Dynamic Interaction Between Rigid Surface Foundations on Multi-Layered Half Space

A numerical approach is presented to calculate the dynamic response of a group of rigid surface foundations. The formulation is unconditionally stable and has the computational simplicity with only the algebraic calculations involved. It imposes no limit to the foundation shape, foundation separations, thickness of the layered medium and magnitude of frequency. In the analysis, the foundation–ground interface is discretized into a number of sub square-regions. The Green’s function, which is obtained by the Fourier–Bessel transform and precise integration method, is employed to calculate the dynamic response of each sub-region. Finally, a system of linear algebraic equation in terms of the contact forces within each sub-region is observed, which leads to the desired dynamic impedance functions of the foundations. Comparison is carried out between the proposed method and the solutions available in the literature. Parametric studies on the dynamic interaction between adjacent foundations are also described. Addressed in this study are the effects of the distance and direction of foundation alignment. Several conclusions are drawn the significance of each factor. Illustrative results for a case of several closely-spaced foundations are also presented. Although the dynamic interaction analysis of foundations is concerned here, further applications of this approach can be extended to the interaction analysis of structures.

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Forced Vibration of Surface Foundation on Viscoelastic Isotropic Multi-Layered Stratum

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455415500613 ◽

2016 ◽

Vol 16 (09) ◽

pp. 1550061 ◽

Cited By ~ 9

Author(s):

Lin Chen

Keyword(s):

Dynamic Response ◽

Forced Vibration ◽

Numerical Approach ◽

Contact Forces ◽

Precise Integration ◽

Irregular Shapes ◽

Layered Stratum ◽

Surface Foundation ◽

Soil Foundation ◽

Impedance Functions

A numerical approach is presented for analyzing the forced vibration of a rigid surface foundation. In the analysis, the foundation is discretized into a number of sub square-elements. The dynamic response within each sub-element is described by the Green’s function, which is obtained by the Fourier–Bessel transform and the precise integration method (PIM). Then, a system of linear algebraic equation in terms of the contact forces within each sub-element is derived, which leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for the foundation not only with a simple geometry, such as circular one, but also with irregular shapes. Comparisons between the results obtained by the proposed approach and the thin layered method are made, for which good agreement is achieved. Also, parametric studies are performed on the dynamic response of the foundation, considering the effects of the material damping, stratum depth, Poisson’s ratio and the contact condition of the soil–foundation interface. Several conclusions are drawn concerning the significance of each parameter. Further application of the method can be easily extended to the analysis of a foundation on a viscoelastic anisotropic multi-layered stratum because no further complexity is introduced except the constitutive matrix needs to be modified.

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Dynamic Response Analysis on the Interaction Between Flexible Bodies of Large-Sized Wind Turbine Under Random Wind Loads

Volume 10: Ocean Renewable Energy ◽

10.1115/omae2018-77444 ◽

2018 ◽

Author(s):

Yilun Li ◽

Shuangxi Guo ◽

Min Li ◽

Weimin Chen ◽

Yue Kong

Keyword(s):

Dynamic Response ◽

Wind Turbine ◽

Elastic Deformation ◽

Dynamic Interaction ◽

Response Analysis ◽

Flexible Bodies ◽

Dynamic Response Analysis ◽

Dynamic Behaviors ◽

Energy Consuming ◽

Turbine Model

As the output power of wind turbine increasingly gets larger, the structural flexibility of elastic bodies, such as rotor blades and tower, gets more significant owing to larger structural size. In that case, the dynamic interaction between these flexible bodies become more profound and may significantly impact the dynamic response of the whole wind turbine. In this study, the integrated model of a 5-MW wind turbine is developed based on the finite element simulations so as to carry out dynamic response analysis under random wind load, in terms of both time history and frequency spectrum, considering the interactions between the flexible bodies. And, the load evolution along its transmitting route and mechanical energy distribution during the dynamic response are examined. And, the influence of the stiffness and motion of the supporting tower on the integrated system is discussed. The basic dynamic characteristics and responses of 3 models, i.e. the integrated wind turbine model, a simplified turbine model (blades, hub and nacelle are simplified as lumped masses) and a rigid supported blade, are examined, and their results are compared in both time and frequency domains. Based on our numerical simulations, the dynamic coupling mechanism are explained in terms of the load transmission and energy consumption. It is found that the dynamic interaction between flexible bodies is profound for wind turbine with large structural size, e.g. the load and displacement of the tower top gets around 15% larger mainly due to the elastic deformation and dynamic behaviors (called inertial-elastic effect here) of the flexible blade; On the other hand, the elastic deformation may additionally consume around 10% energy (called energy-consuming effect) coming from external wind load and consequently decreases the displacement of the tower. In other words, there is a competition between the energy-consuming effect and inertial-elastic effect of the flexible blade on the overall dynamic response of the wind turbine. And similarly, the displacement of the blade gets up to 20% larger because the elastic-dynamic behaviors of the tower principally provides a elastic and moving support which can significantly change the natural mode shape of the integrated wind turbine and decrease the natural frequency of the rotor blade.

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An efficient numerical approach for simulating contact in origami assemblages

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0366 ◽

2019 ◽

Vol 475 (2230) ◽

pp. 20190366 ◽

Cited By ~ 4

Author(s):

Yi Zhu ◽

Evgueni T. Filipov

Keyword(s):

Numerical Approach ◽

Internal Force ◽

Contact Forces ◽

Model Parameters ◽

Full Potential ◽

Stationary Potential ◽

Contact Potential ◽

Proposed Model ◽

Approach Infinity ◽

Internal Force Vector

Origami-inspired structures provide novel solutions to many engineering applications. The presence of self-contact within origami patterns has been difficult to simulate, yet it has significant implications for the foldability, kinematics and resulting mechanical properties of the final origami system. To open up the full potential of origami engineering, this paper presents an efficient numerical approach that simulates the panel contact in a generalized origami framework. The proposed panel contact model is based on the principle of stationary potential energy and assumes that the contact forces are conserved. The contact potential is formulated such that both the internal force vector and the stiffness matrix approach infinity as the distance between the contacting panel and node approaches zero. We use benchmark simulations to show that the model can correctly capture the kinematics and mechanics induced by contact. By tuning the model parameters accordingly, this methodology can simulate the thickness in origami. Practical examples are used to demonstrate the validity, efficiency and the broad applicability of the proposed model.

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