Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Józef Szybiński; Piotr Ruta

doi:10.2478/sgem-2019-0001

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Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Studia Geotechnica et Mechanica

Volume 41 (2019): Issue 1 (April 2019)

By: Józef Szybiński and Piotr Ruta

Open Access

|Mar 2019

Figures & Tables

Coordinate system and local basis vectors for nonprismatic thin-walled beam.

Description of displacements for cross section.

Analysed beams and dimensions of their cross sections.

Table 1

Eigenfrequencies in case of clamped-clamped support (C-C) [Hz].

Mode number	Paper dim = 10	Paper dim = 15	Paper dim = 20	FEM SOFiSTiK beam element 7DOF d = 20	FEM SOFiSTiK beam element 7DOF d = 25	FEM SOFiSTiK beam element 7DOF d = 50	FEM Abaqus shell elements (quad)
1	10.17	10.15	10.15	10.17	10.16	10.15	10.05
2	18.43	18.39	18.39	17.93	17.92	17.89	18.18
3	26.70	26.68	26.68	26.83	26.75	26.64	26.11
4	48.69	48.70	48.69	47.62	47.45	47.20	46.79 (lf)
5	52.71	50.72	50.72	49.49	49.41	49.31	48.18
6	53.11	52.92	52.92	51.86	51.57	51.17	49.32
7	90.71	82.42	82.34	83.58	82.66	81.43	67.38 (lf)

8	96.80	93.59	93.59	94.05	93.45	92.64	85.73 (lf)

Table 2

Eigenfrequencies in case of clamped-free support (C-F) [Hz].

Mode number	Paper dim = 10	Paper dim = 15	Paper dim = 20	FEM SOFiSTiK beam element 7DOF d = 20	FEM SOFiSTiK beam element 7DOF d = 25	FEM SOFiSTiK beam element 7DOF d = 50	FEM Abaqus shell elements (quad)
1	2.20	2.19	2.20	2.15	2.15	2.15	2.19
2	8.33	7.68	7.60	7.68	7.69	7.69	7.55
3	13.44	12.96	12.91	12.26	12.25	12.24	12.77
4	14.42	13.88	13.85	13.66	13.67	13.68	13.77
5	24.31	23.18	23.13	23.97	23.95	23.93	22.75
6	35.95	32.68	32.54	31.07	31.00	30.90	30.89
7	44.18	50.31	50.21	52.13	51.91	51.60	48.68 lf)
8	61.28	59.55	59.30	57.68	57.46	57.17	52.96 (lf)

Table 3

Eigenfrequencies for different models in case of clamped-clamped support (C-C) [Hz].

Mode number	Paper	Paper β = 0	Paper C_z‘ = 0
1	10.15	10.16	9.99
2	18.39	18.41	18.63
3	26.68	26.71	26.55
4	48.70	48.76	48.21
5	50.72	50.78	51.45
6	52.92	52.97	52.92
7	82.42	82.52	81.84
8	93.59	93.70	94.47

Table 4

Eigenfrequencies for different models in case of clamped-free support (C-F) [Hz].

Mode number	Paper	Paper β = 0	Paper C_z‘ = 0
1	2.19	2.20	2.21
2	7.68	7.68	7.60
3	12.96	12.97	13.36
4	13.88	13.89	13.88
5	23.18	23.21	22.44
6	32.68	32.71	33.91
7	50.31	50.37	48.72
8	59.55	59.61	61.33

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DOI: https://doi.org/10.2478/sgem-2019-0001 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 1 - 12

Submitted on: Nov 20, 2018

Accepted on: Jan 2, 2019

Published on: Mar 26, 2019

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2019 Józef Szybiński, Piotr Ruta, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 41 (2019): Issue 1 (April 2019)

Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Figures & Tables

Figure 1

Figure 2

Figure 3

Figure 4

Table 1

Table 2

Table 3

Table 4

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