Response of beams resting on viscoelastically damped foundation to moving oscillators

The response of beams resting on viscoelastically damped foundation under moving SDoF oscillators is scrutinized through a novel state-space formulation, in which a number of internal variables is introduced with the aim of representing the frequency-dependent behaviour of the viscoelastic foundation. A suitable single-step scheme is provided for the numerical integration of the equations of motion, and the Dimensional Analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator. The effects of boundary conditions, span length and number of modes of the beam, along with those of the mechanical properties of oscillator and foundation, are investigated in a new dimensionless form, and some interesting trends are highlighted. The inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation, as usual in the present state-of-practice, is also quantified

An earthquake response spectrum method for linear light secondary substructures

YesEarthquake response spectrum is the most popular tool in the seismic analysis and design of structures. In the case of combined primary-secondary (P-S) systems, the response of the supporting P substructure is generally evaluated without considering the S substructure, which in turn is only required to bear displacements and/or forces imposed by the P substructure (¿cascade¿ approach). In doing so, however, dynamic interaction between the P and S components is neglected, and the seismic-induced response of the S substructure may be heavily underestimated or overestimated. In this paper, a novel CQC (Complete Quadratic Combination) rule is proposed for the seismic response of linear light S substructures attached to linear P substructures. The proposed technique overcomes the drawbacks of the cascade approach by including the effects of dynamic interaction and different damping in the substructures directly in the cross-correlation coefficients. The computational effort is reduced by using the eigenproperties of the decoupled substructures and only one earthquake response spectrum for a reference value of the damping ratio

Peak response of non-linear oscillators under stationary white noise

The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature

A numerical method for the time‐domain dynamic analysis of buildings equipped with viscoelastic dampers

A novel numerical scheme for the time-domain dynamic analysis of buildings incorporating energy dissipation devices of viscoelastic type is presented. Two alternative state-space representations are considered for the frequency-dependent behaviour of the viscoelastic dampers, namely generalized Maxwell's (GM) model and Laguerre's polynomial approximation (LPA) technique. The computational burden is dramatically reduced by using a convenient modal transformation of coordinates, where the equilibrium modulus of the viscoelastic devices is included in the evaluation of modal shapes and undamped modal frequencies. Both GM model and LPA technique lead to closed-form expressions for the parameters characterizing the modal relaxation functions of the building, which in turn are exploited in deriving the exact integration operators for the modal oscillators. Importantly, all the matrices required in the proposed cascade scheme are directly computable from the exact transition matrices of traditional state variables (displacements and velocities) and additional internal variables (for either GM model or LPA technique). A simple application to a Single-DoF oscillator demonstrates the unconditional stability of the numerical method; the numerical efficiency is proved with the dynamic analysis of a discretized structural system with a large number of degrees of freedom; the accuracy is confirmed by the seismic response analysis of a realistic 10-storey building equipped with viscoelastic dampers. Copyright © 2010 John Wiley & Sons, Ltd

An improved computational strategy for vibration- proof structures equipped with nano-enhanced viscoelastic devices

Viscoelastic damping devices are effective in mitigating vibrations experienced by Civil Engineering structures subjected to natural actions, such as earthquakes, wind gusts or ocean waves. In this paper, an efficient computational framework for non-classically damped viscoelastic structures is proposed, allowing rheological information on nano-reinforced elastomeric devices to be incorporated in the time-domain dynamic analysis of structures equipped with such components. For thiss purpose, the Generalized Maxwell (GM) model and the Laguerre’s polynomial approximation (LPA) can be effectively adopted to represent the relaxation function of the viscoelastic materials, leading to an enlarged state-space model. It is also shown that these models can be used beyond the linear range, provided that the strain-dependent values of their mechanical parameters are identified

Transverse vibrations of viscoelastic sandwich beams via a Galerkin-based state-space approach

