Minimizing structural vibrations with absorbers

In a companion paper¹ the authors show that the parameters of an absorber which will minimize the resonant response of a simple elastic body can be determined from known results by treating the body as an equivalent single degree-of-freedom system. In this paper cylindrical shells are considered as examples of dynamically complex structures, for which the ratio of the natural frequencies of adjacent modes tends towards unity. It is shown that as dynamic complexity increases optimum absorber parameters for the reduction of resonant response deviate increasingly from those for an equivalent single degree-of-freedom system. Absorbers can be used also to reduce the random response of structures. Simple expressions for optimum parameters are given for an undamped main system, which has one degree of freedom and is subjected to white noise excitation. Optimum absorber parameters for beams, plates and cylindrical shells show similar qualitative behaviour for random and harmonic response with the concept of an equivalent single degree-of-freedom system being applicable only for the simpler structures.     

Reduction seismic response with heavily-damped vibration absorbers

It is shown that two of the damping ratios of certain systems composed of a building and a small attachment in resonance are given by the average of the damping ratios of the two independent components. Based on this fact and the fact that the seismic response of a building can always be reduced by increasing its damping, it is demonstrated that the attachment of a small heavily-damped system in resonance can increase the damping of a building and reduce thus its response to earthquake excitations. Numerical solutions are presented to confirm the demonstration, and recommendations are given to calculate the parameters of such systems.     

Analysis and design of open trench barriers in screening steady-state surface vibrations

The problem of vibration isolation by rectangular open trenches in a plane strain context is numerically studied using a finite element code, PLAXIS. The soil media is assumed to be linear elastic, isotropic, and homogeneous subjected to a vertical harmonic load producing steady-state vibration. The present model is validated by comparing it with previously published works. The key geometrical features of a trench, i.e., its depth, width, and distance from the source of excitation, are normalized with respect to the Rayleigh wavelength. The attenuation of vertical and horizontal components of vibration is studied for various trench dimensions against trench locations varied from an active to a passive case. Results are depicted in non-dimensional forms and conclusions are drawn regarding the effects of geometrical parameters in attenuating vertical and horizontal vibration components. The screening efficiency is primarily governed by the normalized depth of the barrier. The effect of width has little significance except in some specific cases. Simplified regression models are developed to estimate average amplitude reduction factors. The models applicable to vertical vibration cases are found to be in excellent agreement with previously published results.     

Reduction in ground vibrations by using shaped landscapes

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%.     

Live load induced vibrations in Ullevi Stadium - dynamic dynamic soil analysis

The paper describes a case history where during two rock music concerts the audience at the large outdoor stadium Nya Ullevi, Gothenburg, Sweden, started to jump in time to the music. Violent vibration levels occurred in the ground and a part of the audience observed considerable motion in the structure. Based on finite element analysis, it is concluded that the underlying soft clay of the structure was excited with the same frequency as the beat of the music. The whole clay deposit under the stadium started, therefore, to vibrate with great variations in amplitudes over the field due to the complex geometry. Through interaction with the basement of the structure as well as its deep foundation the waves were transmitted to the superstructure. Parts of the structure framework have natural frequencies close to those of the beat. Consequently they started to vibrate violently.     

Physical model for dynamic analysis of structures with FPS isolators

This article presents a physical model for frictional pendulum isolators (FPS) that is ready to be implemented in most commercial software. The model is capable of accounting for effects such as large deformations, sticking, and uplift and impact by sensing the normal loads in the isolators through a gap element. Sticking has been incorporated into the model by extending the Park–Wen hysteretic model to the case of large deformations. The proposed model has been tested against a theoretically ‘exact’ formulation leading to essentially identical results. To facilitate its use, the physical FPS model has been cast into a typical non‐linear structural element format, i.e. with deformation as input and restoring force as output. Examples of a building and a bridge have been chosen to show the potential of the element and to provide further insight into the earthquake response of structures with FPS isolators; in particular, in aspects such as the orientation in placement of the isolator, sticking, P? Δ, and other large deformation effects. Copyright © 2003 John Wiley & Sons, Ltd.     

Simplified 3-D dynamic analysis of structures with flexible diaphragms

A simplified method of 3-D dynamic analysis, named 3-D quasi-dynamic analysis, is presented. This method has been primarily used to evaluate stress states at identified times of peak dynamic responses of structures with flexible diaphragms. The quasi-dynamic analysis consists of extracting the accelerations predicted by the time-step integration analyses of two 2-D discrete MDOF dynamic models of a given structure (each discrete model corresponding to one of the principal orthogonal directions of the structure) at given times of interest. These accelerations are imposed on a 3-D representation of the structure (for example, a finite element mesh) as equivalent static forces. Accelerations at the diaphragms are assumed to act over the same tributary areas of the diaphragms considered in the 2-D discrete dynamic models. The study of the firehouse of Gilroy (an unreinforced masonry structure with flexible diaphragms) during the Loma Prieta Earthquake is presented to illustrate the 3-D quasi-dynamic seismic analysis. This method was compared to the more traditional 3-D modal time-step integration and 3-D response spectra analyses. The quasi-dynamic analysis had a general good agreement with the more formal, complex and computationally extensive modal time-step integration analysis. The 3-D response spectra analysis was very conservative and had a poor correlation with both the quasi-dynamic and the modal time-step integration analyses. The case study of the firehouse of Gilroy suggested that if 3-D effects have to be considered in the evaluation of a given structure, the quasi-dynamic analysis constitutes a reliable and computationally cheaper alternative to the more traditional methods of 3-D dynamic analysis.     

