Abstract
The open profile thin elastic wavy shell natural oscillations problem is considered. The proposed method for determining the numerical values of the lowest frequencies and the corresponding forms of natural vibrations of shells with a complicated shape is based on the Rayleigh-Ritz energy method. The results of numerical calculation for a thin wavy shell with a rigidly pinched lower contour are presented.
Highlights
IntroductionThe experience of construction increasingly points to the prospects of using the shells of complex shapes, including such wavy shells as coatings for public, industrial, warehouse and agricultural buildings and structures
A method for determining the numerical values of the low frequencies and the corresponding forms of natural vibrations of thin shells of complex shape by the energy method is proposed, which is acceptable for use in design practice
The amplitude values of dimensionless displacements и10 in the cross-sections of the shell with the coordinates 1 = 0 and 1 = ± 1 are zero. On these charts ω1 is the first frequency of natural oscillations of a thin wavy shell; и10, и
Summary
The experience of construction increasingly points to the prospects of using the shells of complex shapes, including such wavy shells as coatings for public, industrial, warehouse and agricultural buildings and structures. The theory of calculating thin shells is well developed, so that it is fully possible to calculate and design the constructions and structures in the form of shells with rather complex outlines. A method for determining the numerical values of the low frequencies and the corresponding forms of natural vibrations of thin shells of complex shape by the energy method is proposed, which is acceptable for use in design practice. This method gives an opportunity to replace the differential equations with a homogeneous system of linear algebraic equations, which greatly simplifies the dynamic calculation of shells of complex structure. This technique is used to calculate smooth shells with any boundary conditions
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