H. Sezer Atamturktur¹, Dr. Linda M. Hanagan², Dr. Thomas E. Boothby³

¹Graduate Research Assistant, Department of Architectural Engineering
²Associate Professor, Department of Architectural Engineering
³Professor, Department of Architectural Engineering

The Pennsylvania State University
University Park, PA 16802

Citation

Atamturktur, S., Hanagan L., Boothby, T., (2007), “Extension of Large Scale Modal Analysis Techniques to Historic Masonry Vaults,” Proceedings of 25th International Modal Analysis Conference, Orlando, Florida, USA.

Abstract

As a result of the increasing demand for the condition assessment and rehabilitation of historic structures, the application of modal analysis techniques to large-scale masonry buildings is a growing area for the field of experimental mechanics. Although a large body of literature discusses testing on various forms of laboratory specimens, modal testing on a large-scale historic masonry structures has completely different practical issues that challenge the selection of testing variables, equipment, and set-up. Recently, the reading room masonry domes of the State Education Building were subject to experimental modal analysis to enhance the quality of the numerical model. The purpose of these experiments is to identify the dynamic parameters of the vaulted structure and to justify two modeling assumptions established during the finite element analysis: masonry behaves as a linearly elastic material under existing loading conditions, and the construction imperfections have minimal influence on global behavior. The paper also shows that the use of experimental modal analysis can be extended to the investigation of the dynamic interaction between adjacent components of a large-scale structure and to the examination of the elastic support conditions exerted by the adjacent elements.

Introduction

Maintenance of historic buildings (risk and serviceability evaluation or appraisal of the necessity and effectiveness of the rehabilitation program) requires some form of condition assessment. Among many available methods for the analysis of masonry systems, the complex interaction of the elements of a monumental vaulted structure (ribs, web, piers, buttresses) are analyzed more conveniently by the computerized tools of finite element (FE) analysis. When these structures are analyzed with the FE method, besides the common difficulties in the assessment of existing engineering systems (such as obtaining physical dimensions, material properties and defining elastic boundary conditions), the unknown construction history, the complexity of the structural behavior and the nonlinear and inelastic nature of masonry assemblies constitute further difficulties. It is crucial to establish appropriate assumptions and simplifications that reduce the scope of the problem to a manageable size. However, such approximations, when not confirmed against reliable knowledge of the system, can potentially cause misinterpretation of the structural behavior. To minimize these inherent risks associated with the FE analysis of vaulted masonry structures, Boothby (2001) recognizes the necessity of the use of nondestructive and non-intrusive experimental techniques [1].

To determine the predictive ability of FE models for masonry structures, researchers have previously used visual comparisons of existing crack locations with analytical estimates of the location of tensile zones [2, 3]. This method concentrates on a few locations in a building and is of limited effectiveness especially when support settlements are present. While successful when applied to bridges, in situ experimental studies focusing on stress, strain or deflection under artificial loading [4] are impractical for historic masonry vaults due to the difficulty in sufficiently loading the structure to achieve a measurable response. Attempts to correlate the stress concentrations measured on a laboratory test specimen with those of FE model are also present in literature. For these purposes researchers conducted experiments on scaled cross vault samples under various loading conditions–including static loads, abutment displacements and cyclic loading [5, 6]. As the procedure includes only a portion of the model, it has the drawback of overlooking the actual elastic restraints exerted by the adjacent elements, and thus, it also overlooks the alternative load distribution paths within the structure.

Experimental modal analysis (EMA) has been in use to assess and improve the quality of the FE models for various kinds of systems. The method has the particular advantage of extracting the information on the spatial distribution of mass and stiffness without disturbing the structure or its occupants. In the last three decades, the application of EMA has extended to wide ranging fields such as vibration serviceability issues in floor systems [7] and stadiums [8, 9], and the dynamic assessment of bridges [10], buildings [11, 12] and historic structures [13, 14].

The use of modal test data, either in the evaluation of dynamic characteristics of the system or in the calibration of the FE model, is based on the assumption that the experimental measurements are the true representations of the actual system dynamics. This necessitates an intelligent use of the proven experimental tools to obtain the dynamic parameters of the structure to an acceptable accuracy. Although the particulars of modal testing on various forms of laboratory specimens have received significant attention in the literature, vaulted masonry structures have different practical requirements and challenges in the selection of test variables, equipment and set-up. It is critical to adopt the best testing plan to obtain sufficiently accurate data in a reasonable amount of time without disturbing the structure or its occupants.

