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Free vibration of piles embedded in soil having different modulus of subgrade reaction. (English) Zbl 1130.74032
Summary: The soil that the pile is embedded in is idealized by a Winkler model and is assumed to be two-layered. The part of the pile extending above the ground is called the first region, and the parts embedded in the soil are called the second and the third regions, respectively. The dynamic displacement function of the pile subjected to an axial force is obtained as a fourth-order partial differential equation taking into account the effects of bending moment and shear force. It is assumed that the behavior of the material is linearly elastic, and axial force along the pile length to be constant. Shear effects are included in the differential equations by second derivative of elastic curve function with respect to shear deformation. Normalized natural circular frequencies of the pile are calculated using a carry-over matrix and the secant method for non-trivial solution of the linear homogeneous system of equations obtained for a specific value of the axial force, and for two combinations of boundary conditions: 1. one end fixed, and the other end free in displacement, but constrained against angular motion (henceforth referred to as a “sliding boundary condition”); 2. one end fixed, and the other end simply supported. Rotary inertia is considered. The results are presented in graphs.

MSC:
74L05 Geophysical solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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References:
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