Narrow Results

Random vibration theory is the natural way to deal with some dynamic actions whose nature is deeply random, such as wind, earthquakes or sea waves. Moreover only in a few cases exact solutions are available, so that approximate solutions are usually adopted: Stochastic equivalent linearization is one of the widely used. Its application needs specific numerical techniques, whose complexity is greater in nonstationary cases than in stationary ones and that are usually approached in time domain instead of frequency domain. In this paper, an iterative integration algorithm is proposed in order to solve this problem for single-degree-of-freedom (SDOF) oscillators, using the evolutive Lyapunov equation for nonlinear mechanical linearized system by stochastic linearization technique. It updates linearized system matrix coefficients step by step, by an iterative procedure based on a predictor–corrector technique. The proposed algorithm is described and applied to an hysteretic Bouc–Wen SDOF system excited by a modulated filtered white noise nonstationary process. The accuracy and computational cost are analyzed showing the efficiency of the proposed integrating procedure.

This study is focused on robust design optimization (RDO) of the tuned mass dampers (TMDs), which are widely used as a passive vibration controller in structural systems. The performance of the TMDs designed under the implicit assumption that all relevant system parameters (such as loading and structural characteristics) are deterministic is greatly affected by the inevitable inherent uncertainties in the system parameters. In this regard, a framework is proposed for the RDO of TMDs to determine its optimal solution which is less sensitive to system parameter variability. RDO is defined as a multi-objective optimization problem that aims to minimize the mean and variance of the performance function. In the case of multiple TMDs, the proposed framework uniquely avoids the presumption of their mass distribution, number, and placement location. In the proposed RDO framework, an augmented formulation is adopted wherein the design parameters are artificially introduced as uncertain variables with some prescribed probability density function (PDF) over the design space. The resulting optimization problem is solved using the stochastic subset optimization (SSO) and KN, a direct search optimization method. The effectiveness of the proposed framework is studied by analyzing four illustrative examples involving a single TMD attached to a single-degree-of-freedom (SDOF) structure, a single TMD attached to a multiple-degree-of-freedom (MDOF) structure, multiple TMDs attached to an MDOF structure, and an 80-story structure equipped with multiple TMDs.

Structural response of linear multi degree of freedom (MDoF) system subject to random Gaussian dynamic actions is defined by mean of vector and covariance matrix in state space. In case of non-stationary inputs, second-order spectral moments evaluation needs the solution of the so-called Lyapunov matrix differential equation. In this work a numerical scheme for its resolution is proposed, with reference to input processes modeled as linear filtered white noise with time-varying parameters, which is a common situation in amplitude and frequency variable loads. Numerical computational effort is minimized by taking into account symmetry characteristic of state space covariance matrix. As application of the proposed method a multi-storey building is analyzed to obtain reliability associated to maximum inter-storey exceeded over a given acceptable limit. It is assumed to be subject to seismic input described by a amplitude and frequency nonstationary process, by using a generalized non-stationary Kanai Tajimi seismic model. Structure is assumed as a plane shear frame MDoF system. Structural reliability evaluation is referred to "first time out-crossing" and different numerical benchmarks are considered.