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The main challenge in predicting structure-borne sound in wood buildings is to accurately model the vibration transmission between the source and the receiving room. Large variations in model parameters make it difficult to predict absolute vibration levels and to make conclusions regarding the relative effects of different designs. A step towards establishing reliable models is to investigate the possibilities and limitations of using deterministic methods, which requires correlations between simulations and measurements. In this paper, we present a multi-level model correlation approach for low-frequency vibration transmission in wood buildings. We apply the proposed approach to a scaled-size experimental structure representing a part of a two-storey wood building, and we evaluate the results for frequencies up to 100 Hz. We perform correlations between simulations and measurements four different levels: structural components (viz. beams and boards), planar structures (viz. floor, ceiling and walls), room structures and the complete structure. The results indicate that the dynamic behaviour of the experimental structure was to a great extent captured by the developed model. Based on the observations made in the multi-level correlations, we discuss important model parameters and propose modelling guidelines. We conclude that it is possible to employ deterministic methods in order to simulate the low-frequency vibration transmission in wood buildings provided that measurement data for calibration purposes are available. The developed numerical model can be used as a reference model for investigations on the effects of variations and uncertainties in the modelling.

Dynamic substructuring is often employed to reduce the size of numerical models for structural dynamic analysis. In this paper, we discuss how elastomeric vibration isolators can be modelled within the framework of dynamic substructuring in order to obtain accurate and efficient reduced order models. For several reasons, it is beneficial to divide a structure containing elastomeric isolators into substructures at the interfaces between elastomers and surrounding parts of the structure. Therefore, we consider the elastomeric isolators as reduced coupling elements in the connections of substructure models. The coupling elements are established by reducing the number of degrees of freedom of 3D finite element models of elastomers. The main purpose of the studies presented in the paper is to evaluate the performance of different reduction method when applied to elastomer models. In addition, the effects of modelling features such as rotational coupling and frequency-dependent material properties of elastomeric isolators are investigated. A model of a wooden building structure with elastomeric isolators is used as an example case, considering steady-state dynamic analysis in the low-frequency range. The results and discussions presented in the paper provide guidance for reduced order modelling of elastomeric isolators in dynamic substructuring.

Population growth and urbanization results in densified cities, where new buildings are being built closer to existing vibration sources, and new transportation systems are constructed closer to existing buildings. Potential disturbing vibrations are one issue to consider in planning urban environments and densification of cities. Vibrations can be annoying for humans but also for sensitive equipment in, for example, hospitals. In determining the risk for disturbing vibrations, the distance between the source and the receiver, the ground properties, and type and size of the building are governing factors. In the paper, a study is presented aiming at investigating the influence of various parameters of the building’s structural design on vibration levels in the structure caused by ground surface loads, e.g. traffic. Parameters studied are related to the type of construction material (if it would be a light or heavy structure), and to the slab thickness. The study is limited to the structural response at frequencies near the first resonance frequency of the soil. The finite element method is employed for discretizing the building structure that is coupled to a semi-analytical model considering a layered ground.

To account for dynamic cross-coupling of structures via the soil, a computational model must be accurate enough to provide the correct overall behaviour of the scattered wave field. However, simplicity is also important when a model should be used for design purposes, especially in the early design stages and feasibility studies. The paper addresses the accuracy of simple models in which an array of structures is simplified into blocks placed on the ground surface or embedded within the soil. Comparisons are made between models that account or do not account, in a proper manner, for the inertia and embedment of the structures. Especially, the limitations of simplified models are discussed regarding their capability to quantify the insertion loss accurately. (Less)

