A transmission tower-line system consists of many towers and cables, which is a long-span structure. Due to topographical restrictions, the structure inevitably passes through wide areas prone to landslide hazards. The landslide causes the failure of the tower foundation and threatens the safety of the power transmission system. Therefore, the aim of this study was to investigate the collapse patterns of a transmission tower-line structure under landslides. The explicit analysis method was used to deal with the nonlinear dynamic response equations of the structure. To prove the effect of the landslides on the collapse patterns of the transmission tower-line structure, two foundation failure cases (Case 1 and Case 2) under landslides were considered. For each case, the displacement responses at tower tops and the progressive collapse behavior were analyzed, which illustrate that the failure patterns of the tower-line structure under landslides are dominated by two factors, i.e., the failure mode of the tower foundation and the pulling effect of cables. The overall tilting and hinge formation in the middle of the tower body are the main collapse patterns of the structure under Case 1 and Case 2, respectively. In addition, because of the pulling of cables, the collapse of one tower induced by the landslides always triggers the local failure of neighboring tower heads.

In the current electromechanical model of cantilevered piezoelectric energy harvesters, the assumption of uniform electric field strength within the piezoelectric layer is commonly made. This uniform electric field assumption seems reasonable since the piezoelectric layer looks like a parallel-plate capacitor. However, for a piezoelectric bender, the strain distribution along the thickness direction is not uniform, which means the internal electric field generated by the spontaneous polarization cannot be uniform. In the present study, a non-uniform electric field in the piezoelectric layer is resolved using electrostatic equilibrium equations. Based on these, the traditional distributed parameter electromechanical model is corrected and simplified to a practical single mode one. Compared with a traditional model adopting a uniform electric field, the bending stiffness term involved in the electromechanical governing equations is explicitly corrected. Through comparisons of predicted power output with two-dimensional finite element analysis, the results show that the present model can better predict the power output performance compared with the traditional model. It is found that the relative corrections to traditional model have nothing to do with the absolute dimensions of the harvesters, but only relate to three dimensionless parameters, i.e., the ratio of the elastic layer’s to the piezoelectric layer’s thickness; the ratio of the elastic modulus of the elastic layer to the piezoelectric layer; and the piezoelectric materials’ electromechanical coupling coefficient squared, ${k_{31}}^2$. It is also found that the upper-limit relative corrections are only related to ${k_{31}}^2$, i.e., the higher ${k_{31}}^2$ is, the larger the upper-limit relative corrections will be. For a PZT-5 unimorph harvester, the relative corrections of bending stiffness and corresponding resonant frequency are up to 17.8% and 8.5%, respectively. An inverse problem to identify the material parameters based on experimentally obtained power output performance is also investigated. The results show that the accuracy of material parameters identification is improved when considering a non-uniform electric field.

Submerged tensioned anchor cables (STACs) are pivotal components utilized extensively for anchoring and supporting offshore floating structures. Unlike tensioned cables in air, STACs exhibit distinctive nonlinear damping characteristics. Although existing studies on the free vibration response and tension identification of STACs often employ conventional Galerkin and average methods, the effect of the quadratic damping coefficient (QDC) on the vibration frequency remains unquantified. This paper re-examines the effect of bending stiffness on the static equilibrium configuration of STACs, and establishes the in-plane transverse free motion equations considering bending stiffness, sag, and hydrodynamic force. By introducing the bending stiffness influence coefficient and the Irvine parameter, the exact analytical solutions of symmetric and antisymmetric frequencies and modal shapes of STACs are derived. An improved Galerkin method is proposed to discretize the nonlinear free motion equations ensuring the accuracy and applicability of the analytical results. Additionally, this paper presents an analytical solution for the nonlinear free vibration response of the STACs using the improved averaging method, along with improved frequency formulas and tension identification methods considering the QDC. Through a case study, it is demonstrated that the improved methods introduced in this paper offer higher accuracy and wider applicability compared to the conventional approaches. These findings provide theoretical guidance and reference for the precise dynamic analysis, monitoring, and evaluation of marine anchor cable structures.