Recently, the Reading Room domes of the State Education Building (SEB) were subjected to experimental modal analysis with impact testing to obtain the sufficient knowledge about the system to verify and validate the FE model. This article discusses the essentials of this verification experiment and the observed challenges in its execution, along with recommended solutions. Lessons learned from this study are presented in detail so that they can be extrapolated to future applications of large-scale modal testing on vaulted masonry structures for analytical model validation and verification purposes.

Structure Under Study: The State Education Building, Albany, NY

The State Education Building (SEB) Reading Room is roofed with a repetitive dome system, constructed by Guastavino Co. in the first decade of the twentieth century. The structure is built in multiple layers of terracotta tile and Portland cement mortar, known as cohesive construction [15]. The twelve identical domes of 6.7 m radius are truncated into square bays by pendentives and slender ribbed arches and are supported by slender piers. The measurements are taken from one of the center domes, symmetrically surrounded by adjacent domes, in a three by four pattern. The views of the intrados and extrados of the dome considered herein are presented in Figure 1 and Figure 2, respectively.

The condition survey at the back of the ceiling reveals that the steel trusses and tile domes are built integrally. At the contact locations, every 45 degrees on plan, miniature tile buttresses of approximately 150 cm by 40 cm are built. The apices of the domes are observed to be fully detached from the upper floor; yet, they are not accessible as the HVAC and electrical equipment occupies the space between the apex and the concrete floor slab. Because the equipment is supported from the ceiling, their self weight does not interfere with the behavior of the domes.

Test Objectives

The primary purpose of the tests is acquiring sufficient and reasonably accurate information that can be used to determine the validity of the numerical model and, if necessary, can be used to update the model. When masonry vaulted structures are concerned, the test deliverables useful for the refinement of FE models are threefold: identification of the dynamic parameters of the system in terms of natural frequencies and associated mode shapes, identification of the dynamic interaction between the different structural components, and investigation of the masonry behavior in the sense of linear and elastic or nonlinear and inelastic trend.

Allemang states that when comparing two alternate methods, FEA and EMA, assuming minimal errors and sufficient test experience, the first 10 modes may show a reasonable agreement, while higher modes may present more difficulty [16]. Previous experience supports this argument [13, 14]; therefore, in this study, the test variables are adjusted to acquire the lowest 10 modes with the highest possible accuracy.

For model calibration purposes, the entire structure, excited during the modal tests, needs to be included in the solid model. However, the dynamic interaction between the adjacent structural components that convolute the domed assembly is complicated and the extent to which the system is excited under impact loading is unobvious. To identify the members that contribute to the dynamic response and to infer knowledge on the support restraint exerted by the unmodeled portions, the response amplitudes of the adjacent structural elements due to a hammer blow at the crown of the central dome is acquired.

The analytical representation of a masonry structure is a particularly challenging task due to the complications caused by the true behavior of masonry. Although masonry is long known to have nonlinear, inelastic and inhomogeneous behavior, the required knowledge of the mechanical properties is seldom available. Assuming masonry as a linearly elastic homogenous material significantly eases the analysis process; however, verification of this assumption is crucial to increase confidence in the analytical estimates. Based on the uniqueness of FRF and reciprocal behavior phenomena, this paper verifies the assumption for the structure under study.

Groundwork Studies

One must consider that, when testing existing masonry structures, the level of expected accuracy is not as high as the tests conducted under fully controlled conditions in laboratories. However, provided that the variables of modal testing are adequately selected, the system behavior of a monumental masonry structure can be identified with reasonable accuracy[14]. Before proceeding to develop the test program, it is of great value to complete groundwork studies.

