,GU,J. P.,WANG,H. W., andZHANG,X. P.Thermal effect on vibrational behaviors of rotating functionally graded microbeams.European Journal of Mechanics-A$/$Solids,75,497-515(2019) |
| 33 | HOSSEINI,S. M. H., andARVIN,H.Thermo-rotational buckling and post-buckling analyses of rotating functionally graded microbeams.International Journal of Mechanics and Materials in Design,17,55-72(2021) |
| 34 | BHATTACHARYA,S., andDAS,D.Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory.Composite Structures,215,471-492(2019) |
| 35 | THAI,H. T.,VO,T. P.,NGUYEN,T. K., andKIM,S. E.A review of continuum mechanics models for size-dependent analysis of beams and plates.Composite Structures,177,196-219(2017) |
| 36 | SENTHILNATHAN,N. R.,LIM,S. P.,LEE,K. H., andCHOW,S. T.Buckling of shear deformable plates.AIAA Journal,25(9),1268-1271(1987) |
| 37 | SHIMPI,R. P.Refined plate theory and its variants.AIAA Journal,40(1),137-146(2002) |
| 38 | YOO,H.H., andKIM,S. K.Free vibration analysis of rotating cantilever plates.AIAA Journal,40(11),2188-2196(2002) |
| 39 | PRADHAN,K. K., andCHAKRAVERTY,S.Effects of different shear deformation theories on free vibration of functionally graded beams.International Journal of Mechanical Sciences,82,149-160(2014) |
| 40 | ?IM?EK,M.Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories.Nuclear Engineering and Design,240(4),697-705(2010) |
| 41 | MA,H. M.,GAO,X. L., andREDDY,J. N.A microstructure-dependent Timoshenko beam model based on a modified couple stress theory.Journal of the Mechanics and Physics of Solids,56(12),3379-3391(2008) |
| 42 | OUISSE,M., andFOLTêTE,E.Model correlation and identification of experimental reduced models in vibroacoustical modal analysis.Journal of Sound and Vibration,342,200-217(2015) |
/
| 〈 |
|
〉 |
Email Alert
RSS