STRUCTURAL SIMILITUDE AND SCALING LAWS OF ANTI-SYMMETRIC CROSS-PLY LAMINATED CYLINDRICAL SHELLS FOR BUCKLING AND VIBRATION EXPERIMENTS

2007 ◽  
Vol 07 (04) ◽  
pp. 609-627 ◽  
Author(s):  
VARIDDHI UNGBHAKORN ◽  
NUTTAWIT WATTANASAKULPONG
Keyword(s):  
Material Properties ◽  
Physical Modeling ◽  
Numerical Experiments ◽  
Scaling Laws ◽  
Cylindrical Shells ◽  
Buckling Loads ◽  
Closed Form Solutions ◽  
Fundamental Frequencies ◽  
Circular Cylindrical Shells ◽  
Predicted Values

Developed herein are the scaling laws for physical modeling of anti-symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration experiments. In the absence of experimental data, the validity of the scaling laws is verified by numerical experiments. This is accomplished by calculating theoretically the buckling loads and fundamental frequencies of the model and substituting into the scaling laws to obtain the corresponding values of the prototype. The predicted values of the prototype from the scaling laws are then compared with existing closed-form solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and length-to-radius ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the need for costly experiments. In reality, either due to the complexity of the scaling laws or to economize experimental cost and time, it may not be feasible to construct the model to fulfil the scaling laws completely. Thus, several possible models of partial similitude are investigated numerically. These include models with distortion in laminated material properties, stacking sequences and number of plies. Model with distortion in material properties yields a high percentage of discrepancy and is not recommended.

SCALING LAW AND PHYSICAL SIMILITUDE FOR BUCKLING AND VIBRATION OF ANTISYMMETRIC ANGLE-PLY LAMINATED CYLINDRICAL SHELLS

2003 ◽  
Vol 03 (04) ◽  
pp. 567-583 ◽  
Author(s):  
VARIDDHI UNGBHAKORN ◽  
PAIROD SINGHATANADGID
Keyword(s):  
Scaling Laws ◽  
Cylindrical Shells ◽  
Scaling Law ◽  
Stacking Sequence ◽  
Buckling Loads ◽  
Fundamental Frequencies ◽  
Numerical Studies ◽  
Yield Values ◽  
Circular Cylindrical Shells ◽  
Similitude Theory

The similitude invariants and scaling laws for the buckling and free vibration of antisymmetric angle-ply laminated circular cylindrical shells were derived by directly applying the similitude transformation to the governing differential equations of the problem considered. The scaling laws relate the buckling load and natural frequency of a model to those of a prototype when the similarity requirements between the two systems are fulfilled. In the absence of experimental data, the validity of the scaling laws was verified by calculating theoretically the buckling loads and fundamental frequencies of vibration of the model and substituting them into the scaling laws to yield values for the prototype, which were then compared with those directly computed for the prototype. The numerical studies show that for the case of complete similitude with various stacking sequence, number of plies, and radius ratio, the solutions predicted by the similitude theory agree exactly with those obtained directly from the theory. Some typical partial similitude cases were also investigated. It was demonstrated that the partial similitude model with distortion in stacking sequence is reliable for predicting the behavior of the prototype. On the other hand, models with distortion in material properties are not recommended because of the existence of large discrepancies in the predicted results.

ON THE FUNDAMENTAL FREQUENCIES AND MODES OF FREE VIBRATION OF CYLINDRICAL SHELLS

1991 ◽  
Vol 15 (2) ◽  
pp. 147-159
Author(s):  
J.L. Urrutia-Galicia ◽  
L.J. Arango
Keyword(s):  
Free Vibration ◽  
Elastic Material ◽  
Cylindrical Shells ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Circular Cylindrical Shells

The fundamental frequencies and modes of free vibration of simply supported circular cylindrical shells are explored. The results include the fundamental frequencies ωmn and the modes (m,n) of steel cylindrical shells which are presented in the form of a nomogram, see Figure 6. Besides, single more general formulas are given for cylindrical shells made out of any elastic material which turn out to be very suitable for design and analysis purposes.

Mechanical buckling of cylindrical shells with varying material properties

2010 ◽  
Vol 224 (8) ◽  
pp. 1551-1557 ◽  
Author(s):  
P Khazaeinejad ◽  
M M Najafizadeh
Keyword(s):  
Exponential Function ◽  
Power Law ◽  
Material Properties ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Buckling Loads ◽  
Young’S Moduli ◽  
Wave Numbers

The analytical solutions of the first-order shear deformation theory are developed to study the buckling behaviour of functionally graded (FG) cylindrical shells under three types of mechanical loads. The Poisson's ratios of the FG cylindrical shells are assumed to be constant, while the Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents given by power-law or exponential function. The stability equations are employed to obtain the closed-form solutions for critical buckling loads of each loading case. The dependence of the critical buckling loads on the variations of the material properties with a power-law or exponential function is studied. It is observed that these effects change appreciably the critical buckling loads. Results for critical loads are tabulated for thin and moderately thick shells. Although the critical buckling load of FG cylindrical shells decreases as the circumferential wave numbers increase, it rises for axially compressed long shells as the longitudinal wave numbers increase.

