The Numerical Analysis for Parametric Resonance of Multicable System considering Interaction between Adjacent Beam Portions

The investigation aims to propose a refined model to analyze the parametric resonance under multicable systems such as cable-stayed bridges. Considering the interaction between the adjacent beam portions, the shear difference is applied to modify the vibration equations derived from the multi-degree-of-freedom stiffness method. Furthermore, the difference method is adopted to make the equations more accessible for numerical analysis. The comparison results indicate that the refined model exhibits the key character of parametric resonance and also further verified the simulation methods. The consequences show that the cable will resonate at the fundamental frequency under the support excitation. In particular, when resonance occurs, most of the energy in the subsystem is transferred to the cable, resulting in the resonance amplitude of the beam portion being weakened to some certain extent. Moreover, the global resonance will have a sufficient excitation on the local resonance only when the resonance condition is satisfied.

Study of seismic-responses and semi-active control of Taizhou Bridge under multi-support excitation

PurposeIn order to make sure of the safety of a long-span suspension bridge under earthquake action, this paper aims to study the traveling wave effect of the bridge under multi-support excitation and optimize the semi-active control schemes based on magneto-rheological (MR) dampers considering reference index as well as economical efficiency.Design/methodology/approachThe finite element model of the long-span suspension bridge is established in MATLAB and ANSYS software, which includes different input currents and semi-active control conditions. Six apparent wave velocities are used to conduct non-linear time history analysis in order to consider the seismic response influence in primary members under traveling wave effect. The parameters α and β, which are key parameters of classical linear optimal control algorithm, are optimized and analyzed taking into account five different combinations to obtain the optimal control scheme.FindingsWhen the apparent wave velocity is relatively small, the influence on the structural response is oscillatory. Along with the increase of the apparent wave velocity, the structural response is gradually approaching the response under uniform excitation. Semi-active control strategy based on MR dampers not only restrains the top displacement of main towers and relative displacement between towers and girders, but also affects the control effect of internal forces. For classical linear optimal control algorithm, the values of two parameters (α and β) are 100 and 8 × 10–6 considering the optimal control effect and economical efficiency.Originality/valueThe emphasis of this study is the traveling wave effect of the triple-tower suspension bridge under multi-support excitation. Meanwhile, the optimized parameters of semi-active control schemes using MR dampers have been obtained, providing relevant references in improving the seismic performance of three-tower suspension bridge.

The dynamics of an omnidirectional pendulum harvester

The pendulum applied to the field of mechanical energy harvesting has been studied extensively in the past. However, systems examined to date have largely comprised simple pendulums limited to planar motion and to correspondingly limited degrees of excitational freedom. In order to remove these limitations and thus cover a broader range of use, this paper examines the dynamics of a spherical pendulum with translational support excitation in three directions that operate under generic forcing conditions. This system can be modelled by two generalised coordinates. The main aim of this work is to propose an optimisation procedure to select the ideal parameters of the pendulum for an experimental programme intended to lead to an optimised pre-prototype. In addition, an investigation of the power take-off and its effect on the dynamics of the pendulum is presented with the help of Bifurcation diagrams and Poincaré sections.

Spatiotemporal seismic excitation of bridges with an anti-symmetrical first mode

This study uses a generalized and parametrized reduced-order model in the frequency-domain to evaluate the effects of asynchronous excitation on the lateral response of bridge structures. Bridge geometry parametric regions, corresponding conceptually to valley profile shapes, are explored. Both modal and bounding analyses, that are dependent on bridge geometry alone, are employed to highlight regions where the first mode is anti-symmetrical and the likely error between identical support excitation (ISE) and multi-support excitation (MSE) analyses is large. Numerical time history analyses, using a heuristic bridge case and spatiotemporal ground motion from the SMART-1 array, are employed. These analyses confirm that in parametric configurations where the first mode is anti-symmetrical the error between MSE and ISE is often larger. This confirms the utility of geometry only modal and bounding analyses in identifying critical regions. These critical parametric cases of a first mode that is anti-symmetrical correspond to shallow valleys with a central rise. In these cases it is recommended that both ISE and MSE analyses should be employed to be conservative.