A new state-space model is formulated for the dynamic analysis of sandwich beams that are made of two thin elastic layers continuously joined by a shear-type viscoelastic (VE) core. The model can accommodate different boundary conditions for each outer layer and accounts for the rate-dependent constitutive law of the core through additional state variables. The mathematical derivation is presented with the Standard Linear Solid (SLS) model (i.e., a primary elastic spring in parallel with a single Maxwell element) and then extended to the generalized Maxwell (GM) model. The kinematics equations are developed by means of Galerkin-type approximations for the fields of axial and transverse displacements in the outer layers, and imposing the pertinent compatibility conditions at the interface with the core. Numerical examples demonstrate the accuracy and versatility of the proposed approach, which endeavors to represent the effects of the VE memory on the vibration of composite beams

Transverse vibration of slender sandwich beams with viscoelastic inner layer via a Galerkin-type state-space approach

A novel state-space model for studying free and forced transverse vibrations of sandwich beams, made of two outer elastic beams of the same length, continuously joined by an inner shear-type viscoelastic layer, is presented. The proposed technique enables one to consider: i) inhomogeneous systems; ii) any boundary conditions; and iii) rate-dependent constitutive laws for the inner layer, which can be represented either through Generalised Maxwell's model or Laguerre's Polynomial Approximation. For the viscoelastic model of the inner layer, the dynamic behaviour is described by the Standard Linear Solid model, which is made of a primary elastic spring in parallel with a Maxwell's element. The kinematics of the outer beams is developed by means of Galerkin-type approximations for the fields of both axial and transverse displacements in the outer beams, and imposing the pertinent compatibility conditions at interface. In the proposed formulation, the assumed modes are selected as the first modes of axial vibration and of lateral buckling for each layer with homogenised mechanical properties and their own boundary conditions. Numerical examples using a novel direct integration method for calculating the response of the dynamic system demonstrate the accuracy and versatility of the proposed formulation, in both frequency- and time-domain analyses

A new modal correction method for linear structures subjected to deterministic and random loadings

In the general framework of linear structural dynamics, modal corrections methods allow improving the accuracy of the response evaluated with a reduced number of modes. Although very often neglected by researchers and practitioners, this correction is particularly important when strains and stresses are computed. Aimed at overcoming the main limitations of existing techniques, a novel dynamic modal acceleration method (DyMAM) is presented and numerically validated. The proposed correction involves a set of additional dummy oscillators, one for each dynamic loading, and can be applied, with a modest computational effort, to discrete and continuous systems under deterministic and random inputs

Spectrum-compatible accelerograms with harmonic wavelets

Modern building codes allow the analysis and design of earthquake-resistant structures with recorded and/or generated accelerograms, provided that they are compatible with the elastic design spectrum. The problem then arises to generate spectrum-compliant accelerograms with realistic non-stationary characteristics, which in turn may play an important role in the non-linear seismic response. In this paper, an iterative procedure based on the harmonic wavelet transform is proposed to match the target spectrum through deterministic corrections to a recorded accelerogram, localised both in time and frequency. Numerical examples demonstrate the performance of this approach, which can be effectively used in the design practice

Seismic performance of buildings retrofitted with nonlinear viscous dampers and adjacent reaction towers

An effective strategy of seismic retrofitting consists of installing nonlinear viscous dampers (NLVDs) between the existing building, with insufficient lateral resistance, and some auxiliary towers, specially designed and erected as reaction structures. This allows improving the seismic performance of the existing building without any major alteration to its structural and non- structural elements, which makes this approach particularly appealing for buildings with heritage value. In this paper, the nonlinear governing equations of the coupled lateral-torsional seismic motion are derived from first principles for the general case of a multi-story building connected at various locations in plan and in elevation to an arbitrary number of multi-story towers. This formulation is then used to assess the performance of the proposed retrofitting strategy for a real case study, namely a five-story student hall of residence in the city of Messina, Italy. The results of extensive time-history analyses highlight the key design considerations associated with the stiffness of the reaction towers and the mechanical parameters of the NLVDs, confirming the validity of this approac