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.

Estimation of Seismic Damage Induced by Near- and Far-Fault Earthquakes Using Modified Equivalent Linearization Method of Mid-Rise RC Buildings

For the seismic design of a mid-rise reinforced concrete (RC) building considering the damage control, the main purpose of this work is to propose a simplified method that can be used to estimate the damage index or damage state induced by the near-fault and far-fault earthquakes. In addition to the maximum deformation response, the hysteretic energy dissipation induced the earthquakes is also considered in the damage index quantification based on the modified equivalent linearization method (MELM). Based on the damage index model in terms of the maximum deformation response and hysteretic energy dissipation under an earthquake, this work provides a convenient method by which an engineer can determine the damage-controlling minimal ductility requirement to ensure that the damage index remains under a specified value. For a mid-rise RC building structure, an engineer can also apply the simplified formula proposed in this work to obtain the damage-controlling yielding strength for a specified ductility capacity.

Equivalent Linearization of Bladed Disk Assemblies With Friction Nonlinearities Under Random Excitation

The present article addresses the vibrational behavior of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behavior. The use of friction dampers for energy dissipation and suppression of large amplitudes adds a nonlinearity to the mechanical system, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from stationary to transient, synchronous to asynchronous as well as deterministic to random excitation. Random excitation in combination with the presence of nonlinearities makes the calculation of the vibrational behavior even more complex. So far, this problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The fundamental idea of the method is to linearize a nonlinear system in such a way that the most suitable equivalent linear system is found taking into account the approximated distribution of the response amplitude. To apply this method to a system with a friction nonlinearity, the linear part of the system is considered in state space and extended with additional nonlinear equations. The nonlinear contact is modelled with a Bouc-Wen formulation to reproduce the hysteretic character of a nonlinearity occurring in the presence of a friction damper. The classical Bouc-Wen formulation is standardized in such a way that the usual parameters can be replaced by physical ones such as the normal force or contact stiffness. The nonlinear force of the friction nonlinearity is linearized regarding the stochastic distribution of the system response. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments do not change over time. However, the spectrum of the excitation is not limited to being constant, as it is the case with Gaussian white noise. The equivalent linearization method could also deal with a narrowband or broadband excitation spectrum. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each sector is represented by a reduced order model with several degrees of freedom.

Equivalent Linearization of Bladed Disk Assemblies with Friction Nonlinearities Under Random Excitation

The present article addresses the vibrational behaviour of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behaviour. The use of friction dampers for energy dissipation and suppression of large amplitudes makes the mechanical system nonlinear, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from clearly defined deterministic to random excitation. So far, the latter problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The nonlinear contact is modelled both with an elastic Coulomb-slider and a Bouc-Wen formulation to reproduce the hysteretic character of a friction nonlinearity occurring in the presence of a friction damper. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments, do not change over time. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each segment is approximated with several degrees of freedom.