Тест 5.1 Variable section beam

Analytical solution: Société Française des Mécaniciens – Commission Validation de Progiciels de Calcul de Structures, Groupe de travail Dynamique, Paris, 1989.

Geometry:

Изгиб в плоскости (x, y). Длина: l = АВ = 0.6 м; толщина: h = 0.01 м. Координаты точек, м A B x 0. 0.6 y 0. 0.

Initial section: b0 = 0.03 м A0 = 3 x 10-4 м2 IZ0 = 0.25 x 10-8 м4

Sectional change (at α = 1): b = b0e-2αx A = A0e-2αx IZ = IZ0e-2αx

Material characteristics: Е=2 х 10¹¹Pа, v =0.3, ρ=7800 кг/м³.

Boundary conditions: Points A and B: pinched (u = v = 0; θ = 0).

Loads: For modal analysis.

CALCULATION RESULTS:

Order of form	Frequency, Hz		Uncertainty,%
	Analytical solution	Calculation results (LIRA)
1	143,303	145,748	1,71
2	396,821	400,063	0,82
3	779,425	782,865	0,44
4	1289,577	1292,848	0,25

Preview image: Array

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