Optimization design for multiple dynamic vibration absorbers on damped structures using equivalent linearization method

The dynamic vibration absorber and tuned mass damper are widely used to suppress harmful vibration of the damped structures under external excitation. The multiple dynamic vibration absorbers have more benefit than the single dynamic vibration absorber. The multiple dynamic vibration absorbers are portability and easy to install because its size is significantly reduced compared to an individual damper. This paper proposes a design method to obtain optimal parameters of multiple dynamic vibration absorbers attached on damped primary structures by using the least squares estimation of equivalent linearization method. An explicit expression of damping ratio and tuning parameters of multiple dynamic vibration absorbers are determined for minimizing the maximum displacement of the primary structures based on the fixed-point theory. The new contribution is provided a reliable theoretical basis for optimizing parameters of the multiple dynamic vibration absorbers that are attached on the damped primary structures. The numerical results reveal the effectiveness of the proposed optimal parameters of multiple dynamic vibration absorbers in reduce vibration of damped primary structures. In the practical applications, this research results allow to divide a large dynamic vibration absorber into many equivalent small dynamic vibration absorbers, which are convenient for manufacturing and installing on the damped primary structures such as high buildings and cable-stayed bridges.

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

Jointed structures in engineering naturally perform with some of nonlinearity and uncertainty, which significantly affect the dynamic characteristics of the structural system. In this paper, the method of Bayesian uncertainty identification of model parameters for the jointed structures with local nonlinearity is proposed. Firstly, the nonlinear stiffness and damping of the joints under the random excitation are represented with functions of excitation magnitude in terms of the equivalent linearization. The process of uncertainty identification is separated from the representation of local nonlinearity. In this way, the dynamic behavior of the joints is penetratingly characterized instead of ascribing the nonlinearity to uncertainty. Secondly, a variable-expanded Bayesian (VEB) method is originally proposed to identify the mixed of aleatory and epistemic uncertainties of model parameters. Different from traditional Bayesian identification, the aleatory uncertainties of model parameters are identified as one of the most important parts rather than only measurement noise of output. Notablely, a series of intermediate variables are introduced to expand the parameter with aleatory uncertainty in order to overcome the difficulty of establishing the likelihood function. Moreover, a 3-DOF numerical example is illustrated with case studies to verify the proposed method. The influence of observed sample size and prior distribution selection on the identification results is tested. Furthermore, an engineering example of the jointed structure with rubber isolators is performed to show the practicability of the proposed method. It is indicated that the computational model updated with the accurately identified parameters with both nonlinearity and uncertainty has shown the excellent predictive capability.

Non-Linear Response of Cable-Mass-Spring System in High-Rise Buildings under Stochastic Seismic Excitation

In high-rise buildings earthquake ground motions induce bending deformation of the host structure. Large dynamic displacements at the top of the building can be observed which in turn lead to the excitation of the cables/ropes within lift installations. In this paper, the stochastic dynamics of a cable with a spring-damper and a mass system deployed in a tall cantilever structure under earthquake excitation is considered. The non-linear system is developed to describe lateral displacements of a vertical cable with a concentrated mass attached at its lower end. The system is moving slowly in the vertical direction. The horizontal displacements of the main mass are constrained by a spring-viscous damping element. The earthquake ground motions are modelled as a filtered Gaussian white noise stochastic process. The equivalent linearization technique is then used to replace the original non-linear system with a linear one with the coefficients determined by utilising the minimization of the mean-square error between both systems. Mean values, variances and covariances of particular random state variables have been obtained by using the numerical calculation. The received results were compared with the deterministic response of the system to the harmonic process and were verified against results obtained by Monte Carlo simulation.

Model-Free Tracking Control with Prescribed Performance for a Shape Memory Alloy-Based Robotic Hand

The shape memory alloy (SMA)-based robotic hand has been a new emerging technology with potential applications ranging from life service to surgical treatment, because of the characteristics of SMA, such as high power-to-weight ratio, small volume and low driving voltage. However, due to the complex dynamic model and nonlinear aspects of SMA, it is complicated to control an SMA-based robotic hand. This paper presents a novel model free adaptive control for the SMA-based robotic hand system. By applying the Taylor series expansion method and the differential mean value theorem, the SMA based robotic hand system can be transformed into an equivalent linearization model, which merely depends on measurement data without any information on the system. Combined with prescribed performance control, the novel control method can constrain the tracking error in a preassigned domain. Experiments are conducted on the SMA-based robotic hand system to verify the performance of the presented control method.