Vibration disturbances in buildings may stem from ambient sources, such as motorway traffic, or from internal sources such as people walking inside the building. Vibrations can exceed requirements for sensitive equipment or cause annoyance to humans and therefore the vibrations may need to be reduced. Vibrations from both external and internal sources can be reduced by modifying the properties of concrete slabs and of the soil underneath. Soil can be improved by being mixed with a binder material in order to increase its stiffness. In this study, parametric finite element analyses were conducted on the achieved vibration reduction on a slab on soil from improving the properties of a concrete slab on soil or of the soil underneath. The size, elastic modulus, and depth of the stabilised soil were found to markedly affect the level of reduction obtained. The soil stabilisation at a vibration-sensitive facility was used as an example case, where the developed finite element model was calibrated to green-field measurements carried out on-site. Frequency spectra of both road traffic loads and internal pedestrian loads were considered in the model. The calibrated finite element model predicted reductions of almost 60% for the road traffic and 80% for the pedestrian load.

In the design of vibration-sensitive structures, large three-dimensional numerical models are frequently used, those occasionally being too large to be simulated in a practical manner. More specifically, the analyses of vibrating complex water-pipe systems require efficient model order reduction strategies. In the paper, a numerical procedure for model order reduction of a water-pipe system housed in a vibration-sensitive research facility is presented. The finite element model employed includes a water-pipe system where fluid–structure interaction effects are accounted for. The reduced model is developed using component mode synthesis and a reduction of the interface degrees of freedom, enabling time-efficient dynamic analyses. The model was proven to be time-efficient and to generate output of high accuracy.

Determining the dynamic behaviour of lightweight buildings by means of finite element analyses requires models representing the geometry involved in great detail, resulting in systems having many millions of degrees of freedom. It is, therefore, important to avoid unnecessarily detailed models by carefully considering what is essential to include in the models and the level of details required for describing the phenomena of interest accurately. In the study presented here, it was investigated whether or not air and insulation in cavities of multi-storey wood buildings affect the transmission of low-frequency structural vibrations. It was concluded, by means of numerical studies, that including air and insulation in cavities, modelled as acoustic media, affects the transmission from a floor to the underlying ceiling and surrounding walls. (C) 2014 Elsevier Ltd. All rights reserved. (Less)

A reduced finite element model for determining the maximum principal stress of a glass pane subjected to dynamic impact load is developed and compared to a full dynamic finite element model. The reduced model is based on the Rayleigh-Ritz method. The Ritz vectors used are determined by simple static load-cases. The model is applicable to centrically and eccentrically applied impact and to glass of various support conditions. It is demonstrated that the model performs well for various types of supported glass panes and impact applied at different locations on the glass pane. The applicability to small or medium sized glass panes is shown through a parametric investigation in which the results are compared to linear and nonlinear finite element solutions. For large glass panes, especially at smaller glass thickness, geometric nonlinear effects must be considered in the analysis. An outline of how to expand the model to include nonlinear geometric effects is given. Finally, it is shown that the reduced model performs excellently in the modeling of a standard laminated glass balustrade with clamp fixings. Apparently, the model is very well suited for strength design of commonly used glass structures.

Reduction in traffic-induced ground vibrations by the use of shaped landscapes is investigated here by shaping the landscape surrounding a high-tech facility, using the landscape thus produced as a wave obstacle. The effects of the geometric parameters of a shaped landscape were examined in parametric studies. An architectural landscape design was also investigated in terms of its effectiveness in reducing traffic-induced ground vibrations. Finite element models, analysed in the frequency domain, were employed. The models involve a layer of soil and the underlying bedrock. It was found that anywhere from an appreciable reduction to an appreciable amplification of the vibrations produced can occur, depending upon the geometric parameters of the shaped landscape involved. The most effective shape was found for a topography that acted as a waveguide that reduced the level of vibration by approximately 35%.

An existing, recently developed solid-shell finite element is proposed for efficient and accurate modeling of laminated glass structures. The element is applied to one test example treating a thin laminated glass structure subjected to biaxial bending and the performance concerning accuracy and efficiency is compared with standard three-dimensional solid elements. Further examples illustrate how the element could be applied in the modeling of laminated glass structures with bolted and adhesive joints. For these examples, experimental data for relevant quantities are provided as a comparison. It is concluded that the element is an excellent candidate for the modeling of laminated glass.

