Gaussian-filtered Horizontal Motion (GHM) plots of non-synchronous ambient microtremors for the identification of flexural and torsional modes of a building

Highlights

• Determination of flexural and torsional modes through non-synchronous data.

• Ambient vibrations acquired by a single sensor at several points.

• Flexural and torsional modes identified by means of simple Gaussian filters.

• Comparison of measured Eigenmodes and modal analysis via FEM.

Abstract

It is often assumed that, in order to identify flexural and torsional vibration modes of a building, it is necessary to record synchronous data from a series of sensors deployed at different points. In the present paper, we present a simple and straightforward methodology to unambiguously identify flexural and torsional modes through the analysis of non-synchronous data collected by a single sensor placed in succession at different points of the structure.

This is accomplished by recording few minutes of ambient microtremor data by means of a 3-component geophone placed at different points of the same floor. Amplitude spectra are computed for determining the vibration frequencies. Successively, in order to identify the type of motion, we apply a series of narrow Gaussian filters centered at the previously-identified frequencies. By plotting the horizontal motion for each considered point, we are then able to simply and unambiguously determine whether the motion of a given frequency refers to a flexural or torsional mode. If, for a given frequency, the motion at two (or more) points has the same direction and similar amplitude, that frequency represents a flexural mode, while in case the directions and the amplitude are different, elementary considerations indicate that this is predominantly torsional.

The methodology is first introduced by considering a case study where synchronous microtremor data are also recorded. In a second case study, the method is applied to non-synchronous microtremor data collected at a 25-storey building and results are compared with the numerical simulations performed by means of the Finite Element Method (FEM).

Introduction

The proper identification of the vibration modes of a building is a crucial process for the evaluation of the dynamic behavior of a structure with respect to earthquake safe design or to dynamic wind assessment. In particular, when it comes to the increase of the safety of existing structures by means of retrofitting measures or to the verification of the dynamic behavior of a new building, in situ vibration measurements and analysis are routinely performed.

Although some empirical relationships between the height of a building and its natural vibration period are available (e.g. [1]), they might provide approximate values for the fundamental swinging mode only.

In order to comprehensively describe the actual dynamic behavior of a structure, both numerical simulations and empirical methods based on the analysis of vibration data are available [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17].

Depending on the type of structure and specific goals, the measurement procedures and data acquisition can become very expensive.

The insight gained about the structural behavior in respect to the dynamic behavior and state of damage can be very comprehensive accordingly ([18]).

Although some authors have implemented measurement procedures based on remote microwave gauges placed externally to the studies structure [7], most of the standard methods rely on the analysis of synchronous data recorded by a series of sensors placed at different points of the structure and analyzed by computing the cross-spectra (that provide the vibration frequencies) and phase functions (that indicate whether a mode is flexural or torsional) (e.g. [2] - see in particular Section 2.5.2).

This means that in the classical approach it is typically necessary to use two or more synchronized sensors. The synchronization of the sensors is usually obtained via GPS or by connecting the sensors to the same cable (that transmits the signals to the data logger). From a practical point of view, it is clear that in both cases the acquisition procedures can become relatively cumbersome.

In the present paper, a simpler approach for the determination and separation of predominantly flexural or torsional vibration modes through the analysis of non-synchronous data acquired by a single sensor (placed in succession in two or more points of the building) is illustrated.

The methodology has a very concrete goal: trying to get as much information as possible from data acquired in complex real-world situations where more comprehensive (i.e, synchronized) data cannot be acquired and the measurement points are constrained by logistical reasons.

Two case studies are presented. The first one is used to compare the traditional method, that relies on synchronous data, with the results of a new method based on the analysis of non-synchronous data acquired by a single 3-component geophone placed at different points of the same floor. Data are processed by means of a narrow Gaussian band pass filter thus obtaining a series of GHM (Gaussian-filtered Horizontal Motion) plots that allow the identification of flexural and torsional modes.

The second case study documents the assessment of a 25-storey building in Zürich (Switzerland) and represents a further application of the GHM methodology. In this second case, obtained results are compared with the outcomes of the numerical simulations accomplished by means of the Finite Element Method (FEM).