Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports
Exact solutions of buckling configurations and vibration response of post-buckled configurations of beams with non-classical boundary conditions (e.g., elastically supported) are presented using the Euler-Bernoulli theory. The geometric nonlinearity arising from mid-plane stretching (i.e., the von K...
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014001400010&lng=en&tlng=en |
| _version_ | 1811283501453934592 |
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| author | B. G. Sinira B. B. Özhanb J. N. Reddyc |
| author_facet | B. G. Sinira B. B. Özhanb J. N. Reddyc |
| author_sort | B. G. Sinira |
| collection | DOAJ |
| description | Exact solutions of buckling configurations and vibration response of post-buckled configurations of beams with non-classical boundary conditions (e.g., elastically supported) are presented using the Euler-Bernoulli theory. The geometric nonlinearity arising from mid-plane stretching (i.e., the von Kármán nonlinear strain) is considered in the formulation. The nonlinear equations are reduced to a single linear equation in terms of the transverse deflection by eliminating the axial displacement and incorporating the nonlinearity and the applied load into a constant. The resulting critical buckling loads and their associated mode shapes are obtained by solving the linearized buckling problem analytically. The buckling configurations are determined in terms of the applied axial load and the transverse deflection. The first buckled shape is the only stable equilibrium position for all boundary conditions considered. Then the pseudo-dynamic response of buckled beams is also determined analytically. Natural frequency versus buckling load and natural frequency versus amplitudes of buckling configurations are plotted for various non-classical boundary conditions. |
| first_indexed | 2024-04-13T02:12:52Z |
| format | Article |
| id | doaj.art-884d4cfa5cf84a74a4b3e0cf34c820ba |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-04-13T02:12:52Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-884d4cfa5cf84a74a4b3e0cf34c820ba2022-12-22T03:07:14ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782511142516253610.1590/S1679-78252014001400010S1679-78252014001400010Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supportsB. G. Sinira0B. B. Özhanb1J. N. Reddyc2Texas A&M UniversityTexas A&M UniversityTexas A&M UniversityExact solutions of buckling configurations and vibration response of post-buckled configurations of beams with non-classical boundary conditions (e.g., elastically supported) are presented using the Euler-Bernoulli theory. The geometric nonlinearity arising from mid-plane stretching (i.e., the von Kármán nonlinear strain) is considered in the formulation. The nonlinear equations are reduced to a single linear equation in terms of the transverse deflection by eliminating the axial displacement and incorporating the nonlinearity and the applied load into a constant. The resulting critical buckling loads and their associated mode shapes are obtained by solving the linearized buckling problem analytically. The buckling configurations are determined in terms of the applied axial load and the transverse deflection. The first buckled shape is the only stable equilibrium position for all boundary conditions considered. Then the pseudo-dynamic response of buckled beams is also determined analytically. Natural frequency versus buckling load and natural frequency versus amplitudes of buckling configurations are plotted for various non-classical boundary conditions.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014001400010&lng=en&tlng=enAnalytical solutionsbuckling analysisEuler-Bernoulli beam theorypseudo-dynamic analysisvon Kármán nonlinearity |
| spellingShingle | B. G. Sinira B. B. Özhanb J. N. Reddyc Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports Latin American Journal of Solids and Structures Analytical solutions buckling analysis Euler-Bernoulli beam theory pseudo-dynamic analysis von Kármán nonlinearity |
| title | Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports |
| title_full | Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports |
| title_fullStr | Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports |
| title_full_unstemmed | Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports |
| title_short | Buckling configurations and dynamic response of buckled Euler-Bernoulli beams with non-classical supports |
| title_sort | buckling configurations and dynamic response of buckled euler bernoulli beams with non classical supports |
| topic | Analytical solutions buckling analysis Euler-Bernoulli beam theory pseudo-dynamic analysis von Kármán nonlinearity |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014001400010&lng=en&tlng=en |
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