Numerical technique for dynamic analysis of structures with friction devices

In recent years a number of studies on employing friction elements for the seismic protection of buildings has demonstrated conclusively that such devices can markedly reduce earthquake-induced vibrations. Any numerical estimate of the effectiveness of such isolation systems implies a correct solution of the pertinent nonlinear equations of motion. In direct integration algorithms, the phase transitions between adherence and sliding, or the sliding phase may be accompanied by marked high-frequency oscillation of the relative velocity difference. The paper presents a numerical technique for overcoming these problems, thus leading to increased accuracy of the solutions of equations of motions with Coulomb damping. Since only the damping matrix and the loading vector are involved, the procedure is also computationally efficient. In order to validate the proposed numerical technique, an experimental study of a friction system has been carried out. The dynamic response of a four-storey braced frame with friction devices is presented as an example for the practical application of the proposed numerical technique.     

Nonlinear dynamic analysis of complex structures

A general step-by-step solution technique is presented for the evaluation of the dynamic response of structural systems with physical and geometrical nonlinearities. The algorithm is stable for all time increments and in the analysis of linear systems introduces a predictable amount of error for a specified time step. Guidelines are given for the selection of the time step size for different types of dynamic loadings. The method can be applied to the static and dynamic analysis of both discrete structural systems and continuous solids idealized as an assemblage of finite elements. Results of several nonlinear analyses are presented and compared with results obtained by other methods and from experiments.     

Building vibrations and dynamic pavement loads induced by transit buses

The purpose of this study was to investigate the effect of bus suspension systems on building vibrations and dynamic pavement loads. Building vibrations and pavement loads induced by two instrumented buses having different characteristics were measured simultaneously under controlled field conditions. Field tests were performed at several vehicle speeds, normal and reduced tire pressures, and with roads having good surface condition as well as abrupt surface irregularities. Tests were carried out at two vibration complaint sites in Montréal. The level and frequency content of vibrations and loads induced by the two buses were evaluated and compared. The results show that the dynamic component of pavement loads induced by the two buses were significantly different but the difference in building vibration levels was not as significant.     

Non-classical damping in dynamic analysis of base-isolated structures with internal equipment

It has been shown that the use of base isolation not only attenuates the response of a primary structural system but also reduces the response of a secondary system mounted on or within the main structure. The isolation system, superstructure and equipment may be made of different materials with significantly different energy dissipation characteristics such that the damping matrix for the combined system is non-classical and can only be approximately expressed by modal damping ratios if the classical mode method is used for analysis. The object of this paper is to evaluate the accuracy of this procedure in approximating the responses of base-isolated structures and internal equipment. The complex mode method can provide exact solutions to problems with non-classical damping and is used here to find the exact response of the isolation-superstructure-equipment system. The entire system is assumed to be linear elastic with viscous damping and the superstructure is assumed to be proportionally damped so that the deformation of the superstructure can be expressed in terms of its classical modes. Recognizing that the ratio of the equipment mass to the structural mass and the ratio of the stiffness of the isolation system to the superstructural stiffness are both small, perturbation methods are used to find the response. This study shows that the response of base-isolated structures can be determined by the classical mode method to some degree of accuracy, but the higher frequency content is distorted. The equipment response derived by the classical mode method is much smaller than the exact solution so that the complex mode method should be applied to find equipment response.     

Tuned vibration absorbers with dry friction damping

The response of a linear SDOF system subjected to harmonic excitation to which a Tuned Vibration Absorber with linear stiffness and dry friction damping is attached is considered. Based on an intuitive examination of the physical behaviour of the system, closed-form expressions for TMD optimum parameters and for the steady-state amplitudes of vibration are presented. Two examples allow the comparison between the predicted behaviour and that found by numerically integrating the equations of motion. Copyright © 1999 John Wiley & Sons, Ltd.     

GPS in dynamic monitoring of long-period structures

Global Positioning System (GPS) technology with high sampling rates (10 samples per second) allows scientifically justified and economically feasible dynamic measurements of relative displacements of long-period structures—otherwise difficult to measure directly by other means, such as the most commonly used accelerometers that require post-processing including double integration. We describe an experiment whereby the displacement responses of a simulated tall building are measured clearly and accurately in real-time. Such measurements can be used to assess average drift ratios and changes in dynamic characteristics, and therefore can be used by engineers and building owners or managers to assess the building performance during extreme motions caused by earthquakes and strong winds. By establishing threshold displacements or drift ratios and identifying changing dynamic characteristics, procedures can be developed to use such information to secure public safety and/or take steps to improve the performance of the building.     