Buckling of Axially Compressed Circular Cylindrical Shells at Stresses Smaller Than the Classical Critical Value

1965 ◽  
Vol 32 (3) ◽  
pp. 542-546 ◽  
Author(s):  
N. J. Hoff ◽  
L. W. Rehfield
Keyword(s):  
Critical Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Critical Value ◽  
Closed Form Solutions ◽  
Stress Resultant ◽  
Simple Support ◽  
Circumferential Displacement ◽  
Circular Cylindrical Shells ◽  
Support Conditions

Closed-form solutions are given of the linear Donnell equations defining the buckling of thin-walled circular cylindrical shells subjected to uniform axial compression. In addition to the classical simple support conditions requiring the vanishing of the radial displacement, the axial bending-moment resultant, the axial additional normal-stress resultant, and the circumferential displacement, three other, equally justifiable, simple support conditions are defined and studied in the case of the semi-infinite shell. Two of them yield buckling stresses amounting to about one half the classical critical stress.

An Analytical and Experimental Study of Cylindrical Shells under Localised Impact Loads

1966 ◽  
Vol 17 (1) ◽  
pp. 72-82 ◽  
Author(s):  
John C. Yao
Keyword(s):  
Experimental Study ◽  
Closed Form ◽  
Cylindrical Shells ◽  
Impact Loads ◽  
Strain Response ◽  
Elastic Shells ◽  
Closed Form Solutions ◽  
Predicted Values ◽  
Symmetric Response

SummaryNon-symmetric response of elastic shells to localised impact loads is studied. Closed-form solutions for the response to four particular kinds of pulse shapes are given. Experimentally measured values of the strain response of a cylinder to impact loads are obtained which compare satisfactorily with theoretical predicted values.

Limit Point Buckling Loads of Axially Compressed, Circular Cylindrical Shells—The Effect of Nonlinear Material Behavior

1979 ◽  
Vol 46 (2) ◽  
pp. 386-392 ◽  
Author(s):  
R. P. Nimmer ◽  
J. Mayers
Keyword(s):  
Deformation Theory ◽  
Cylindrical Shells ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Polyhedral Surface ◽  
Buckling Loads ◽  
Accurate Representation ◽  
Mechanism Model ◽  
Previously Treated ◽  
Circular Cylindrical Shells

The elasto-plastic buckling and postbuckling of imperfect, thin, circular cylindrical shells in axial compression is studied with the use of a mechanism model specifically designed to achieve an accurate representation of the developable polyhedral surface of Yoshimura. The formulation makes it possible to study the influence of asymmetric imperfection patterns of significantly larger amplitudes than previously treated. Elasto-plastic effects are included using a deformation theory of plasticity and Reissner’s variational principle. Material-sensitive load-shortening curves are obtained exhibiting initial-maximum values for the average axial stresses of imperfect shells that tend toward vanishingly small magnitudes with increasing radius-to-thickness ratio and attendant imperfections.

The Ritz formulation applied to the study of the vibration frequency characteristics of functionally graded circular cylindrical shells

2009 ◽  
Vol 224 (1) ◽  
pp. 43-54 ◽  
Author(s):  
M N Naeem ◽  
S H Arshad ◽  
C B Sharma
Keyword(s):  
Vibration Frequency ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Frequency Spectra ◽  
Closed Form Solutions ◽  
Graded Material ◽  
Circular Cylindrical Shells ◽  
Direct Variational Method ◽  
Thin Shell Theory

In this article vibration frequencies of functionally graded circular cylindrical shells are analysed and studied using the Ritz formulation. Since closed-form solutions are limited to simple cases, an approximate method is employed to solve the shell problem, and numerical evaluation is carried out using a direct variational method. Axial modal dependence is chosen in terms of Ritz polynomials to ascertain a rapid convergence of the method. Sanders and Budiansky's thin shell theory is utilized for strain—displacement and curvature—displacement relations. Functionally graded material characteristics for the constituent materials are distributed in accordance with a volume fraction law. Influence of boundary conditions and volume fraction exponents on the vibration frequency spectra is analysed. The present results are compared with some previous works and excellent agreement is found.

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