H∞ Optimization of Tuned Inerter Damper with Negative Stiffness Device Subjected to Support Excitation

In this study, H∞ optimization is conducted for a tuned inerter damper (TID) with negative stiffness device (denoted as TID_NSD) subjected to harmonic support excitation. The study shows that there are still two nonzero-frequency fixed points independent of the damping of the TID_NSD; therefore, the optimum tuning frequency and damping ratio for the TID_NSD are, respectively, derived based on the well-known fixed points theory. By imposing the zero-frequency fixed point having the same amplitude as the other two nonzero-frequency fixed points, the optimum negative stiffness ratio, which makes the primary system with a TID_NSD remain stable, is obtained. Moreover, the role of a negative stiffness device of a TID_NSD system in response control of a single degree-of-freedom (SDOF) structure is evaluated through parametric study. Also, a numerical analysis is conducted on both a SDOF and multiple DOFs structure to validate the feasibility of the derived formulas by simulations with real earthquake records. Numerical results demonstrate that the maximum displacement and the maximum absolute acceleration of the structure equipped with TID_NSD system are reduced by increasing the absolute value of negative stiffness ratio. The results also show that the optimally designed TID_NSD system outperforms the optimally designed TID system in terms of the displacement and absolute acceleration mitigation control. The closed-form solutions proposed in this study can be useful for the optimal design of the structure equipped with TID_NSD.

Error Caused by Damping Formulating in Multiple Support Excitation Problems

The effect of multiple support excitation is an important issue in studying large-span structures. Researchers have shown that the damping related terms in the equation of motion can induce errors in the analysis. Wrongly modelling the damping matrix can induce false damping forces between the structure and the reference coordinates. In multiple support excitation problems, this error is increased when absolute coordinates are used. In this paper, this part of the error is defined as virtual damping error. The error caused by using Rayleigh damping instead of Modal damping is called damping truncation error. This study focuses on the virtual damping error and the damping truncation error that exist in the modeling methods widely used in multiple support excitation problems, namely, large mass method (LMM), relative motion method (RMM), and absolute displacement method (ADM). A new Rayleigh damping formula is proposed for LMM to prevent virtual damping error. A form of equation of motion derived from the converged LMM was proposed in the authors’ previous work. This equation of motion is proved in this paper to be equivalent to RMM when modal damping and the new Rayleigh damping formula are used. RMM is proved free from the virtual damping error. The influence of multiple support excitation effect on the damping formulating errors is studied by spectral analysis. One simplified spring-mass model and two bridge models are used for numerical simulation. The results from the numerical simulation testify to the conclusions from the spectral analysis.

Effects of bending stiffness and support excitation of the cable on cable rain-wind induced inclined vibration

The main objective of this paper is to investigate the responses of the inclined cable due to rain-wind induced vibration (RWIV) considering the bending stiffness and support excitation of the cable. The single-degree-of-freedom (SDOF) model is employed to determine the aerodynamic forces. The 3D model of a cable subjected to RWIV is developed using the linear theory of the cable oscillation and the central difference algorithm in which the influences of wind speed change according to the height above the ground, bending stiffness, and support excitation of the cable are considered. The numerical results showed that the cable displacement calculated by considering cable bending stiffness in RWIV is slightly smaller than in the case of neglecting it. And, the cable diameter had a nonlinear relationship with cable displacement, where when both diameter and mass per unit length of cable increase cable displacement will decrease. In addition, the periodic oscillation of cable supports extremely increases the amplitude of RWIV if its frequency is nearby that of the cable. Keywords: 3D model; inclined cable; rain-wind induced vibration; rivulet; analytical model; vibration.