Free spans or suspended spans normally occur in subsea pipelines due to the irregularity of seabed and byscouring phenomena around the installed non-buried pipeline. The hydrodynamic around the pipeline canlead to a vibration of the pipeline.This kind of vibration may cause fatigue damage to the pipeline. In orderto study the hydrodynamic around the pipeline, calculating the natural frequency o...

In this paper, the dynamic response of resonating nano-beams is investigated using a strain gradient elasticity theory. A nonlinear model is obtained based on the Galerkin decomposition method to find the dynamic response of the investigated beam around its statically deflected position. The mid-plane stretching, axial residual stress and nonlinear interaction due to the electrostatic force on ...

In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part ...