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 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

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

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

A Galerkin-type state-space approach for transverse vibrations of slender double-beam systems with viscoelastic inner layer

A novel state-space form for studying transverse vibrations of doublebeam systems, made of two outer elastic beams continuously joined by an inner viscoelastic layer, is presented and numerically validated. As apposite to other methods available in the literature, the proposed technique enables one to considerer i) inhomogeneous systems, ii) any boundary conditions and iii) rate-dependent constitutive law for the inner layer. The formulation is developed by means of Galerkin-type approximations for the fields of transverse displacements in the system. Numerical examples demonstrate that the proposed approach is accurate and versatile, and lends itself to be used for both frequency- and time-domain analyses

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

Monitoring 3D vibrations in structures using high resolution blurred imagery

Photogrammetry has been used in the past to monitor the laboratory testing of civil engineering structures using multiple image based sensors. This has been successful, but detecting vibrations during dynamic structural tests has proved more challenging. Detecting vibrations during dynamic structural tests usually depend on high speed cameras, but these sensors often result in lower image resolutions and reduced accuracy. To overcome this limitation, a novel approach described in this paper has been devised to take measurements from blurred images in long-exposure photos. The motion of the structure is captured in individual motion-blurred image, without dependence on imaging speed. A bespoke algorithm then determines each measurement point’s motion. Using photogrammetric techniques, a model structure’s motion with respect to different excitation frequencies is captured and its vibration envelope recreated in 3D. The approach is tested and used to identify changes in the model’s vibration response

Optimal design of double skin façades as vibration absorbers

In this paper, several layouts of double skin façades (DSF) used as mass dampers to reduce the vibrations in structures under seismic events are discussed. Firstly, the mathematical coupled problem is studied considering a non-classically damped system excited by a set of accelerogram records. The design problem aims to determine the optimal values of four parameters, namely the flexural stiffness and damping of the DSF panel and the stiffnesses of the elements that connect the DSF to the primary structure. Secondly, four objective functions are presented. Two of these functions aim to minimise respectively the displacements and the accelerations of the primary structure for each earthquake. The remaining two, instead, minimise the average of the displacements and accelerations calculated for all the accelerograms given. Finally, numerical analysis are performed on a six-storey building and four DSF designs are proposed. The Particle Swarm Optimisation (PSO) is used to estimate the optimal parameters. Comparisons among the DSF layouts are presented in terms of minima of the objective functions and in terms of the power transfer functions. Moreover, a simplified design method for the connection elements is discussed

Seismic response of subsystems in irregular buildings

The component-mode synthesis method is applied to investigate the seismic response of secondary subsystems multi-connected to primary structures with irregularities. The proposed approach is more accurate than the cascade approximation, often used in the design practice, as the primarysecondary dynamic interaction is considered through the modes of vibration of the two components. The results of parametric analyses on a representative case study reveal similar trends in the displacements of the two components for mass irregularities in elevation, while sti ness irregularities in plan can result in significant torsional motion in both components, with the effects in terms of absolute accelerations being in general larger than those associated with the lateral drifts. This suggests that dynamic analyses with the component-mode synthesis method are particularly indicated for the seismic assessment of acceleration-sensitive secondary subsystems