Modified transfer matrix method for steady-state forced vibration: a system of bar elements
The Elements by a System of Transfer (EST) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is ass...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Estonian Academy Publishers
2020-04-01
|
| Series: | Proceedings of the Estonian Academy of Sciences |
| Subjects: | |
| Online Access: | http://www.kirj.ee/public/proceedings_pdf/2020/issue_2/proc-2020-2-143-161.pdf |
| _version_ | 1818406084471160832 |
|---|---|
| author | Andres Lahe Andres Braunbrück Aleksander Klauson |
| author_facet | Andres Lahe Andres Braunbrück Aleksander Klauson |
| author_sort | Andres Lahe |
| collection | DOAJ |
| description | The Elements by a System of Transfer (EST) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that in a steady state a bar/beam will vibrate with the circular frequency of a harmonic excitation force. The universal equation of elastic displacement (2nd/4th order differential equation) is described as a system of first order differential equations in matrix form. For the differential equations the compatibility conditions of a bar/beam element displacements at joint serve as essential boundary conditions. As the natural boundary conditions at joints, the equilibrium equations of elastic forces of bar/beam elements are considered. At the supports, restrictions to displacements (support conditions) have been applied. For steady-state forced vibration the phenomena of dynamic vibration absorption near the saddle points are observed and the response curves for displacement amplitude and elastic energy are calculated. The magnification factor at the excitation frequency is determined. |
| first_indexed | 2024-12-14T09:06:19Z |
| format | Article |
| id | doaj.art-c4120d07a28a40e998e47e428efe72a7 |
| institution | Directory Open Access Journal |
| issn | 1736-6046 1736-7530 |
| language | English |
| last_indexed | 2024-12-14T09:06:19Z |
| publishDate | 2020-04-01 |
| publisher | Estonian Academy Publishers |
| record_format | Article |
| series | Proceedings of the Estonian Academy of Sciences |
| spelling | doaj.art-c4120d07a28a40e998e47e428efe72a72022-12-21T23:08:42ZengEstonian Academy PublishersProceedings of the Estonian Academy of Sciences1736-60461736-75302020-04-0169214316110.3176/proc.2020.2.0610.3176/proc.2020.2.06Modified transfer matrix method for steady-state forced vibration: a system of bar elementsAndres Lahe0Andres Braunbrück1Aleksander Klauson2Department of Civil Engineering and Architecture, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, EstoniaDepartment of Civil Engineering and Architecture, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, EstoniaDepartment of Civil Engineering and Architecture, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, EstoniaThe Elements by a System of Transfer (EST) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that in a steady state a bar/beam will vibrate with the circular frequency of a harmonic excitation force. The universal equation of elastic displacement (2nd/4th order differential equation) is described as a system of first order differential equations in matrix form. For the differential equations the compatibility conditions of a bar/beam element displacements at joint serve as essential boundary conditions. As the natural boundary conditions at joints, the equilibrium equations of elastic forces of bar/beam elements are considered. At the supports, restrictions to displacements (support conditions) have been applied. For steady-state forced vibration the phenomena of dynamic vibration absorption near the saddle points are observed and the response curves for displacement amplitude and elastic energy are calculated. The magnification factor at the excitation frequency is determined.http://www.kirj.ee/public/proceedings_pdf/2020/issue_2/proc-2020-2-143-161.pdfsteady-state forced vibrationsdynamic vibration absorptionstanding wavesforcing functionstransfer equationsessential boundary conditions at jointsnatural boundary conditions at jointssupport conditionsmagnification factor. |
| spellingShingle | Andres Lahe Andres Braunbrück Aleksander Klauson Modified transfer matrix method for steady-state forced vibration: a system of bar elements Proceedings of the Estonian Academy of Sciences steady-state forced vibrations dynamic vibration absorption standing waves forcing functions transfer equations essential boundary conditions at joints natural boundary conditions at joints support conditions magnification factor. |
| title | Modified transfer matrix method for steady-state forced vibration: a system of bar elements |
| title_full | Modified transfer matrix method for steady-state forced vibration: a system of bar elements |
| title_fullStr | Modified transfer matrix method for steady-state forced vibration: a system of bar elements |
| title_full_unstemmed | Modified transfer matrix method for steady-state forced vibration: a system of bar elements |
| title_short | Modified transfer matrix method for steady-state forced vibration: a system of bar elements |
| title_sort | modified transfer matrix method for steady state forced vibration a system of bar elements |
| topic | steady-state forced vibrations dynamic vibration absorption standing waves forcing functions transfer equations essential boundary conditions at joints natural boundary conditions at joints support conditions magnification factor. |
| url | http://www.kirj.ee/public/proceedings_pdf/2020/issue_2/proc-2020-2-143-161.pdf |
| work_keys_str_mv | AT andreslahe modifiedtransfermatrixmethodforsteadystateforcedvibrationasystemofbarelements AT andresbraunbruck modifiedtransfermatrixmethodforsteadystateforcedvibrationasystemofbarelements AT aleksanderklauson modifiedtransfermatrixmethodforsteadystateforcedvibrationasystemofbarelements |