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The non‐linear damping mechanisms are expressed in two general forms: velocity dependent and displacement dependent. The non‐linear damping phenomena are expressed by an array of ‘local constants’, whose value depends upon excitation frequency, excitation amplitude, and type of non‐linearity. Thus, the non‐linear system is replaced by several localized linear systems corresponding to every discrete frequency and amplitude of excitation. Each of the localized linear systems, thus formulated, characterizes the response behaviour of the original non‐linear system, quite accurately in the vicinity of the specific frequency and amplitude of excitation. An algorithm is developed, which expresses the non‐linear damping by an array of ‘local constants’. The algorithm then employs the usual linear design tools to generate the response characteristics almost identical to the response behaviour of the non‐linear system.

A local equivalent linearization methodology is proposed to simulate non‐linear shock absorbers and dual‐phase dampers in the convenient frequency domain. The methodology based on principle of energy similarity, characterizes the non‐linear dual‐phase dampers via an array of local damping constants as function of local excitation frequency and amplitude, response, and type of non‐linearity. The non‐linear behaviour of the dual‐phase dampers can thus be predicted quite accurately in the entire frequency range. The frequency response characteristics of a vehicle model employing non‐linear dual‐phase dampers, evaluated using local linearization algorithm, are compared to those of the non‐linear system, established via numerical integration, to demonstrate the effectiveness of the algorithm. An error analysis is performed to quantify the maximum error between the damping forces generated by non‐linear and locally linear simulations. The influence of damper parameters on the ride improvement potentials of dual‐phase dampers is further evaluated using the proposed methodology and discussed.

Condition assessment on reinforced concrete (RC) structures is one of the critical issues as a result of structure degradation due to aging in many developed countries. The purpose of this paper is to examine the sensitivity and reliability of the conventional dynamic response approaches, which are currently applied in the RC structures. The key indicators include: natural frequency and damping ratio. To deal with the non-linear characteristics of RC, the concept of random decrement is applied to analyze time domain data and a non-linear damping curve could be constructed to reflect the condition of RC structure.

A full-scale RC structure was tested under ambient vibration and the impact from a rubber hammer. Time history data were collected to analyze dynamics parameters such as natural frequency and damping ratio.

The research demonstrated that the measured natural frequency is not a good indicator for integrity assessment. Similarly, it was revealed that the traditional theory of viscous damping performed poorly for the RC with non-linear characteristics. To address this problem, a non-linear curve is constructed using random decrement and it can be used to retrieve the condition of the RC structure in a scientific manner.

The time domain analysis using random decrement can be used to construct a non-linear damping curve. The results from this study revealed that the damage of structure can be reflected from the changes in the damping curves. The non-linear damping curve is a powerful tool for assessing the health condition of RC structures in terms of sensitivity and reliability.

The paper aims to focus on adjacent buildings response, equipped with damper, to analyze the vibration reduction in the nearby buildings. The nearby buildings were also equipped with dampers. The occurrence of adjacent buildings with adequate or inadequate space in between is a common phenomenon. However, many a times not much attention is paid to provide or check gap adequacy or to connect the two buildings suitably to avoid pounding of two structures on each other. This study emphasizes the utility of providing a damper in between two adjacent buildings for better performance.

The two steel structures taken for study are prototype of two structures normally found in industrial structure such as power plant, where in one of boiler structure is often tall and braced and short structure of turbine building which is moment resistant, modeled in SAP. There could be similar such structures which are often connected to a platform or a walkway with a sliding end, so as not to transfer horizontal force to other structures. If the advantage of stiffness of tall braced structure is taken into account, shorter structure can be suitably connected to braced structure to transfer forces during seismic cases under nonlinear conditions, thereby avoiding pounding (incase gap is too less), reducing response and thus optimizing the section sizes. The structures were subjected to El Centro earthquake, to simulate MCE (which could be the other site TH scaled up as desired for real site PGA), and damper location and parameters were varied to find optimum value which offers reduced base shear, reduced top floor displacement and minimum inter story drift and highest energy absorption by fluid viscous dampers.

The findings show that taller structures, which are braced, have more stiffness; the effect of damper is more pronounced in reducing displacement of shorter moment resistant structure to the tune of 60%, with suitably defined Cd value which is found to be 600 KNs/m for the present study. Thus, advantage of stiffener structure is taken to leverage and reduce the displacement of shorter moment resistant structure in reducing its displacement under nonlinear conditions of seismic case.

This work shows the original findings, of the adjacent buildings response, equipped with damper, to analyze the vibration reduction on other buildings which were planned to be constructed nearby.

An equivalent linear damping model is developed for forward flight condition, with the flap/lag/pitch kinematics and nonlinear characteristics of hydraulic damper taken into account. Damper axial velocity is analyzed from the velocities of the damper‐to‐blade attachment point in time domain. For the case of blade lead‐lag oscillations without forced excitation and kinematics, the equivalent linear damping is calculated from transient response with energy balance method, Fourier series based moving block analysis and Hilbert transform based technology, respectively. Results indicate that equivalent linear damping decreases significantly with lead‐lag forced excitation and flap/lag/pitch kinematics, especially with the latter in flight condition.

The purpose of this paper is to report the implementation of an alternative time integration procedure for the dynamic non-linear analysis of structures.

The time integration algorithm discussed in this work corresponds to a spectral decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthogonal Legendre polynomials are used to define the time approximation basis required by the model.