Before the knowledge of the experimental results is available, a preliminary FE model of the structure considered herein is built to assist the development of the test plan. The commercially available FE software ANSYS v. 8.0 is used to analyze the model which includes 9 identical domes in a three by three grid as shown in Figure 3. At this stage of the analysis, the available data on the structural system is limited. The material properties are obtained by consulting reference material [17], while boundary conditions are applied according to the previous experience on the Guastavino style vaulting [14]. The initial FE model estimated the first mode as a breathing mode around 20 Hz, followed by several bending modes in the same frequency range (Figure 4).

For the structure described herein, a reconnaissance trip is completed to identify the limitations on the physical accessibility of the structure, and a preliminary test is conducted to investigate the quality of the test data with respect to the coherence functions and the number of observable modal peaks. During these tests, nine accelerometers are mounted on the back of the dome shell in a circumferential ring to capture the induced vibrations from the controlled excitation of the hammer blow as shown in Figure 4. The preliminary test is able to identify three clear bending modes. This initial data is used to refine the preliminary FE model through which the improved estimates of higher order modes are obtained.

As the preliminary test results are in good agreement with the data obtained through the more extensive final tests, the results are discussed together in later sections. The combined contribution of the preliminary measurements and the improved FE estimates are used when deciding the final test layout discussed in detail in the next section.

The Particulars of the Test Set-Up

The combined effect of the test objectives and the specifics of the structure determine the equipment selection and test layout. The subsequent paragraphs in this section are the steps in the development of the test plan to achieve the explicit goals of the present paper: acquiring knowledge necessary to verify and validate the analytical model. The test variables in consideration are discussed under the following headings: response transducer, excitation source, and data acquisition and signal processing system.

Response Transducer

The subsequent sections discuss the important aspects related to response transducer, selection of the transducer, mounting and the placement scheme.

Transducer selection: Although it is possible to acquire the system response in terms of acceleration, velocity or displacement, piezoelectric acceleration-based transducers (accelerometers) yield a wider frequency range and are the most common and well established in practice. Since wide varieties of accelerometers are available in market, the problem of selecting the right transducer is reduced to the two principal features: the amplitude and frequency range of the measurable vibration. The detectable amplitude range is determined by the sensitivity of the transducers, while the detectable frequency range is dictated by their resonant frequency.

Experience gained through vibration tests on numerous monumental masonry vaults† has shown that the usual response due to an impact blow is limited between 0.1- 1.0 g and a substantial number of natural frequencies fall between 0.5- 250 Hz. Thus, when testing on such structures, the selected accelerometer needs to be capable of detecting this amplitude and frequency range. The weight of the accelerometers, which might be a concern when used on small-scale laboratory specimens, is not sufficient to influence the dynamic behavior of the masonry vaults. Model 393A03 uniaxial seismic accelerometers, manufactured by PCB Piezotronics, Inc., with a frequency range of 0.5- 2000 Hz and a sensitivity of 1 volt/g are decided to be suitable for the purpose of this study [18].

Accelerometer Mounting: The axis system employed in the FE model dictates the direction vibration needs to be measured. As the analytical model of the domes discussed in this paper is created in global Cartesian coordinates; obtaining the vertical response, rather than the radial, facilitates the comparison of experimental and analytical results, on the other hand this choice makes mounting the transducers more difficult.

In the standard theory of vibration tests, it is initially assumed that the transducer motion is identical to that of the system; thus particular care must be given to accelerometer mounting to assure good bond. Although there are numerous methods of mounting accelerometers (stud mounting, magnetic mounting or adhesive mounting) the double curvature of dome and the contact surface of masonry limit the method that can be used. Hanagan states that mounting the accelerometer directly on concrete with beeswax, clay or double-sided tape yields excellent results in low frequency testing [7]. Supporting this statement, in the present study the use of modeling clay proved itself to provide sufficient bond and coupling between the transducers and masonry (Figure 5) within the temperature limitations of clay. It is important to note that, for environmental temperatures higher than 40° C, the clay adds a noticeable artificial amplification to the measurements [18].

The coupling of the transducer with the vibration surface must endure throughout the test. The lengthy cables, usually required when large-scale modal testing on civil structures, may cause excessive stress on the bond and detach the accelerometers from the vibration surface. In this study, by taping the cables on the vibration surface we secure the bond of the accelerometers and release the strain on the cable, the cables are taped on the dome shell at multiple points with duct tape.

