Nonlinear Vibrations of Thin-Walled Composite Frames
A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect t...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1994-1502 |
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| _version_ | 1832560407459397632 |
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| author | Ahmed K. Noor Jeanne M. Peters |
| author_facet | Ahmed K. Noor Jeanne M. Peters |
| author_sort | Ahmed K. Noor |
| collection | DOAJ |
| description | A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect to the material and lamination parameters of the frame. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The flanges and webs of the frames are modeled by using geometrically nonlinear two-dimensional shell and plate finite elements. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the frame, using the Linstedt–Poincaré perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. Numerical results are presented for semicircular thin-walled frames with I and J sections, showing the convergence of the nonlinear frequency and the sensitivity coefficients obtained by both the reduced-basis and perturbation techniques. |
| format | Article |
| id | doaj-art-a1c1753bee914382a8311a6fa53a3e95 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-a1c1753bee914382a8311a6fa53a3e952025-02-03T01:27:47ZengWileyShock and Vibration1070-96221875-92031994-01-011541542910.3233/SAV-1994-1502Nonlinear Vibrations of Thin-Walled Composite FramesAhmed K. Noor0Jeanne M. Peters1Center for Computational Structures Technology, University of Virginia, NASA Langley Research Center, Hampton, VA 23681, USACenter for Computational Structures Technology, University of Virginia, NASA Langley Research Center, Hampton, VA 23681, USAA reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect to the material and lamination parameters of the frame. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The flanges and webs of the frames are modeled by using geometrically nonlinear two-dimensional shell and plate finite elements. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the frame, using the Linstedt–Poincaré perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. Numerical results are presented for semicircular thin-walled frames with I and J sections, showing the convergence of the nonlinear frequency and the sensitivity coefficients obtained by both the reduced-basis and perturbation techniques.http://dx.doi.org/10.3233/SAV-1994-1502 |
| spellingShingle | Ahmed K. Noor Jeanne M. Peters Nonlinear Vibrations of Thin-Walled Composite Frames Shock and Vibration |
| title | Nonlinear Vibrations of Thin-Walled Composite Frames |
| title_full | Nonlinear Vibrations of Thin-Walled Composite Frames |
| title_fullStr | Nonlinear Vibrations of Thin-Walled Composite Frames |
| title_full_unstemmed | Nonlinear Vibrations of Thin-Walled Composite Frames |
| title_short | Nonlinear Vibrations of Thin-Walled Composite Frames |
| title_sort | nonlinear vibrations of thin walled composite frames |
| url | http://dx.doi.org/10.3233/SAV-1994-1502 |
| work_keys_str_mv | AT ahmedknoor nonlinearvibrationsofthinwalledcompositeframes AT jeannempeters nonlinearvibrationsofthinwalledcompositeframes |