Many cities experience an increasing population leading to a need for urban densification. In these cities, unused land close to railways will have to be developed with new residential and office buildings. The infrastructural demand will also increase, resulting in heavily trafficked roads and railways close to where people work and live. Annoyance from traffic-induced vibrations and noise is expected to be a growing issue. To predict the level of vibration and noise in buildings caused by railway and road traffic, calculation models are needed.In the present paper, a simplified prediction model is briefly described. This prediction model is based on the assumption that the ground and railway embankment can be described in an axisymmetric model, to provide the transfer functions between the track and the free-field. In the paper, the error that arise by assuming axisymmetric response is studied by comparing the response in a three-dimensional finite-element model. Transfer functions at several positions in the free-field are compared.

in Undetermined general method for determining stress concentration factors for laminated glass balustrades with two plus two bolt fixings with variable positions is developed. It is demonstrated how the stress concentration factors can be presented graphically in design charts and representative charts are displayed for the case of a more specific bolt-fixed balustrade type. In general, the use of simple formulas and design charts allows the maximum principal stresses of the balustrade to be determined for any relevant combination of variable geometry parameters involved.

Lightweight buildings are sensitive to low-frequency vibrations, making it difficult to construct them in such a way that noise and disturbing vibrations are kept at an acceptable level. In the design of vibration reduction measures, it is desirable to have computational models for predicting the effects of structural modifications. Validations of the models to experimental data have to be performed to ensure reliable predictions. The experimental studies are simplified if full-scale models can be scaled down in size. In the paper, methods for designing scaled experimental models of building structures are discussed. An example, the scaling of a wooden building structure, is presented.

In order to reduce the vibration transmission in multi-storey wood buildings, it is common to insert viscoelastic elastomer materials between parts of the buildings. The studies presented here investigate to which extent different design choices for the elastomer layers affect the isolation of low-frequency vibrations (0–100 Hz). A finite element model of two storeys of a multi-storey wood building, involving blocks of elastomer material in between the storeys, was used to perform numerical investigations. Parametric studies were carried out, considering different properties of the elastomer material and different placements of the elastomer blocks. Considering the transmission from the floor of the upper storey to the underlying ceiling, the material properties of the elastomer material were found to affect the vibration levels appreciably. A too stiff elastomer material can result in an amplification of the vibration levels in the ceiling for certain frequencies, whilst a less stiff material, in general, reduces the vibration transmission. The placement of the elastomer blocks was varied by shifting the position of the blocks while maintaining their centre-to-centre distance, resulting in a small effect on the vibration levels.

in Undetermined This paper presents a numerical study on the reduction of vibrations in the ground. The influence of landscape shaping to reduce vibration levels induced by traffic is investi-gated by means of the finite element method with dynamic analyses. Both two-dimensional as well as three-dimensional finite element models are employed for the investigations. A har-monic point force is applied where the force is scaled to represent the frequency dependent traffic load. Finally, the vibration reduction effect is evaluated by comparing RMS-values at a number of different evaluation points. It is concluded from the analyses that the two-dimensional and three-dimensional models correlates fairly well. The performance of a hill is increased if it is preceded by a valley but when applying more valleys than hills, amplification may occur. When using continuous hills instead of a checkered pattern, the hills seem to cap-ture and guide waves in the direction of the hill. Locally this could reduce vibrations of sig-nificant importance. Applying the constraints given within the numerical example, vibration reductions of approximately 20 % could be seen. (Less)

In the present study, different model order reduction methods were compared in terms of their effects on the dynamic characteristics of individual building components. A wide variety of methods were employed in two numerical examples, both being models of wooden floor structures, in order to draw conclusions regarding their relative efficiency when applied to models of such structures. It was observed that a comparison of the methods requires the reduced models to be exposed to realistic boundary conditions, free–free eigenvalue analyses being insufficient for evaluating the accuracy of the reduced models when employed in an assembly of substructures.