Accelerometer Placement: In all test cases, the accelerometer placement should be arranged to define the significant geometric features and to prevent the spatial aliasing of higher order modes as lower order ones. On the other hand, for practical reasons, it also is crucial to keep the number of test points to a minimum. This task is especially challenging when testing on spherical segmental domes. The inherent symmetry in the spherical geometry of domes allows many opportunities to locate the accelerometers on stationary points (nodal lines) and to fail to notice certain bending modes. The number of modes to be captured is closely related to the spatial resolution of the data points; thus, an intelligent use of time and equipment is crucial.

The vibration tests conducted on the domes of SEB aim to capture, a circumferential resolution of 8 measurement points and a meridional resolution of 4 measurement points, as illustrated in the Figure 6. The tests on SEB are executed in three steps; in each, the nine accelerometers at one ring along with the reference point on apex are simultaneously captured. In each measurement, an accelerometer is kept at apex as a reference point to scale the separate measurements of the multi-run test.

Excitation Source

There are several practical issues related to the excitation sources when testing on monumental masonry vaulted systems. The topics discussed herein are the selection of excitation source and excitation locations, as well as some of the practical issues related to the impact-hammer excitation.

Excitation Source Selection: Although it is possible to obtain the dynamic parameters of structures by outputonly (operational modal analysis) techniques, which makes use of the ambient vibration due to natural exciter; exciting the structure under controlled conditions typically yields better quality results when the exciter is capable of fully and evenly exciting the system. The most common controlled excitation devices that apply to civil structures are shakers and impact (impulse) hammers. In theory, these two give identical outcomes [20]; however, practical aspects guide the preference based on the particulars of the test case. When testing on vaulted structures, a hammer exciter is superior to a shaker exciter because of its portability and applicability on curved surfaces.

To achieve reliable and coherent results, the selected impact-hammer must be capable of exciting the structure sufficiently above the ambient vibration level, such that the signal to noise ratio remains greater than 40 dB [7]. During the preliminary visits to SEB, the noise level is recorded to be 5×10-4 g. When excited by an impact force of approximately 2 kN, the SEB domes of about 10 tons are recorded to undergo a vibration of 0.5-1 g; yielding a signal to noise ratio of approximately 60 dB. Based on these observations, the PCB model 086D20 instrumented impulse hammer, capable of applying a peak force of 22 kN [18], is deemed to be suitable for the purpose of this study. Among the available tip options, the softest, a nylon tip, is preferred, since it offers the lowest frequency range of 0-400 Hz. When applied to the tile domes in consideration, the nylon tip adequately excites frequencies up to 200Hz (with a 10 db drop in the energy content).

Excitation Locations: The selection of excitation locations depends on early decisions on the test plan and is closely related to the available equipment. In the present study, a set of nine nodal points are measured simultaneously. Thus, it is possible to obtain a complete set of data by keeping the excitation location fixed and moving the nine accelerometers three times. On the other hand, one set of data is often not sufficient to identify the clustered modes of domed systems. In general, the closely spaced modes, near the point of excitation, are excited in phase and amplify the motion while they tend to neutralize each other at a different point; thus, only by analyzing the multiple datasets due to excitations at different locations, it is possible to accurately isolate these closely spaced modes. Moreover, some particular modes, hidden when the excitation point coincides with the nodal lines, may be acquired when the impact force is applied elsewhere. Therefore, to increase the number of captured modes, several points on the dome surface are excited, which can be seen in Figure 6.

Particulars of Hammer Excitation: The quality of the measurements is dependent on the proficiency and consistency of the impact-hammer operator. Since the higher order modes of a domed structure become complicated, even insignificant deviations in the excitation location or angle may stimulate different modes and degrade the precision of the acquired natural frequencies as well as the quality of the mode shape definitions. In the tests on SEB, the excitation points are located precisely 10 cm below the accelerometer locations and particular attention is paid to hit these predefined points with an optimum driving force over all of the excitation locations.

