Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory
Source abstract
Abstract
Abstract In the present study, vibration response of non-homogenous and non-uniform microbeams is investigated in conjunction with Bernoulli–Euler beam and modified couple stress theory. The boundary conditions of the microbeam are considered as fixed at one end and free at the other end. It is taken into consideration that material properties and cross section of the microbeam vary continuously along the longitudinal direction. Rayleigh–Ritz solution method is utilized to obtain an approximate solution to the free transverse vibration problem. A detailed study is carried out to show the effects of material properties and taper ratios on natural frequencies of axially functionally graded tapered microbeams. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed between them.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (83)
Show source-provided references
1. Buckling of variable section columns under axial loading10.1061/(ASCE)EM.1943-7889.0000096 ↗
2. Buckling loads for variable cross-section members with variable axial forces10.1016/0020-7683(91)90224-4 ↗
3. Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading10.1016/S0997-7538(01)01143-3 ↗
4. Vibration of non-uniform rods and beams10.1006/jsvi.1995.0410 ↗
5. Vibration of a variable cross-section beam10.1016/j.mechrescom.2006.06.005 ↗
6. Application of differential transform method in free vibration analysis of rotating non-prismatic beams
7. Basic displacement functions for centrifugally stiffened tapered beams10.1002/cnm.1365 ↗
8. Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods10.12989/sem.2008.28.2.221 ↗
9. Analysis of functionally graded plates10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8 ↗
10. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method10.1016/j.compstruct.2004.08.003 ↗
11. Natural frequencies of functionally graded plates by a meshless method10.1016/j.compstruct.2006.04.018 ↗
12. Free vibration analysis of functionally graded beams with simply supported edges10.1016/j.matdes.2006.02.007 ↗
13. Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation10.1016/j.compstruct.2007.01.019 ↗
14. Free vibration and buckling analyses of functionally graded beams with edge cracks10.1016/j.compstruct.2007.03.006 ↗
15. Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations10.1016/j.compstruct.2007.07.004 ↗
16. An analytical method for free vibration analysis of functionally graded beams10.1016/j.matdes.2008.05.015 ↗
17. Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method10.1016/j.jsv.2008.09.018 ↗
18. Buckling and vibration analysis of functionally graded composite structures using the finite element method10.1016/j.compstruct.2008.07.022 ↗
19. Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories10.1016/j.nucengdes.2009.12.013 ↗
20. Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load10.1016/j.compstruct.2009.04.024 ↗
21. Vibration analysis of a functionally graded beam under a moving mass by using different beam theories10.1016/j.compstruct.2009.09.030 ↗
22. A new beam finite element for the analysis of functionally graded materials10.1016/S0020-7403(03)00058-4 ↗
23. Bending response of functionally graded plates by using a new higher order shear deformation theory10.1016/j.compstruct.2011.09.007 ↗
24. Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load10.1016/j.compstruct.2012.03.016 ↗
25. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates10.1016/j.compositesb.2011.08.009 ↗
26. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates10.1016/j.compstruct.2011.12.005 ↗
27. Closed-form solutions for natural frequency for inhomogeneous beams with one sliding support and the other pinned10.1006/jsvi.2000.3009 ↗
28. Inverse buckling problem for inhomogeneous columns10.1016/S0020-7683(00)00049-4 ↗
29. Apparently first closed-form solution for vibrating: inhomogeneous beams10.1016/S0020-7683(00)00266-3 ↗
30. Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode10.1016/j.jsv.2004.08.038 ↗
31. Semi-inverse method for vibration and buckling of axially functionally graded beams10.1177/0731684407081369 ↗
32. Buckling of columns of variable flexural rigidity10.1061/(ASCE)0733-9399(1992)118:3(640) ↗
33. A new approach for free vibration of axially functionally graded beams with non-uniform cross-section10.1016/j.jsv.2009.12.029 ↗
34. Buckling analysis of nonuniform and axially graded columns with varying flexural rigidity10.1061/(ASCE)EM.1943-7889.0000206 ↗
35. Free vibration characteristics of a functionally graded beam by finite element method10.1016/j.apm.2010.07.006 ↗
36. Free vibration and stability of axially functionally graded tapered Euler–Bernoulli beams10.1155/2011/591716 ↗
37. Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions10.1016/j.compositesb.2011.01.017 ↗
38. Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials10.1016/j.apm.2011.09.073 ↗
39. Extending the travel range of analog-tuned electrostatic actuators10.1109/84.809065 ↗
40. Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques10.1016/S0304-3991(03)00077-9 ↗
41. Miniaturized flexible temperature sensor10.1109/JMEMS.2007.908437 ↗
42. Mechanical response of a capacitive microsensor under thermal load10.1016/j.cnsns.2005.06.006 ↗
43. Strain gradient plasticity: theory and experiment10.1016/0956-7151(94)90502-9 ↗
44. A microbend test method for measuring the plasticity length scale10.1016/S1359-6454(98)00153-0 ↗
45. Experiments and theory in strain gradient elasticity10.1016/S0022-5096(03)00053-X ↗
46. Couple stress based strain gradient theory for elasticity10.1016/S0020-7683(02)00152-X ↗
47. Bernoulli–Euler beam model based on a modified couple stress theory10.1088/0960-1317/16/11/015 ↗
48. The size-dependent natural frequency of Bernoulli–Euler micro-beams10.1016/j.ijengsci.2007.10.002 ↗
49. A microstructure-dependent Timoshenko beam model based on a modified couple stress theory10.1016/j.jmps.2008.09.007 ↗
50. A nonclassical Reddy–Levinson beam model based on a modified couple stress model10.1615/IntJMultCompEng.v8.i2.30 ↗
51. Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory10.1016/j.ijengsci.2010.09.027 ↗
52. Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams10.1016/j.ijengsci.2010.12.009 ↗
53. On the size-dependent behavior of functionally graded micro-beams10.1016/j.matdes.2009.12.006 ↗
54. A nonlinear Timoshenko beam formulation based on the modified couple stress theory10.1016/j.ijengsci.2010.09.025 ↗
55. Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration10.1016/j.ijengsci.2010.04.010 ↗
56. The modified couple stress functionally graded Timoshenko beam formulation10.1016/j.matdes.2010.08.046 ↗
57. Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory10.1016/j.compstruct.2010.09.008 ↗
58. Microstructure-dependent couple stress theories of functionally graded beams10.1016/j.jmps.2011.06.008 ↗
59. Dynamic behavior of an axially functionally graded beam under action of a moving harmonic10.1016/j.compstruct.2012.03.020 ↗
60. Free vibration of an axially functionally graded pile with pinned ends embedded in Winkler–Pasternak elastic medium10.12989/sem.2011.40.4.583 ↗
61. Bending relationships between the modified couple stress-based functionally graded Timoshenko beams and homogeneous Bernoulli–Euler beams10.1007/s12356-012-0026-z ↗
62. Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory10.1016/j.ijmecsci.2012.02.004 ↗
63. A new Kirchhoff plate model based on a modified couple stress theory10.1016/j.ijsolstr.2009.03.004 ↗
64. Vibration analysis of microscale plates based on modified couple stress theory10.1016/S0894-9166(10)60040-7 ↗
65. The size-dependent vibration analysis of micro-plates based on a modified couple stress theory10.1016/j.physe.2010.11.005 ↗
66. A non-classical Mindlin plate model based on a modified couple stress theory10.1007/s00707-011-0480-4 ↗
67. Geometrically nonlinear micro-plate formulation based on the modified couple stress theory10.1016/j.ijengsci.2011.08.013 ↗
68. Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory10.1016/j.jsv.2011.08.020 ↗
69. A nonlinear modified couple stress-based third-order theory of functionally graded plates10.1016/j.compstruct.2011.10.006 ↗
70. Nonlinear theories of axisymmetric bending of functionally graded circular plates with modified couple stress10.1016/j.compstruct.2012.04.019 ↗
71. Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory10.1016/j.compstruct.2012.08.023 ↗
72. A size-dependent functionally graded Reddy plate model based on a modified couple stress theory
73. A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory10.1016/j.compstruct.2012.09.025 ↗
74. Analysis of Mindlin micro plates with a modified couple stress theory and a meshless method10.1016/j.apm.2012.09.063 ↗
75. Static analysis of tapered nanowires based on nonlocal Euler–Bernoulli beam theory via differential quadrature method10.1590/S1679-78252012000200007 ↗
76. Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory10.1016/j.physe.2009.04.015 ↗
77. Free transverse vibration of an axially loaded non-prismatic single-walled carbon nanotube embedded in a two-parameter elastic medium10.1016/j.commatsci.2010.10.005 ↗
78. Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique10.1016/j.physe.2010.08.022 ↗
79. Stability of single-walled carbon nanotubes and single-walled carbon nanocones under self-weight and an axial tip force10.1016/j.ijengsci.2010.12.006 ↗
80. Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method10.1016/j.mechrescom.2011.09.004 ↗
81. Small scale effect on axial vibration of non-uniform and non-homogeneous nanorods10.1016/j.commatsci.2011.10.033 ↗
82. Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods10.1016/j.commatsci.2012.04.001 ↗
83. Rao · 1995