Transmitted vibrations from water-pipe systems, involving supports standing on a concrete slab and the underlying ground, are investigated here. The effects of varying parameters of the supports, such as location, their elastic modulus and their cross-section, on the level of vibrations transmitted by the water-pipe system are analysed in order to minimise vibrations transmitted to sensitive parts in a facility. A finite element model involving use of both finite and infinite elements was employed for analyses in the frequency domain where account was taken of both fluid-structure interaction and soil-structure interaction. It was concluded from the analyses performed that the parameters of the supports had an appreciable effect on the vibration level in the facility.

Accurately modelling the dynamic behaviour of multi-storey buildings in wood requires the geometry involved to be represented in great detail, resulting in systems having many millions of degrees of freedom. Consequently, there is a need for model order reduction and the methodology of substructure modelling is employed here to create reduced models for analysis of low-frequency vibrations. The full finite element model of a building is divided into substructures which are reduced in size before being assembled to form the global model. The efficiency of the reduced models is strongly dependent on the number of degrees of freedom at the interface surfaces of the substructures, why it may be necessary to perform interface reduction of some sort. Multi-storey buildings in wood are often constructed with elastomer layers separating the structural components, these offering a natural choice of dividing the buildings into substructures. In this paper, the methodology of introducing a condensation node is adopted for employing interface reduction at the interfaces between the elastomer layers and the structural components in wood. Different methods of coupling the condensation node to the interface surfaces were compared in a test model consisting of a floor–ceiling structure in wood, where the floor and the ceiling are separated by elastomer blocks. It was concluded that a rigid coupling is the most appropriate choice for the interface surfaces of the elastomer blocks, while a distributed coupling provides the most accurate results for the interface surfaces of the floor and the ceiling.

In multi-storey buildings, the use of lightweight material has many advantages. The low weight, the low energy consumption and the sustainability of the material are some attractive benefits from using lightweight materials. Compared with heavier structures i.e. concrete the challenge in constructing a building compliant with building codes vis-a-vis the propagation of sound and vibrations within the structure is a challenge. Focusing on junctions in a multi-storey lightweight buildings, a modular finite element model is developed to be used for analyses of vibration transmission in lightweight buildings subjected to different types of loads.

A fracture mechanics model for analysis of crack initiation and propagation in wood is defined and applied. The model has the advantage of being simple, yet it enables reasonably general and accurate analysis commonly associated with more complex models. The present applied calculations are made by means of the finite element method and relate to progressive cleavage fracture along grain. The calculations concern a tapered double cantilever beam specimen and an end-notched beam. Comparisons are made of experimental test results. The fracture properties of the wood are modelled by means of a very thin linear elastic layer located along the crack propagation path. The properties of the layer are such that the strength and fracture energy of the wood are represented correctly. This makes a single linear elastic calculation sufficient for strength prediction. Both crack development and pre-existing cracks can be analyzed. Both material strength and fracture energy and stiffness are taken into account, their relative influence on structural strength being different for different elements. The fracture layer is in the finite element context represented by joint elements. Propagation of a crack can be analyzed either by a series of elastic calculations corresponding to different crack lengths or by use of a finite element code for non-linear analysis. The computational results include sensitivity analysis with respect to the influence of the various material parameters on structural strength.

To predict ground-borne vibration levels caused by railway traffic, models for estimating the load from the vibration source, as well as the vibration transmission through the ground, are needed. In the present paper, a finite element formulation in a frame of reference following the moving load, is used for modeling a railway slab track. The response of the underlying soil is represented through a dynamic stiffness matrix, obtained via the Green’s function for a horizontally layered visco-elastic half-space in a moving frame of reference in the frequency–wavenumber domain. The track can be modeled as continuously connected beams, but the use of plate elements allows for more general stress and displacement distributions in the transverse direction of the slab to be resolved. Here, the free-field response due to a harmonic load moving along a slab track, is evaluated and compared using different modeling strategies for the slab. (Less)

