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This paper focuses on linear vibration analysis of uncracked and cracked pipes. Finite element analysis (FEA) of the pipes is done by using the ANSYS software where three mode shapes have been extracted and plotted for different depths of crack, situated in the midpoint of the pipe. An experimental analysis has been also done to validate the developed model. A comparison between the obtained results from cracked and uncracked pipes haves been done to identify the influence of the crack’s depth on the behavior of the pipe. Various specimens of pipe’s configurations have been analyzed, and the sensitivity of the used mesh has been also studied. These aspects play an important role in the determination of the real response of the pipes where the measured frequencies depend on the significance of the crack’s depth and the chosen type of mesh.

The soil–structure interaction has often a significant effect on the nonlinear structures response especially when the soil is modeled as a random medium. In fact, to ensure the design of economical and safe structure and to obtain a more realistic behavior of a beam, deterministic and probabilistic analyses of large displacements of a beam resting on linear and nonlinear soil are investigated. However, finite element models of Euler–Bernoulli and Timoshenko beam resting on elastic linear and nonlinear soil (Winkler and Pasternak) have been developed. The geometric nonlinear analysis of the beam is based on the updated Lagrangian Euler–Bernoulli and Timoshenko Von Karman beam formulations, which are then combined with the random field theory of soil using Monte Calro simulations. A Matlab code has been developed to solve the nonlinear equations by using the Newton–Raphson method. Various coefficients of soils, boundary conditions, beam properties and load types are taken into account to assess their effect on beam response. Moreover, to quantify the shear deformation effects on the nonlinear analysis, a comparison between Euler–Bernoulli and Timoshenko beams has been made and the influence of different beam heights has been taken into account to illustrate the divergence and the importance of the geometric nonlinearity. The obtained results indicated that the geometric nonlinearity of beam combined to material nonlinearity and spatial variability of soil and by taking into account the shear deformation effects, allowed us to obtain a more realistic behavior of beam and demonstrate the efficiency and accuracy of the developed models.

In the analysis of non-linear behaviour of buried structures, the soil–structure interaction is the most important cause of buried pipeline failure, especially when the soil is modelled as a random elastic medium. In order to design safe and economical means of transporting energy and fluid, it is necessary to predict realistic behaviour of buried pipeline. In this work, the influence of spatially random soil properties on the geometric non-linear behaviour of pipeline is investigated. However, a numerical model has been developed, by modelling the pipeline as a geometric non-linear long beam resting on linear elastic random soil. Due to large deflections and moderate rotations of pipeline, the von Karman-type non-linearity based on the finite element formulation of non-linear pipeline response is adopted and then combined with random field theory of soil based on Monte Carlo simulations. The equation of motion is obtained using the principal of virtual works and solved using the Newton–Raphson incrementa...