Thick General Shells Under General Loading

1989 ◽  
Vol 56 (2) ◽  
pp. 391-394 ◽  
Author(s):  
Lloyd H. Donnell
Keyword(s):  
Cylindrical Shells ◽  
Small Strain ◽  
Equilibrium Equations ◽  
Flat Plates ◽  
Circular Cylindrical Shells

Three equilibrium equations in terms of three displacements are derived in scalar mathematics form, by linear, small-strain elasticity principles, for the case of general thick-walled shells under general loading. These reduce to well-known forms for the particular cases of flat-plates and thick circular cylindrical shells.

Free vibration analysis of porous laminated rotating circular cylindrical shells

2019 ◽  
Vol 25 (18) ◽  
pp. 2494-2508 ◽  
Author(s):  
Ahmad Reza Ghasemi ◽  
Mohammad Meskini
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Equilibrium Equations ◽  
Rotating Speed ◽  
Simply Supported ◽  
Numerical Result ◽  
Love’S Shell Theory ◽  
Circular Cylindrical Shells

In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

Energy Expressions and Differential Equations …. for Stress and Displacement Analyses of Arbitrary Cylindrical Shells

1958 ◽  
Vol 2 (02) ◽  
pp. 8-19
Author(s):  
Joseph Kempner
Keyword(s):  
Differential Equations ◽  
Cylindrical Shells ◽  
Arbitrary Cross Section ◽  
Natural Boundary ◽  
Equilibrium Equations ◽  
Small Deflection ◽  
Circular Cylindrical Shells ◽  
Natural Boundary Conditions ◽  
Theory Of Shells

Energy expressions and the related equilibrium equations and natural boundary conditions for the determination of the stresses in and displacements of uniform, thin-walled cylinders of arbitrary cross section loaded in an arbitrary manner by surface and edge forces and moments are presented. The derivations are based upon the Kirchhoff-Love assumptions of the classical theory of shells and are performed to within a degree of accuracy employed by Flügge in his derivation of the equilibrium equations applicable to circular cylindrical shells; hence, in terms of stress resultants, the exact, small-deflection equilibrium equations are obtained. Methods of simplification of the relations derived and of solution of the differential equations presented are indicated.

Power flow between circular cylindrical shells and flat plates

1995 ◽  
Vol 98 (5) ◽  
pp. 2929-2929
Author(s):  
Benjamin F. Willis ◽  
Courtney B. Burroughs
Keyword(s):  
Power Flow ◽  
Cylindrical Shells ◽  
Flat Plates ◽  
Circular Cylindrical Shells

Mode Count and Modal Density of Isotropic Circular Cylindrical Shells Using a Modified Wavenumber Space Integration Method

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Mohammad H. Farshidianfar ◽  
Anooshiravan Farshidianfar ◽  
Mahdi Mazloom Moghadam
Keyword(s):  
Boundary Condition ◽  
Acoustic Radiation ◽  
Cylindrical Shells ◽  
Exact Equation ◽  
Flat Plates ◽  
Integration Algorithm ◽  
Geometrical Properties ◽  
Acoustical Properties ◽  
Modal Density ◽  
Circular Cylindrical Shells

A new method based on the wavenumber space integration algorithm is proposed in order to obtain mode count and modal density of circular cylindrical shells. Instead of the simplified equation of motion, the exact equation is applied in mode count calculations. Modal plots are changed significantly in the k-space when using the exact equation. Mode repetition in cylindrical shells is represented by additional mode count curves in the k-space. On the other hand, a novel technique is presented in order to implement boundary condition effects in mode count and modal density calculations. Integrating these two significant corrections, a modified wavenumber space integration (MWSI) method is developed. Mode count and modal densities of three shells with different geometrical and acoustical properties are obtained using the MWSI method and conventional WSI. Results are verified using the exact mode count calculations. Moreover, effects of geometrical properties are studied on mode count plots in the k-space. Modal densities are obtained for cylindrical shells of different lengths, radii, and thicknesses. Finally, modal densities of cylindrical shells are compared to flat plates of the same size and boundary condition. Interesting results are obtained which will contribute in calculation of acoustic radiation efficiency and sound transmission in cylindrical shells.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

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