Pairod Singhatanadgid

Similitude invariants and scaling laws for buckling experiments on anti-symmetrically laminated plates subjected to biaxial loading

Abstract Establishing the similitude between the model and prototype rigorously is a necessary step in designing an experiment efficiently. So far, to the best of the authors’ knowledge, no one has ever derived the similitude invariant for anti-symmetric cross- and angle-ply laminated plates subjected to biaxial loading before. This research paper is the first to establish the similitude invariant of anti-symmetric cross- and angle-ply laminated plates by applying the similitude transformation to the governing differential equations of buckling directly. Then the scaling laws for buckling loads of laminated plates subjected to biaxial loads are derived. But in reality, either due to the complexity of the scaling laws or to economize on costly experiments, it may not be feasible to construct the model conforming to the scaling laws completely, therefore partial similitude is investigated theoretically and approximate scaling laws are recommended. The buckling loads of the prototype predicted from the scaling laws are then compared with the available theoretical values. The complete similitude cases show exact agreement between results predicted from the scaling laws and the available analytical solutions. For partial similitude cases, the models distorted in stacking sequences, number of plies, and material properties are studied and the approximate scaling laws which yield good agreement are recommended.

Similitude and physical modeling for buckling and vibration of symmetric cross-ply laminated circular cylindrical shells

The similitude invariant and the scaling laws of the symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration problems are derived by applying the similitude transformation to the governing differential equations directly. The scaling laws obtained by this approach are unique because they are forced by the governing differential equations. In the absence of the experimental data, the validity of the scaling laws is verified by numerical experiments. This is done by calculating theoretically the buckling loads and fundamental frequencies for free vibration of the model and substituting into the scaling laws. The predicted values of the prototype from the scaling laws are then compared with those values from the closed-form solution. Examples for the complete similitude cases with various stacking sequences, number of plies, and radius ratios show exact agreement. The presented relationships between the model and prototype will greatly facilitate and reduce the costly experiment. In reality, it may not be feasible to construct the model to fulfill the similarity requirements completely. Several cases of partial similitude are investigated and verified numerically. Modeling with distortion in stacking sequences is recommended, but model with distortion in material properties yields moderately high percent of discrepancy.

A Scaling Law for Vibration Response of Laminated Doubly Curved Shallow Shells by Energy Approach

This research paper derives the scaling law for physical modeling of generally laminated doubly curved shallow shells for free vibration response by applying the similitude transformation to the governing total energy of the system. Validity of the scaling law is verified by numerical experiments on laminated doubly curved shallow shells. This is accomplished by calculating theoretically the natural frequencies for free vibration of the model specimen and substituting into the scaling law to obtain the corresponding values of the prototype. The predicted natural frequencies of the prototype from the scaling law are then compared with those from the theoretical solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and planform ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the costly experiment. In practice, either due to the complexity of the similitude requirements or to reduce experimental cost and time, it may not be feasible to construct the model to fulfill the requirements completely. Thus, partial similitude models are also investigated numerically. These include models with distortion in stacking sequences and laminated material properties. Distortion model in stacking sequences is proven to be fairly accurate. However, the model with distortion in material properties yields high percent of discrepancy of the scaling natural frequencies, so it is not recommended.

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

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.

Vibration analysis of stepped rectangular plates using the extended Kantorovich method

ABSTRACT In this study, vibration behaviors of stepped plates are investigated based on the variational principle of minimum total energy and the extended Kantorovich method. The out-of-plane displacement is represented by a separable function of parameters x and y. A set of governing equations, boundary conditions, and continuity conditions in the form of ordinary differential equations are derived from the energy condition. The natural frequency and out-of-plane displacement function can be determined numerically from the derived equations and conditions. Solutions from the proposed approach are in good agreement with results from past studies and those of the finite element method.

Determination of buckling load of rectangular plates using measured vibration data

In this study, the vibration correlation technique was introduced to determine the buckling load of rectangular thin plates. It is theoretically shown that the natural frequency approaches zero when the applied compressive load approaches the buckling load of the plate. To avoid the effects of premature out-of-plane deformation, it is proposed in this study that the buckling load is to be identified using the natural frequencies of plates under tensile loading. A set of aluminum plates was tested for natural frequencies using an impact test method. Specimens with two types of boundary conditions, i.e., CCCC and CCCF, were included in the experiment. The square of the measured natural frequency was plotted against the applied load and extrapolated to determine the predicted buckling load. The buckling loads from vibration data compare closely with numerical solutions. The average percentage differences between the measured buckling loads and the numerical solutions are 1.24 % and -1.14 % for specimens with CCCC and CCCF boundary conditions, respectively. In conclusion, the buckling load of rectangular thin plates can be experimentally identified with acceptable accuracy using vibration data. This approach is very useful especially for structures with unknown or imperfect boundary conditions where analytical or numerical solutions to the problem are not available.

A preliminary study on the utilization and effectiveness of a flipped classroom in Thailand

This paper described the preliminary study on the effectiveness of flipped classroom teaching for an engineering course, the Mechanics of Materials which demanded strong theoretical knowledge. Students who took this compulsory course studied in several engineering programs and completed different pre-requisite courses. For this course, there were five sections, of which two were flipped; students freely chose the section. The preliminary results showed that the performances from the flipped classroom sections were at least as good as the sections with traditional teachings. For students of whom the course was not vital for the study progress, the ratio of withdrawal in the flipped section was less than half those of the traditional sections. For course management, the coordinated flipped classroom provided a better in-built system that reduced course drift and allow flexible teaching schedule for lecturers. The key component for course improvement was better communication to students about the learning philosophy and intentions.

The Kantorovich method applied to bending, buckling, vibration, and 3D stress analyses of plates: A literature review

ABSTRACT This study presents a thorough review of the applications of the Kantorovich method to several plate problems. The main objective of this review is to compile an up-to-date list of studies that employ the Kantorovich method, which is a semi-analytical numerical method, to bending, buckling, vibration, and three-dimensional elasticity problems of plates. The reviews highlight the derivations of the governing equations, which are written in form of ordinary differential equations, and the solution methods used to solve those equations. This review should be helpful for researchers and engineers to quickly gain an overview of the application of the method to thin-walled structures.