Abstract
This paper presents a computationally efficient mode-matching method to predict the relative axial motion of two elastic rods in frictional contact. The motion is of the stick-slip type and is non-uniform along the rods. The proposed method utilizes the piecewise linearity of the problem in time and space. The original set of nonlinear partial differential equations describing the dynamics of the coupled system is first reduced to a system of linear, per time interval, ordinary differential equations by means of modal decomposition. The global modes are used for one of the two rods, while for the other rod, different modes are identified per time interval based on the regions in stick or slip phase. Subsequently, the system response is obtained by combining the piecewise linear solutions. A comparison of the solution method proposed with standard numerical techniques shows its advantage both in terms of computational time and accuracy. Numerical examples demonstrate the capability of the method to analyse cases involving either harmonic- or impact-type forces that drive the relative motion. Although the discussion in this paper is limited to the one-dimensional configuration, the approach is generic and can be extended to problems in more dimensions.
Highlights
In the area of offshore engineering and offshore wind, large-diameter monopiles comprise the most dominant type of substructure used as a foundation for offshore wind turbines [1]
Monopile installation is customarily performed by mounting a hammer on the top of the pile and exerting a forcing, either by impact or vibratory motion [2], adequate enough to drive the pile up to the predefined embedment depth. The analysis of this dynamic problem is traditionally conducted in practice by one-dimensional models [3,4], representing the pile as an elastic rod supported by nonlinear springs and dashpots, a local soil reaction analogue, subjected to the hammer forcing
The main objective is the introduction of a mode-matching method that can analyse the motion of two linear elastic rods in frictional contact
Summary
In the area of offshore engineering and offshore wind, large-diameter monopiles comprise the most dominant type of substructure used as a foundation for offshore wind turbines [1]. Awrejcewicz and Olejnik [10] studied the complex nonlinear dynamic behaviour, including bifurcations and chaotic motions, for various friction laws Further considerations, such as the stochastic nature of friction in modelling may be advantageous for certain applications [11]. In a relevant work by Quinn and Segalman [13], an elastic rod on a frictional foundation was studied to investigate further the influence of microslip in the dynamic behaviour of mechanical joints, by employing a regularization of Coulomb friction [17] in conjunction with numerical integration of the equations of motion by the Runge–Kutta method.
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