A classical example with known analytical solution is presented to validate the model, in linear and non-linear analysis. The efficiency of the numerical technique is assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear and non-linear dynamics. The mixed time integration technique presents some interesting features making very attractive its application to the analysis of non-linear dynamic systems. It corresponds in essence to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion.

One of the main advantages of this technique is the possibility of considering relatively large time step increments which enhances the computational efficiency of the numerical procedure. Due to its characteristics, this method is well suited to parallel processing, one of the features that have to be conveniently explored in the near future.

To propose novel predictor‐corrector time‐integration algorithms for pseudo‐dynamic testing.

The novel predictor‐corrector time‐integration algorithms are based on both the implicit and the explicit version of the generalized‐α method. In the non‐linear unforced case second‐order accuracy, stability in energy, energy decay in the high‐frequency range as well as asymptotic annihilation are distinctive properties of the generalized‐α scheme; while in the non‐linear forced case they are the limited error near the resonance in terms of frequency location and intensity of the resonant peak. The implicit generalized‐α algorithm has been implemented in a predictor‐one corrector form giving rise to the implicit IPC‐ρ_∞ method, able to avoid iterative corrections which are expensive from an experimental standpoint and load oscillations of numerical origin. Moreover, the scheme embodies a secant stiffness formula able to approximate closely the actual stiffness of a structure. Also an explicit algorithm has been implemented, the EPC‐ρ_b method, endowed with user‐controlled dissipation properties. The resulting schemes have been tested experimentally both on a two‐ and on a six‐degrees‐of‐freedom system, exploiting substructuring techniques.

The analytical findings and the tests have indicated that the proposed numerical strategies enhance the performance of the pseudo‐dynamic test (PDT) method even in an environment characterized by considerable experimental errors. Moreover, the schemes have been tested numerically on strongly non‐linear multiple‐degrees‐of‐freedom systems reproduced with the Bouc‐Wen hysteretic model, showing that the proposed algorithms reap the benefits of the parent generalized‐α methods.

Further developments envisaged for this study are the application of the IPC‐ρ_∞ method and of EPC‐ρ_b scheme to partitioned procedures for high‐speed pseudo‐dynamic testing with substructuring.

The implicit IPC‐ρ_∞ and the explicit EPC‐ρ_b methods allow a user to have defined dissipation which reduces the effects of experimental error in the PDT without needing onerous iterations.

The paper proposes novel time‐integration algorithms for pseudo‐dynamic testing. Thanks to a predictor‐corrector form of the generalized‐α method, the proposed schemes maintain a high computational efficiency and accuracy.

Subsynchronous resonance (SSR) problem is often created in generator rotor systems with long shafts (non‐rigid shaft) and large inertias constituting a weakly damped mechanical system. When the electrical network resonance frequency (in which the transmission line is compensated by series capacitors) approaches shaft natural frequencies, the electrical system increases torsional torques amplitude on the shaft. The purpose of this paper is to propose a self‐tuning proportional, integral, derivative (PID) controller to damp the SSR oscillations in the power system with series compensated transmission lines.

To accommodate the PID controller in all power system loading conditions, the gradient descent (GD) method and a wavelet neural network (WNN) are used to update the PID gains on‐line. All parameters of the WNN are trained by the gradient descent method using adaptive learning rates (ALRs). The ALRs are derived from discrete Lyapunov stability theorem, which are applied to guarantee the convergence of the proposed control system. Also, the suggested controller is designed based on a non‐linear model.

The proposed self‐tuning PID controller is applied to a power system non‐linear model. Simulation results are used to demonstrate the effectiveness and performance of the proposed controller. It has been shown that self‐tuning PID is able to damp the SSR under any circumstances, because the WNN ensures the robustness of the controller. Simplicity and practicality of the proposed controller with its excellent performance make it ideal to be implemented in real excitation systems.

The proposed self‐tuning PID approach is interesting for the design of an intelligent control scheme based on non‐linear model to damp the torsional oscillations. In this suggested controller, the system conditions and requirements adjust on‐line the PID gains. On other words, to damp the SSR, PID gains are intelligently computed by the controlled system. The main contributions of this paper are: the overall control system is globally stable and hence, the SSR is controlled; the control error can be reduced to zero by appropriate chosen parameters and learning rates; and the self‐tuning PID can achieve favorable controlling performance.

To provide a model that allows testing and understanding special damping techniques.

The finite element modeling takes into account the piezoelectric coupling. It is used with a non linear electrical circuit. The approach leads to an accurate tool to observe the behavior of the non linear damping techniques such as synchronized switch damping.

The model has been validated by comparison with Ansys® but the CPU time required for the model is around one hundred times shorter.

The proposed model is 1D and the assumptions to use it are not verified for all structures.

The authors obtain a useful tool for the design of damping structures (for example to find the best localisation of the piezoelectric patches and to test electrical circuits).

The model is used for the design and conception of damping as well as for harvesting structures.

The simplified modeling of many physical processes results in a second-order ordinary differential equation (ODE) system. Often the damping of these resonating systems cannot be defined in the same simplified way as the other parameters due to the complexity of the physical effects. The purpose of this paper is to develop a mathematically stable approach for damping resonances in nonlinear ODE systems.

Modifying the original ODE using the eigenvalues and eigenvectors of a linearized state leads to satisfying results.

An iterative approach is presented, how to modify the original ODE, to achieve a well-damped solution.

The method can be applied for every physical resonating system, where the model complexity prevents the determination of the damping.

The iterative algorithm to modify the original ODE is novel. It can be used on different fields of the physics, where a second-order ODE is describing the problem, which has only measured or empirical damping.