Analysis on the Influence of Increasing Seismic Fortification Intensity on Seismic Performance of Underground Station

China Earthquake Parameter Zoning (2016) has increased the seismic fortification intensity in Chengdu from VII to VIII. It is necessary to conduct in-depth discussion on the impact of the seismic performance of the built underground station structure. In this paper, a stratum-structure finite element model is established with a Chengdu subway station as an example. The model boundary adopts viscoelastic boundary, and the ground motion is input in the form of equivalent nodal force. The equivalent linearization method is used to consider the nonlinearity of soil materials. The time-history analysis of seismic fortification intensity of VII and VIII degrees is carried out, respectively. By comparing the calculation results of the two seismic fortification intensity ground motion conditions, it is concluded that the connection between the side wall and the floor is the weakest position of the station structure under the action of the earthquake; the seismic fortification intensity is increased from VII to VIII to the internal force of the structure. It has a relatively large impact, especially the most obvious impact on the bending moment. The results of the verification of the seismic time-history analysis show that the increase of fortification intensity will have a more obvious impact on the structural deformation, and the structural design of the station can meet the safety performance requirements of VII and VIII degrees of seismic fortification. The research has certain reference significance for the seismic safety evaluation of the built underground station structure in Chengdu area.

Study on the Seismic Effect of the Interbedded Soil Layer in the Yinchuan Alluvial Plain

This paper presents a numerical analysis of two types of representative site profiles in the Yinchuan Plain under earthquake loading. The analyzed soil profiles, based on borehole investigations performed over the years, are used to explore the seismic response of the sites in this area. In total, eleven stratified soil models are used in this study, which can be grouped into two categories: a single interbedded soil model and multiple interbedded soil model. A one-dimensional equivalent linearization method is applied to evaluate the seismic response of different soil models under four exceeding probabilities in terms of peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), and spectral acceleration (Sa). The results show that the significant amplification effect of PGA occurs in rare and extremely rare earthquakes, with an amplification ratio of 1.4∼1.7 when the single silty clay layer is located at the model ground. In this scenario, the spectral acceleration is amplified at a period of approximately 1.0 s. For the multilayered soil cases, the amplification effect tends to decrease, whereas the characteristic periods increase with increasing numbers of soil layers and the ground acceleration is deamplified under a high motion intensity when the number of soil layers is ≥ 5. This study, to a certain degree, has reference value for seismic microzonation in this area.

Calculation of Nonlinear Systems Under Narrow Band Excitation Using Equivalent Linearization and Path Continuation

Turbomachines experience a wide range of different types of excitation during operation. On the structural mechanics side, periodic or even harmonic excitations are usually assumed. For this type of excitation there are a variety of methods, both for linear and nonlinear systems. Stochastic excitation, whether in the form of Gaussian white noise or narrow band excitation, is rarely considered. As in the deterministic case, the calculations of the vibrational behavior due to stochastic excitations are even more complicated by nonlinearities, which can either be unintentionally present in the system or can be used intentionally for vibration mitigation. Regardless the origin of the nonlinearity, there are some methods in the literature, which are suitable for the calculation of the vibration response of nonlinear systems under random excitation. In this paper, the method of equivalent linearization is used to determine a linear equivalent system, whose response can be calculated instead of the one of the nonlinear system. The method is applied to different multi-degree of freedom nonlinear systems that experience narrow band random excitation, including an academic turbine blade model. In order to identify multiple and possibly ambiguous solutions, an efficient procedure is shown to integrate the mentioned method into a path continuation scheme. With this approach, it is possible to track jump phenomena or the influence of parameter variations even in case of narrow band excitation. The results of the performed calculations are the stochastic moments, i.e. mean value and variance.

Random analysis of coupled vehicle-bridge systems with local nonlinearity based on explicit time-domain method

Based on the explicit time-domain method in conjunction with the equivalent linearization technique, an efficient analysis algorithm is developed for the random vibration analysis of the coupled vehicle-bridge system with local nonlinear components under the random irregular excitation from a bridge deck. With the coupled vehicle-bridge system divided into two subsystems, the equivalent linearized subsystem for the vehicle subsystem with the hysteretic suspension spring is constructed for the given time instant using the equivalent linearization technique. Then the dimension-reduction vibration analysis for the equivalent linearized coupled vehicle-bridge system can be carried out based on the time-domain explicit method, which has been proven to be highly efficient. The numerical example indicates that the proposed approach is of feasibility.