In this thesis, transverse vibration of a cracked beam on an elastic foundation and the effect of crack and foundation parameters on transverse vibration natural frequencies are studied. Analytical formulations are derived for a beam with rectangular cross section. The crack is an open type edge crack placed in the medium of the beam and it is uniform along the width of the beam. The cracked beam rests on an elastic foundation. The beam is modeled by two different beam theories, which are Euler-Bernoulli beam theory and Timoshenko beam theory. The effect of the crack is considered by representing the crack by rotational springs. The compliance of the spring that represents the crack is obtained by using fracture mechanics theories. Different foundation models are discussed / these models are Winkler Foundation, Pasternak Foundation, and generalized foundation. The equations of motion are derived by applying Newton&#039 / s 2nd law on an infinitesimal beam element. Non-dimensional parameters are introduced into equations of motion. The beam is separated into pieces at the crack location. By applying the compatibility conditions at the crack location and boundary conditions, characteristic equation whose roots give the non-dimensional natural frequencies is obtained. Numerical solutions are done for a beam with square cross sectional area. The effects of crack ratio, crack location and foundation parameters on transverse vibration natural frequencies are presented. It is observed that existence of crack reduces the natural frequencies. Also the elastic foundation increases the stiffness of the system thus the natural frequencies. The natural frequencies are also affected by the location of the crack.

In many engineering structures transmission of vertical or horizontal forces to the foundation is a major challenge. As a first approach to model it may be assumed that the foundation behaves elastically. For generalized foundations the model assumes that at the point of contact between plate and foundation there is not only pressure but also moments caused by interaction between the springs. In this study, the exact stiffness, geometric stiffness and consistent mass matrices of the beam element on two-parameter elastic foundation are extended to solve plate problems. Some examples of circular and rectangular plates on two-parameter elastic foundation including bending, buckling and free vibration problems were solved by the finite grid solution. Comparison with known analytical solutions and other numerical solutions yields accurate results.

Geosynthetic tubes filled with a slurry-mix are considered. The mix is usually dredged from a nearby area and pumped directly into the tubes. The tubes are used in a variety of applications including breakwaters, groins, and temporary levees. This thesis considers single and stacked geosynthetic tubes resting on rigid and deformable foundations. A two-dimensional analysis is performed on the cross-section of a very long tube. The program Mathematica is utilized for the analysis. A few assumptions are made regarding the general behavior of the tube. The tube is assumed to be an inextensible membrane with no bending stiffness. To allow for a closed-form integral solution, it is assumed that no friction exists between the tubes and at the foundation. A single tube, two stacked tubes, and a 2-1 formation are studied. Both rigid and deformable foundations are considered. The deformable foundation is modeled as a tensionless Winkler foundation with normal forces proportional to the downward deflection of the ground. An external water load on one side is also investigated for a single tube and a 2-1 formation, with rigid blocks to prevent the structure from sliding along the ground. Example cross-sectional profiles are given. Results from the analysis include structure height, circumferential tension, and ground deflections. / Master of Science