Adding redundant cables to tensegrity structures is an inevitable requirement for the engineering application of this type of structure. Here we investigated the form-finding and stability of several typical classes of tensegrities with additional cables. An energy minimization–based form-finding method was presented and validated by the analytical solutions developed for prismatic and antiprismatic tensegrities. Some new multistable configurations of typical tensegrities were identified by the proposed algorithm, which demonstrates the robustness of the present form-finding method. It can be revealed from the present analysis that the stability and mechanical properties of the tensegrities with additional cables depended both on the number and the method of adding cables. The stiffness of the antiprismatic tensegrity increased with the increase of the number of additional cables and the reduction of the natural length of the additional cable. But for a more general case, the resistance to deformation of the tensegrity could not always be increased by increasing the number of additional cables. Additional cables could improve the possibility of obtaining more equilibrium states of the tensegrity, but the stability of those equilibrium states was not guaranteed. The transition between two stable self-equilibrated states of a tensegrity could be achieved by just reducing the length of additional cables.

The numerical analysis technique is one of the primary methods for the design and development of floating offshore wind turbines (FOWTs). This study presents a detailed investigation into the influences of fully coupled and decoupled numerical analysis methods on the dynamic responses of a floating offshore wind turbine. The fully coupled analysis is implemented via bidirectional FAST-OrcaFlex co-simulation, considering the dynamic interaction between rotor operation and platform motions. The decoupled analysis is conducted using OrcaFlex for wave-induced response analysis, incorporating unidirectional imported FAST-based thrust time series. First, the numerical tools used for simulating fully coupled numerical model of OC5 DeepCwind are verified against published model test data, including free-decay test, white noise wave test and working condition test. Then, the fully coupled and decoupled numerical models are compared under wind fields of different turbulence intensities and wind speeds to reveal the dynamic coupling effects. The results indicate that the predictions of the decoupled model are more aligned with the experimental data compared to those of the fully coupled model under conditions of combined wave and steady winds. The differences between the fully coupled and decoupled models are minor under wave-only condition. However, under turbulent condition, the decoupled model overestimates surge by up to 10% and mooring tension by less than 5%, while pitch deviations can reach 17%. These findings support the use of the decoupled method in preliminary design stages—especially for mooring system optimal design—to save computational cost and time. For detailed designs involving turbulent winds, low-frequency structure response analysis or pitch-sensitive performance, the fully coupled approach is recommended to ensure accuracy. This study could offer practical guidance for selecting suitable numerical methods in FOWT design and analysis.

A computationally efficient isogeometric collocation (IGA-C) method based on nonuniform rational B-splines (NURBS) is adopted to analyze the large amplitude, low frequency, and self-excited vibrations of an iced conductor. Governing partial differential equations (PDEs) involving the axial, horizontal, vertical, and torsional motion of the iced conductor are developed by employing the Hamilton’s variational principle. Taking advantage of the high-continuity properties of NURBS basis functions and Greville collocation points, the authors employ the IGA-C method to discretize the exact PDEs without neglecting high-order nonlinear terms. The Newmark-$\beta$ incremental method and Newton-Raphson nonlinear iteration algorithm are adopted to solve that discretized system of dynamic equations of the iced conductor. The accuracy of the present model scheme and numerical implementation is demonstrated through two illustrative examples. Comparing with conventional finite element methods, the present IGA-C method has less calculation points so that it opens the door to a higher-order accurate analysis for galloping problems with a minimum computational effort.

This study integrates offshore wind power and wave power generation technologies to build a multi-energy complementary renewable energy system, which provides references for marine clean energy development and is highly consistent with the global sustainable development goals. The platform consists of a UMaine VolturnUS-S semi-submersible platform and a group of flap-type wave energy converters. A 15 MW wind turbine is installed on the platform. The hydrodynamic model is established using AQWA. Combined with the upper wind load, the fully coupled time domain model of the integrated power generation platform is constructed using the open-source software F2A. The main purpose is to optimize the parameters of the flap-type wave energy device through frequency domain hydrodynamic analysis and then explore the influence of the wave energy device on the platform under the combined action of regular waves and turbulent wind through a series of working conditions. The results show that when the PTO stiffness is 8 × 10⁷ N·m/rad, the PTO damping takes the optimal damping and has a higher power generation capacity. Secondly, the coupled wave energy device induces minimal hydrodynamic interference between multiple bodies, resulting in negligible impact on the natural frequency of the wind-wave combined platform motion. Overall, the wave energy device can effectively suppress the freedom of shaking degree of the floating wind-wave combined platform.

A reduced model of a transmission tower was established based on the principle of equivalent stiffness. The finite particle method was used to analyse the wind-induced response of the reduced model. The analysis of the dynamic characteristics of the reduced model shows that the accuracy of the equivalent formula proposed in this paper was very high. Compared with the first five order natural frequencies of the complete model, the maximum calculation error of the reduced model was only 0.87%. Since the first order shear deformation beam theory was used in the reduced model, the interpolation-independent element shape functions were developed to avoid the shear locking phenomenon. Moreover, the formula for calculating the internal force of Timoshenko beam for finite particle method was derived. By using two successive Euler angles, a new method for separating the rigid motion and pure deformation of the element was proposed. The computational efficiency of this method is significantly improved, and the computational time is less than half of that of the traditional finite particle method. The results of wind-induced response analysis of the transmission tower show that the simplified model proposed in this paper can obtain highly accurate displacement response of the structure, and the maximum error of the RMS of the displacements at the top of the tower is less than 3.2%. This model is suitable for studying the dynamic response of transmission tower line system and evaluating the effect of the wind-induced vibration control of damping device.