Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell
Equations for the parametric resonance of a three-layered cylindrical shell with composite layers stiffened with ribs and containing a hollow isotropic cylinder are obtained. The shell is loaded by axial forces and an external pressure varying harmonically in time. The influence of the cylinder is m...
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| Veröffentlicht in: | Mechanics of composite materials 2021-11, Vol.57 (5), p.623-634 |
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| creator | Bakulin, V. N. Boitsova, D. A. Nedbai, A. Ya |
| description | Equations for the parametric resonance of a three-layered cylindrical shell with composite layers stiffened with ribs and containing a hollow isotropic cylinder are obtained. The shell is loaded by axial forces and an external pressure varying harmonically in time. The influence of the cylinder is modeled as an elastic foundation whose modulus of subgrade reaction was determined from equations of 3D elasticity theory. Their solution is sought in the form of a trigonometric series in the axial coordinate. The infinite system of inhomogeneous differential equations of Mathieu–Hill type obtained is solved using a trigonometric series in time. Using a numerical example, the main regions of instability were obtained for the first time, and plots for the critical frequencies on the channel radius, the elastic modulus of cylinder material, and the number and height of ribs are found. The mathematical model proposed extends the range of relevant scientific and applied problems in studying three-layered stiffened shells. |
| doi_str_mv | 10.1007/s11029-021-09984-9 |
| format | Article |
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Using a numerical example, the main regions of instability were obtained for the first time, and plots for the critical frequencies on the channel radius, the elastic modulus of cylinder material, and the number and height of ribs are found. 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N.</creatorcontrib><creatorcontrib>Boitsova, D. A.</creatorcontrib><creatorcontrib>Nedbai, A. Ya</creatorcontrib><title>Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell</title><title>Mechanics of composite materials</title><addtitle>Mech Compos Mater</addtitle><description>Equations for the parametric resonance of a three-layered cylindrical shell with composite layers stiffened with ribs and containing a hollow isotropic cylinder are obtained. The shell is loaded by axial forces and an external pressure varying harmonically in time. The influence of the cylinder is modeled as an elastic foundation whose modulus of subgrade reaction was determined from equations of 3D elasticity theory. Their solution is sought in the form of a trigonometric series in the axial coordinate. The infinite system of inhomogeneous differential equations of Mathieu–Hill type obtained is solved using a trigonometric series in time. Using a numerical example, the main regions of instability were obtained for the first time, and plots for the critical frequencies on the channel radius, the elastic modulus of cylinder material, and the number and height of ribs are found. The mathematical model proposed extends the range of relevant scientific and applied problems in studying three-layered stiffened shells.</description><subject>Axial forces</subject><subject>Ceramics</subject><subject>Characterization and Evaluation of Materials</subject><subject>Chemistry and Materials Science</subject><subject>Classical Mechanics</subject><subject>Composite materials</subject><subject>Composites</subject><subject>Critical frequencies</subject><subject>Cylinders</subject><subject>Cylindrical shells</subject><subject>Differential equations</subject><subject>Elastic foundations</subject><subject>External pressure</subject><subject>Glass</subject><subject>Materials Science</subject><subject>Mathematical models</subject><subject>Modulus of elasticity</subject><subject>Natural Materials</subject><subject>Resonance</subject><subject>Shells</subject><subject>Solid Mechanics</subject><subject>Subgrade reaction</subject><issn>0191-5665</issn><issn>1573-8922</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kU1rGzEQhkVpoW6SP5DTQk45KBl97a6OwfTDYEhju2cha0eOwnrlSGuo_32VbCDkUuYwMDzPzMBLyCWDGwbQ3GbGgGsKnFHQupVUfyIzphpBW835ZzIDphlVda2-km85PwEUDeoZefhtk93jmIKrVpjjYAeHVfSVrTaPCZEu7QkTdtX81IehK5jtq3ncH2IOI1arsKXrMXiPQ2HWj9j35-SLt33Gi7d-Rv78-L6Z_6LL-5-L-d2SOqH5SFshJDolRON0g8i8hK71zHrGu4ZZvUUhueeS1e229S1Y5YUDKZzgjdKgxRm5mvYeUnw-Yh7NUzymoZw0vAbF65orKNTNRO1sjyYMPo7JulId7oOLA_pQ5nd1K5VSIGURrj8IhRnx77izx5zNYr36yPKJdSnmnNCbQwp7m06GgXnJxUy5mJKLec3FvPwtJikXeNhhev_7P9Y_1QuNxg</recordid><startdate>20211101</startdate><enddate>20211101</enddate><creator>Bakulin, V. 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| subjects | Axial forces Ceramics Characterization and Evaluation of Materials Chemistry and Materials Science Classical Mechanics Composite materials Composites Critical frequencies Cylinders Cylindrical shells Differential equations Elastic foundations External pressure Glass Materials Science Mathematical models Modulus of elasticity Natural Materials Resonance Shells Solid Mechanics Subgrade reaction |
| title | Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell |
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