Publicação
Vibração de vigas com secção aberta de parede fina - Efeito das tensões iniciais
| Resumo: | The bending rigidities in the main plane of lesser inertia and torsion of the thin-walled open section profiles are reduced, which causes them to exhibit low vibration frequencies in the lateral bending and torsion modes. The influence of the internal stresses (initial tensions) on the natural frequencies and modes of vibration of these structures are a relevant issue in the design and verification of their safety. In order to obtain results of practical interest, a one-dimensional mathematical model is presented for the influence of the initial stresses (generalized tensions) on the vibration by lateral flexion and twisting of thin-walled I-beams, of equal flanges (double symmetrical section) or unequal (monosymmetric section).The model was based on the classical hypotheses of Vlasov (1961) for the non-uniform twist, which allow to realize the required dimensional reduction, neglecting the distortions by shear strenght and considering the effects of the inertia associated with the rotation of the cross sections around its weak axis and inertia associated with twist warpage. The equations of motion (partial differential equations) and boundary conditions are established through Hamilton's variational principle. The technique of separating variables allows us to define a problem of values and proper functions (with ordinary differential equations), which provides the own frequencies and modes of vibration.As you would expect, the vibration frequency itself decreases as the initial stress increase. |
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| Autores principais: | Silva, Tatiana Andreia Marinha |
| Assunto: | Vibrações Tensões iniciais Flexão lateral e torção Vigas de secção em I de parede fina Inércias de rotação e empenamento Vibrations Initial stress Lateral flexion and torsion Thin-walled I-beams Rotacional and warping inertias |
| Ano: | 2017 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Coimbra |
| Idioma: | português |
| Origem: | Estudo Geral - Universidade de Coimbra |
| Resumo: | The bending rigidities in the main plane of lesser inertia and torsion of the thin-walled open section profiles are reduced, which causes them to exhibit low vibration frequencies in the lateral bending and torsion modes. The influence of the internal stresses (initial tensions) on the natural frequencies and modes of vibration of these structures are a relevant issue in the design and verification of their safety. In order to obtain results of practical interest, a one-dimensional mathematical model is presented for the influence of the initial stresses (generalized tensions) on the vibration by lateral flexion and twisting of thin-walled I-beams, of equal flanges (double symmetrical section) or unequal (monosymmetric section).The model was based on the classical hypotheses of Vlasov (1961) for the non-uniform twist, which allow to realize the required dimensional reduction, neglecting the distortions by shear strenght and considering the effects of the inertia associated with the rotation of the cross sections around its weak axis and inertia associated with twist warpage. The equations of motion (partial differential equations) and boundary conditions are established through Hamilton's variational principle. The technique of separating variables allows us to define a problem of values and proper functions (with ordinary differential equations), which provides the own frequencies and modes of vibration.As you would expect, the vibration frequency itself decreases as the initial stress increase. |
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