A rigorous solution for the axisymmetrical buckling of simply supported cylindrical sandwich shells under axial load

1985 ◽  
Vol 6 (2) ◽  
pp. 157-168
Author(s):  
Wang Zhen-ming ◽  
Dai Fu-ling
Keyword(s):  
Axial Load ◽  
Rigorous Solution ◽  
Simply Supported ◽  
Sandwich Shells ◽  
Axisymmetrical Buckling

Buckling of Bars of Variable Rigidity with Varying Axial Load

1963 ◽  
Vol 67 (635) ◽  
pp. 734-736
Author(s):  
K. T. Sundara Raja Iyengar ◽  
S. Anantharamu
Keyword(s):  
Numerical Methods ◽  
Approximate Method ◽  
Convenient Method ◽  
Axial Load ◽  
Difficult Problem ◽  
Variable Rigidity ◽  
Rigorous Solution ◽  
Approximate Methods ◽  
Buckling Loads ◽  
End Conditions

The Evaluation of buckling loads of columns presents a difficult problem whose rigorous solution may be very difficult particularly when the variation of moment of inertia or the axial load does not follow a simple law. Hence approximate methods such as the variational and numerical methods will have to be employed. An approximate method is suggested in this note which offers a convenient method for the calculation of buckling loads of bars with any type of end conditions.

Optimal Forms of Shallow Cylindrical Panels With Respect to Vibration and Stability

1986 ◽  
Vol 53 (1) ◽  
pp. 135-140 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Surface Area ◽  
Fundamental Frequency ◽  
Axial Load ◽  
Cylindrical Panel ◽  
Buckling Load ◽  
Material Surface ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Cylindrical Panels

Thin, shallow, elastic, cylindrical panels with rectangular planform are considered. We seek the midsurface form which maximizes the fundamental frequency of vibration, and the form which maximizes the buckling value of a uniform axial load. The material, surface area, and uniform thickness of the panel are specified. The curved edges are simply supported, while the straight edges are either simply supported or clamped. For the clamped case, the optimal panels have zero slope at the edges. In the examples, the maximum fundamental frequency is up to 12 percent higher than that of the corresponding circular cylindrical panel, while the buckling load is increased by as much as 95 percent. Most of the solutions are bimodal, while the rest are either unimodal or trimodal.

Buckling and Vibration of Isosceles Triangular Plates having the Two Equal Edges Clamped and the Other Edge Simply–Supported

1955 ◽  
Vol 59 (530) ◽  
pp. 151-152 ◽  
Author(s):  
Hugh L. Cox ◽  
Bertram Klein
Keyword(s):  
Differential Equation ◽  
Axial Load ◽  
Unit Length ◽  
Approximate Solutions ◽  
The Other ◽  
Thin Plates ◽  
Critical Buckling Load ◽  
Simply Supported ◽  
Governing Differential Equation ◽  
Image Position

Approximate Solutions obtained by the method of collocation are presented for the lowest critical buckling load of an isosceles triangular plate loaded as shown in Fig. 1. Also, the fundamental frequency is given. The base of the triangle is simply supported and the other equal edges are clamped. The usual assumptions regarding the bending of thin plates are made. The governing differential equation for the plate loaded as shown in Fig. 1 is1where D is the plate stiffness, N is axial load per unit length, w is deflection, positive downward, and the quantities a and h are dimensions shown in Fig.1.

Bounds for the Natural Frequencies of a Simply Supported beam Carrying a Uniformly Distributed Axial Load

1967 ◽  
Vol 9 (2) ◽  
pp. 149-156 ◽  
Author(s):  
G. Fauconneau ◽  
W. M. Laird
Keyword(s):  
Lower Bounds ◽  
Axial Load ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Distributed Load ◽  
Made In

Upper and lower bounds for the eigenvalues of uniform simply supported beams carrying uniformly distributed axial load and constant end load are obtained. The upper bounds were calculated by the Rayleigh-Ritz method, and the lower bounds by a method due to Bazley and Fox. Some results are given in terms of two loading parameters. In most cases the gap between the bounds over their average is less than 1 per cent, except for values of the loading parameters corresponding to the beam near buckling. The results are compared with the eigenvalues of the same beam carrying half of the distributed load lumped at each end. The errors made in the lumping process are very large when the distributed load and the end load are of opposite signs. The results also indicate that the Rayleigh-Ritz upper bounds computed with the eigenfunctions of the unloaded beam as co-ordinate functions are quite accurate.

Mises limit load for simply supported conical sandwich shells under internal pressure

1969 ◽  
Vol 37 (5) ◽  
pp. 281-287 ◽  
Author(s):  
R. H. Bryant ◽  
S. L. Lee ◽  
T. Mura
Keyword(s):  
Internal Pressure ◽  
Limit Load ◽  
Simply Supported ◽  
Sandwich Shells

Parametric Instability of a Leipholz Column Under Periodic Excitation

1999 ◽  
Author(s):  
Bongsu Kang ◽  
Chin An Tan
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Parametric Instability ◽  
Periodic Excitation ◽  
Combination Resonance ◽  
Simply Supported ◽  
Free Boundary Conditions ◽  
Difference Type ◽  
Instability Regions ◽  
The Difference

Abstract In this paper, the parametric instability of a Leipholz column under four boundary conditions is studied. The distributed, follower-type axial load is assumed to be uniform and periodic. Instability regions are obtained and the existence of combination resonance of sum and difference types is discussed for each set of boundary conditions. It is found that combination resonance of sum type exists in all the cases of boundary conditions considered, but the difference type exists only in the cases of clamped-simply supported and clamped-free boundary conditions. The combination resonance is shown to be as important as the simple parametric resonance. Results, when compared to a column under a periodic end load, show that the instability characteristics of these two columns are considerably different.

scholarly journals Vibration Analysis of Viscoelastically Damped Sandwich Shells

1996 ◽  
Vol 3 (6) ◽  
pp. 403-417 ◽  
Author(s):  
Ji-Fan He ◽  
Bang-An Ma
Keyword(s):  
Asymptotic Solution ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Governing Equations ◽  
Modal Strain Energy ◽  
Simply Supported ◽  
Modal Strain Energy Method ◽  
Sandwich Shells ◽  
Method Accuracy ◽  
Loss Factors

The simplified governing equations and corresponding boundary conditions of vibration of viscoelastically damped unsymmetrical sandwich shells are given. The asymptotic solution to the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the modal strain energy method. By taking more terms of the asymptotic solution with successive calculations and use of the Padé approximants method, accuracy of natural frequencies and modal loss factors of sandwich shells can be improved. The lowest three or four natural frequencies and modal loss factors of simply supported cylindrical sandwich shells are calculated.

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