带TMD的结构基于动力可靠性约束的优化设计

本文在运用复模态法求得多自由度带TMD结构随机地震响应解析解的基础上．采用基于动力可靠性约束的优化设计方法对TMD装置参数的优化取值进行了系统研究,以结构最大位移响应的期望值为目标函数,以TMD装置响应的动力可靠性为约束条件,运用罚函数法获得到TMD装置的优化设计参数．并给出了算例,从而建立了带TMD结构基于动力可靠性约束的抗震优化设计的一整套方法,本文方法也可用于基础隔震结构、带TLD减震结构以及带TMD和TLD抗风结构的优化设计。     

Nonlinear finite element analysis of three‐dimensional free and harmonically forced vibrations of stranded conductor cables

The 3D finite deformation beam model originally developed by Simo is appropriately modified to derive a finite element formulation for the static and dynamic analysis of flexible electrical conductors. In contrast to what is currently carried out in the literature, a linear viscoelastic constitutive equation and an additional mass proportional damping mechanism are introduced to account for energy dissipation in a physically consistent way. The model is used for simulation of free and forced vibration tests performed on an actual electrical conductor. Energy balance calculations illustrate the reliability of the computations. The experiments reveal amplitude dependence of both stiffness and damping, pointing out the presence of material nonlinearity in the cable. The development of numerical models that can account for the amplitude dependence of bending stiffness and energy dissipation capacity is subject of current computational and experimental work. Copyright © 2014 John Wiley & Sons, Ltd.     

Flexibility-based linear dynamic analysis of complex structures with curved-3D members

A flexibility-based formulation of a new mass matrix for the dynamic analysis of spatial frames consisting of curved elements with variable cross-sections is presented. The main characteristic of such formulations is the exact equilibrium of forces at any interior point, with no additional hypotheses about the distribution of displacements, strains or stresses. Accordingly, the derived element mass matrix takes into account the exact stiffness and mass distribution throughout each element. In validation tests, results obtained with this method are compared with those obtained by other numerical or analytical formulations, showing the accuracy of the proposed method. The comparison of experimental results for a multispan arch bridge subjected to a dynamic load with those achieved by means of the proposed method are finally included to illustrate its efficiency in the treatment of complex structures. © 1998 John Wiley & Sons, Ltd.     

Investigation of dynamic response of masonry minaret structures

Almost all historical minarets in Turkey were constructed using cut stone, masonry blocks or combination of these two materials. The structural and geometrical properties of each masonry minaret, or slender tower structure, depend on many factors including the structural knowledge and applications at the time of construction, experience of the architect or engineer, seismicity of the region, and availability of construction materials in that area. Recent earthquakes in Turkey have shown that most masonry minarets in high seismic regions are vulnerable to structural damage and collapse. In this study, in order to investigate the dynamic behavior of historical unreinforced masonry minarets, three representative minarets with 20, 25, and 30 m height were modeled and analyzed using two ground motions recorded during the 1999 Kocaeli and Duzce, Turkey earthquakes. The modal analyses of the models have shown that the structural periods and the overall structural response are influenced by the minaret height and spectral characteristics of the input motion. The dynamic displacement and axial stress time histories are computed at the critical points on the minarets. During recent earthquakes, most minaret failures occurred above the base of the structure. Consistent with the observed response, the largest stresses were calculated at the same location.     

Pile response and free field vibrations due to low strain dynamic loading

This paper presents the results of in situ measurements during dynamic pile testing at a construction site in Louvain-la-Neuve. Main objectives are the investigation of the pile response and the free field vibrations due to low strain dynamic loading on a single cast in situ pile with a 5.5 kg hammer impact on the pile head. Whereas low strain testing is usually performed to assess the integrity of the pile as a structural member, this study focuses on both pile and ground vibrations. The pile head response and ground motions are measured with accelerometers during different blows with the impact hammer. The dynamic characteristics of the soil are determined with a SASW test. Experimental results are compared with predictions obtained with a coupled finite element–boundary element model. The computed pile head and free field response show a good correspondence with the measured response. In addition, the static stiffness of the pile estimated by means of the mobility function shows a very good agreement with the value calculated by an analytical formulation.     

Benchmarking dynamic properties of structures using non-contact sensing

Non-contact sensing can be a rapid and convenient alternative for determining structure response compared to conventional instrumentation. Computer vision has been broadly implemented to enable accurate non-contact dynamic response measurements for structures. This study has analyzed the effect of non-contact sensors, including type, frame rate, and data collection platform, on the performance of a novel motion detection technique. Video recordings of a cantilever column were collected using a h...     

On the dynamic properties of asymmetric wall-frame structures

An efficient approximate hand method is proposed for the evaluation of the dynamic properties of asymmetric wall-frame structures. The approximation is based on a two-degree-of-freedom zeroth order solution of the coupled differential equations of motion. The restrictions on the structural geometry of the building imposed in a previous paper¹ are relaxed and the accuracy of the approximation is made dependent on the similarity between the mode shapes of the uncoupled lateral and torsional systems.