Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies
A mathematical model of the dynamic instability of a three-layer conical shells with honeycomb structure made using additive technologies has been obtained. Dynamic instability is recognized as the interaction of the shell with a supersonic gas flow. The middle layer of the structure is a honeycomb...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
NAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering Problems
2022-03-01
|
| Series: | Journal of Mechanical Engineering |
| Subjects: |
| _version_ | 1828490876842672128 |
|---|---|
| author | Kostiantyn V. Avramov Borys V. Uspenskyi Iryna V. Biblik |
| author_facet | Kostiantyn V. Avramov Borys V. Uspenskyi Iryna V. Biblik |
| author_sort | Kostiantyn V. Avramov |
| collection | DOAJ |
| description | A mathematical model of the dynamic instability of a three-layer conical shells with honeycomb structure made using additive technologies has been obtained. Dynamic instability is recognized as the interaction of the shell with a supersonic gas flow. The middle layer of the structure is a honeycomb that is homogenized into an orthotropic homogeneous medium. The top and bottom layers of the shell are made of carbon fiber. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of displacements of the layer middle surface and two rotation angles of the normal of the layer middle surface. The high-order shear theory is used to describe the deformation state of the structure. The relation between stresses and strains is expressed by a power expansion in the transverse coordinate up to its cubic terms. To obtain a system of ordinary differential equations describing dynamic instability, the method of given forms is used. To assess the dynamic instability, characteristic indicators are calculated by solving the generalized problem of eigenvalues. The natural vibrations of the structure are studied by the Rayleigh-Ritz method. The minimum natural frequency in the cantilevered shell is observed when the number of waves in the circumferential direction is 6. It is also observed in the shell clamped on both sides when the number of waves in the circumferential direction is 1. The dynamic instability properties of the trivial equilibrium state of the structure are studied using numerical simulation. Shells that are cantilevered and clamped on both sides are analyzed. It is shown that the minimum critical pressure is observed when the number of waves in the circumferential direction is 1. The dependence of the critical pressure on the Mach number and angle of attack is studied. It has been established that with an increase in the Mach number and angle of attack, the critical pressure decreases. |
| first_indexed | 2024-12-11T10:52:21Z |
| format | Article |
| id | doaj.art-4bbfcf3181f848728bf94f174b0298c1 |
| institution | Directory Open Access Journal |
| issn | 2709-2984 2709-2992 |
| language | English |
| last_indexed | 2024-12-11T10:52:21Z |
| publishDate | 2022-03-01 |
| publisher | NAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering Problems |
| record_format | Article |
| series | Journal of Mechanical Engineering |
| spelling | doaj.art-4bbfcf3181f848728bf94f174b0298c12022-12-22T01:10:15ZengNAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering ProblemsJournal of Mechanical Engineering2709-29842709-29922022-03-0125161410.15407/pmach2022.01.006Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive TechnologiesKostiantyn V. Avramov0https://orcid.org/0000-0002-8740-693XBorys V. Uspenskyi1https://orcid.org/0000-0001-6360-7430Iryna V. Biblik2https://orcid.org/0000-0002-8650-1134A. Pidhornyi Institute of Mechanical Engineering Problems of NASU, Kharkiv, UkraineA. Pidhornyi Institute of Mechanical Engineering Problems of NASU, Kharkiv, UkraineA. Pidhornyi Institute of Mechanical Engineering Problems of NASU, Kharkiv, UkraineA mathematical model of the dynamic instability of a three-layer conical shells with honeycomb structure made using additive technologies has been obtained. Dynamic instability is recognized as the interaction of the shell with a supersonic gas flow. The middle layer of the structure is a honeycomb that is homogenized into an orthotropic homogeneous medium. The top and bottom layers of the shell are made of carbon fiber. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of displacements of the layer middle surface and two rotation angles of the normal of the layer middle surface. The high-order shear theory is used to describe the deformation state of the structure. The relation between stresses and strains is expressed by a power expansion in the transverse coordinate up to its cubic terms. To obtain a system of ordinary differential equations describing dynamic instability, the method of given forms is used. To assess the dynamic instability, characteristic indicators are calculated by solving the generalized problem of eigenvalues. The natural vibrations of the structure are studied by the Rayleigh-Ritz method. The minimum natural frequency in the cantilevered shell is observed when the number of waves in the circumferential direction is 6. It is also observed in the shell clamped on both sides when the number of waves in the circumferential direction is 1. The dynamic instability properties of the trivial equilibrium state of the structure are studied using numerical simulation. Shells that are cantilevered and clamped on both sides are analyzed. It is shown that the minimum critical pressure is observed when the number of waves in the circumferential direction is 1. The dependence of the critical pressure on the Mach number and angle of attack is studied. It has been established that with an increase in the Mach number and angle of attack, the critical pressure decreases.linear dynamic systemthree-layer conical shellcharacteristic exponentsmach numbers |
| spellingShingle | Kostiantyn V. Avramov Borys V. Uspenskyi Iryna V. Biblik Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies Journal of Mechanical Engineering linear dynamic system three-layer conical shell characteristic exponents mach numbers |
| title | Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies |
| title_full | Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies |
| title_fullStr | Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies |
| title_full_unstemmed | Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies |
| title_short | Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies |
| title_sort | dynamic instability of a three layer conical shell with honeycomb structure made by additive technologies |
| topic | linear dynamic system three-layer conical shell characteristic exponents mach numbers |
| work_keys_str_mv | AT kostiantynvavramov dynamicinstabilityofathreelayerconicalshellwithhoneycombstructuremadebyadditivetechnologies AT borysvuspenskyi dynamicinstabilityofathreelayerconicalshellwithhoneycombstructuremadebyadditivetechnologies AT irynavbiblik dynamicinstabilityofathreelayerconicalshellwithhoneycombstructuremadebyadditivetechnologies |