An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

Flutter analysis of an airfoil with nonlinear damping using equivalent linearization

The equivalent linearization method （ELM） is modified to investigate the nonlinear flut- ter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flut- ter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation （LCO） is chosen as an active increment to produce bifurca- tion charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.

An equivalent linearization method for nonlinear Van der Pol oscillator subjected to random vibration using orthogonal functions

This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean-square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.

A statistical approach to determine 2D optimal equivalent linear parameters with application to earthquake engineering

The equivalent linearization method approximates the maximum displacement response of nonlinear structures through the corresponding equivalent linear system. By using the particle swarm optimization technique, a new statistical approach is developed to determine the key parameters of such an equivalent linear system over a 2D space of period and damping ratio. The new optimization criterion realizes the consideration of the structural safety margin in the equivalent linearization method when applied to the performance-based seismic design/evaluation of engineering structures. As an application, equations for equivalent system parameters of both bilinear hysteretic and stiffness degrading single-degree-of- freedom systems are deduced with the assumption of a constant ductility ratio. Error analyses are also performed to validate the proposed approach.

ON INFLUENCE OF KINEMATICS TO EQUIVALENT LINEAR DAMPING OF HELICOPTER BLADE HYDRAULIC DAMPER

An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve. The fourth order Runge-Kutta was applied to calculate the damper axial velocity in time domain. Fourier series based moving block analysis was applied to calculate equivalent linear damping in terms of transient responses of damper axial velocity. Results indicate that equivalent linear damping will be significantly reduced if pitch/flap/lag kinematic coupling introduced for notional model and flight conditions.

Sensitivity study of the SiGe heterojunction bipolar transistor single event effect based on pulsed laser and technology computer-aided design simulation

The single event effect of a silicon–germanium heterojunction bipolar transistor(SiGe HBT) was thoroughly investigated. By considering the worst bias condition, the sensitive area of the proposed device was scanned with a pulsed laser.With variation of the collector bias and pulsed laser incident energy, the single event transient of the SiGe HBT was studied.Moreover, the single event transient produced by laser irradiation at a wavelength of 532 nm was more pronounced than at a wavelength of 1064 nm. Finally, the impact of the equivalent linear energy transfer of the 1064 nm pulsed laser on the single event transient was qualitatively examined by performing technology computer-aided design simulations, and a good consistency between the experimental data and the simulated outcomes was attained.

Evaluation of FEMA-440 for including soil-structure interaction

Replacing the entire soil-structure system with a fixed base oscillator to consider the effect of soil-structure interaction （SSI） is a common analysis method in seismic design. This technique has been included in design procedures such as NEHRP, ASCE, etc. by defining an equivalent fundamental period and damping ratio that can modify the response of the structure. However, recent studies indicate that the effects of SSI should be reconsidered when a structure undergoes a nonlinear displacement demand. In recent documents on Nonlinear Static Procedures （NSPs）, FEMA-440 （2005）, a modified damping ratio of the replacement oscillator was proposed by introducing the ductility of the soil-structure system obtained from pushover analysis. In this paper, the damping defined in FEMA-440 to include the soil-structure interaction effect is evaluated, and the accuracy of the Coefficient Method given in FEMA-440 and the Equivalent Linearization Method is studied. Although the improvements for Nonlinear Static Procedures （NSPs） in FEMA-440 are achieved for a fixed base SDOF structure, the soil effects are not perfectly obtained. Furthermore, the damping definition of a soil-structure system is extended to structures to consider bilinear behavior.

SEISMIC RANDOM RESPONSE ANALYSIS OF HYSTERETIC SYSTEMS WITH PSEUDO EXCITATION METHOD

The stationary random responses of nonlinear shear-typeMulti-Degrees-of-Freedom (MDOF) hysteretic system are analyzed byusing the Pseudo Excitation Method (PEM) combined with the EquivalentLinerization Method (ELM). The solution of the equivalent linearsystem is obtained by iteratively solving complex algebraic equationsinstead of the Lyapunov equations. The efficiency of this method ismuch higher For practical engineering systems with manydegrees-of-freedom.

In-plane Auto-Parametric Vibration of Inclined Cables under Random Transverse Excitation

In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.

Finding Non-liner Register on Binary M-Sequence Generating Binary Multiplication Sequence

In the current time there is an important problem that is for a received linear or nonlinear binary sequence{z_(n)}how we can find the nonlinear feedback shift register and its linear equivalent which generate this sequence.The linear orthogonal sequences,special M-Sequences,play a big role in these methods for solving this problem.In the current research trying give illuminations about the methods which are very useful for solving this problem under short sequences,and study these methods for finding the nonlinear feedback shift register of a multiplication sequence and its linear equivalent feedback shift register of a received multiplication binary sequence{z_(n)}where the multiplication on h degrees of a binary linear sequence{a_(n)},or finding the equivalent linear feedback shift register of{z_(n)},where the sequence{z_(n)}of the form M-sequence,and these methods are very effectively.We can extend these methods for the large sequences using programming and modern computers with large memory.

Nonlinear Dynamic Modeling for Joint Interfaces by Combining Equivalent Linear Mechanics with Multi-objective Optimization

The nonlinear dynamic modeling by combining the equivalent linear mechanics with the multi-objective optimization algorithm is proposed to describe the nonlinear behaviors of the joint interfaces.The joint interfaces are simplified as the equivalent virtual material or linear spring damper element.The genetic algorithm for multi-objective optimization is then used to identify the mechanical properties of the equivalent joint by minimizing the error between the simulated dynamic characteristics and the experimental results,including the modal frequencies of the bolted joint beam and the frequency response functions(FRFs)of the rubber isolation system.The FRFs are divided into several subsections with frequency-varied dynamic properties of the joint to consider the nonlinear dynamic behaviors,and the effects of subsection number and excitation amplitudes on the FRFs are also investigated.The results show that the simulated dynamic characteristics of modal frequencies and FRFs agree well with the experimental results.With the increase in the subsection number,the simulated FRFs agree better with the experimental results,indicating a good performance of modeling the nonlinear dynamic behaviors of the joint interfaces forced by different excitation amplitudes.Larger excitation amplitudes will decrease the joint stiffness.