As a result of the increasing interest of constructing environmentally friendly lightweight buildings, analyses of vibrational and acoustical transmission in these buildings have become increasingly important. Structures where vibrational transmission may result in undesirable vibrations with possible sound emission as a consequence, must be avoided. A parametric modular finite element model has been developed for this purpose as described in a companion paper presented at this conference. In [1]. This model is intended as a basis for vibro-acoustic analysis of lightweight buildings.With the number of modules in the three axial directions defined, wall and floor panels are constructed, placed and coupled in the global model. The core of this modular finite element model consists of connecting the different panels to each other in a rational manner, where the accuracy is as high as possible, with as many applications as possible, for the least possible computational cost. The coupling method of the structural panels in the above mentioned modular finite element model is in this paper discussed and evaluated.The coupling of the panels are performed using the commercial finite element program ABAQUS [2], where the built-in element constraints applications are utilised. The models are setup in scripts, using the Python language, to ensure a fast and consistent model.It is found that the modules, i.e. panels, are easy to couple, if an auxiliary skeleton is introduced in all panel intersections. In this way a well-defined master geometry is present onto which all panels can be tied. But as the skeleton is an element itself, it will have a physical mass and a corresponding stiffness to be included in the linear system of equations. This means that the skeleton will influence the structure with an increased overall mass and stiffness. This influence is quantified with the aim to reduce it to a minimum.By selecting a small profile, low stiffness and an insignificant mass for this skeleton, the effects of the non-real structure are limited and the structural response resembles the response of a similar construction without a skeleton. These parameters are selected in a way where decoupled pseudo-modes of the skeleton are avoided, alongside the insignificant influence of the overall structure achieved with a low mass, small profile, and a relatively low Young's modulus, approximately 1/30 of the value used for the panels. The problem with the pseudo-modes is further reduced, by choosing similar mesh refinements in both the skeleton and the panels. This will also ensure a converging model.

The application of wood as a construction material when building multi-storey buildings has many advantages, e.g., light weight, sustainability and low energy consumption during the construction and lifecycle of the building. However, compared to heavy structures, it is a greater challenge to build lightweight structures without noise and disturbing vibrations between storeys and rooms. The dynamic response of floor and wall structures may be investigated using finite element models with three-dimensional solid elements [1]. In order to analyse the global response of complete buildings, finite element models may be created by assembling models of floor and wall structures into large models of complete buildings. When assembling the floor and wall models, the number of degrees of freedom quickly increases to exceed the limits of computer capacity, at least in a reasonable amount of computational time. The objective of the analyses presented in this paper is to evaluate methods for model reduction of detailed finite element models of floor and wall structures and to investigate the influence of reducing the number of degrees of freedom and computational cost on the dynamic response of the models in terms of eigenfrequencies, eigenmodes and vibration transmission. The finite element model of a floor [1], created and validated by measurements on a full-scale experimental wooden floor-wall structure, that was used as a reference model in the model reduction studies. The studies were restricted to frequencies below 100 Hz. Three different methods of model reduction were investigated; Guyan reduction, component mode synthesis and a third approach where a new finite element model was created with structural elements. Eigenvalue and steady-state analyses were performed in order to compare the errors in eigenfrequencies, eigenmodes and vibration transmission for the reduced models relative the reference model. It was concluded that both Guyan reduction and structural elements leads to large errors in the frequency range studied. However, the model with structural elements behaves similar to the full model but with a shift in frequencies which produces large errors at particular frequencies. In order to obtain good accuracy, it is concluded that component mode synthesis is preferable. With a proper amount of retained eigenmodes in the component mode synthesis, a very good correlation in eigenmodes is obtained. The drawback of component mode synthesis compared to modelling with structural elements is the increased computational cost, although the number of degrees of freedom is small in comparison, as a result of the large bandwidth of the system matrices.