Buckling and post-buckling of pinned Euler beams on weakened Winkler foundation under thermal loading

Piezoelectric nanobeams with excellent mechanical, thermal and electrical properties are important components in micro-nano electromechanical systems, which are widely used as sensors, brakes and resonators. Based on the Euler-Bernoulli beam model, the influence of surface effect on the post-buckling behavior of piezoelectric nanobeams is analyzed. According to the surface elasticity theory and the ' core-shell ' model, the surface energy model is used to introduce the influence of surface effect. The governing equations and boundary conditions of the post-buckling of piezoelectric nanobeams under the influence of surface effects are derived by the principle of minimum potential energy. The analytical solution of post-buckling is obtained by the eigenvalue method. The influence of surface effect on post-buckling configuration, post-buckling path, amount of induced charge and critical load of piezoelectric nanobeams with different external constraints and cross-sectional dimensions are discussed. The results show that surface effect has a significant influence on the post-buckling of piezoelectric nanobeams. Considering surface effect, the effective elastic modulus and critical load of piezoelectric nanobeams are increased, and the post-buckling configuration, post-buckling path and amount of induced charge are reduced. These findings contribute to the study of micro-nano electromechanical systems based on nanobeam structures and provide a theoretical basis for the design and manufacture of nanodevices.

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“…According to von-Kármán nonlinear strain-displacement relationship [23,24], the strain at any point on the axis of piezoelectric nanobeams is:…”

Section: Basic Equations and Calculation Methods 21 Basic Equationsmentioning

confidence: 99%

“…Substituting equation (27) into equation (24), then the post-buckling configuration amplitudes of piezoelectric nanobeam can be expressed as:…”

Section: Calculation Methodsmentioning

confidence: 99%

Influence of surface effect on post-buckling behavior of piezoelectric nanobeams

et al. 2023

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“…The film deformed out of a plane only can be modeled into a beam, which greatly simplifies theoretical analysis [ 24 ]. The compliant substrate is considered to be a Winkler elastic foundation [ 47 , 48 , 49 , 50 ], whose reaction at any point is proportional to the deflection, with stiffness

and deflection of the thin film

shown in Figure 1 b, where

is the function of Cartesian coordinate

, which is along the axial direction of the thin film.…”

Section: Buckling Analysismentioning

confidence: 99%

Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Fan

Wang

et al. 2020

Sensors

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Buckling stability of thin films on compliant substrates is universal and essential in stretchable electronics. The dynamic behaviors of this special system are unavoidable when the stretchable electronics are in real applications. In this paper, an analytical model is established to investigate the vibration of post-buckled thin films on a compliant substrate by accounting for the substrate as an elastic foundation. The analytical predictions of natural frequencies and vibration modes of the system are systematically investigated. The results may serve as guidance for the dynamic design of the thin film on compliant substrates to avoid resonance in the noise environment.

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“…Kurguzov and Demeshkin [20] carried out axial compression experiments on polished steel strips glued to a cellular or vacuum rubber, and compared the numerically calculated critical loads and buckling modes with the experimental data. Wen et al [21] investigated the buckling and post-buckling behavior of beams on a weakened Winkler foundation under thermal loading. The stability of the critical state is an important problem.…”

Section: Introductionmentioning

confidence: 99%

“…The stability of the column on the elastic foundation has been investigated for a long time. Research [3][4][5][6][7][8][9][10][11][12][13][14][15][16] has focused on the buckling load and efforts are underway [17][18][19][20][21]. Additional motivation has emerged in the semiconductor field in the study of microscopic column structures of entities such as carbon nanotubes (CNTs), where it has been possible to model them as columns placed on an elastic foundation [3].…”

Section: Introductionmentioning

confidence: 99%

Stability of the critical equilibrium of a compressed column on a Winkler foundation

Gao

Jin

2021

Mathematics and Mechanics of Solids

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In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.

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Buckling and post-buckling of pinned Euler beams on weakened Winkler foundation under thermal loading

Cited by 9 publications

References 27 publications

Influence of surface effect on post-buckling behavior of piezoelectric nanobeams

Influence of surface effect on post-buckling behavior of piezoelectric nanobeams

Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Stability of the critical equilibrium of a compressed column on a Winkler foundation

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