The question of the optimum excitation level has to comply with several criteria: exciting the structure evenly and uniformly while keeping the system behavior in the linear range and keeping the response amplitudes in the detectable measurement range of the equipment. Providing an even and uniform excitation is difficult because the inherent damping in masonry structures tends to absorb the localized energy introduced by the impact propagates to distant accelerometer locations. The energy level must be adjusted to excite all measurement locations. On the other hand, the response due to an unnecessarily hard impact may exceed the voltage limits of the data acquisition window or may induce the nonlinearity in the system. For the domes concerned herein, an instantaneous peak force of 0.5– 2.5 kN is found to be suitable; however, the range of ideal excitation force level may vary for historic structures.

When the hammer swinger is standing on the vibration surface, the additional mass of the operator and the reaction forces due to swinging action increase the complexity of the mode shapes and degrade the coherence function. Therefore, during the tests, particular attention is given to have the hammer operator standing off the vault. This, however, is not possible at certain excitation locations as seen in Figure 7. In those cases, a slight reduction in coherence function is observed.

Data Acquisition System

The FFT-based data acquisition and signal-processing system, DSP Technology, Inc. Siglab model 20-42 dynamic signal analyzer, is utilized to obtain and post-process the vibratory data. Siglab presents bandwidth and record length as variables that, when combined, define the frequency resolution and the data capture time (frame size). The bandwidth is defined as 200 Hz, which, according to the improved preliminary FE model, covers a sufficient number of modes for analytical model validation and verification purposes.

Window functions that are commonly used to avoid the leakage problems are not preferable when testing on masonry structures, since they introduce artificial damping to the measurements and potentially cause lower magnitude peaks to be dominated by higher magnitude ones. Avitabile suggests that to prevent the leakage problems and to avoid the use of a window function, the data capture time must be adjusted so that the response attenuates over the time frame and the captured data is periodic [20]. In this study, the data capture time is adjusted as 1.8 seconds to allow the response attenuate over the time frame and eliminate potential leakage problems.

Results and Discussions

The Reading Room domes of State Education Building function as a good case study in which to execute a vibration test. As evidenced by the coherence functions and the clarity of the mode shapes (Figure 8), high quality data is collected for all measurement sets and can be attributed to the two aspects of the test structure that served to achieve a high signal-to-noise ratio:

• The domes are small in dimension, and the dome shell is very thin and lightweight; hence, inducing a uniform excitation on the system and obtaining an appreciable system response are possible with the selected impact hammer.
• The domes, concealed within the building and are almost detached from the upper floor, have insignificant ambient vibration.

Corresponding to the three objectives of the study, the three major findings; the identification of dynamic parameters, the dynamic interaction between adjacent members, and the verification of the linearly elastic behavior assumption; are discussed separately in the following sections.

Identification of Dynamic Parameters

System identification is the last step in modal analysis. In this step, the measurement datasets are investigated to obtain the natural frequencies and mode shapes of the system (Figure 9). Masonry vaults in general are heavily damped with several clustered bending modes. Therefore, the use of single degree of freedom identification methods, which assumes the multiple degree of freedom FRF to be a superposition of multiple single degree of freedom FRFs, has limited use. To extract the modal parameters, this study utilizes the polynomial curve-fitting algorithms offered by STARModal software (Spectral Dynamic Inc.). The list of the natural frequencies obtained through both methods is presented in Table 1. Corresponding mode shapes and damping values are also obtained.

Table 1: The experimentally identified natural frequencies.

Identification of the Dynamic Interaction

When FE model validation based on modal parameters is attempted, particular care must be exercised to include the entire structure participating in the dynamic response in the model. For complicated structures, it may be difficult to decide what structural components must be modeled. The techniques of dynamic testing can be utilized to determine the existing boundary constraints and the structural influence of adjacent members on each other.

For the building under discussion, the evaluation of the dynamic interaction between the steel truss, tile buttresses and the adjacent tile domes presents difficulties, as their connectivity is dependent on unknown mechanical properties and physical configuration of the materials. When measured via accelerometers mounted on adjacent steel members, the frames displayed an insignificant response to a hammer blow on the apex of the center dome. Based on this observation, the steel frame is not included in the FE model; instead, their structural influence is represented in terms of boundary conditions. To assess the restraint induced by the buttresses, a similar approach is applied by locating the accelerometers on the buttresses. It is noted that the even numbered (orthogonal) buttresses displayed a relatively greater vertical response compared to the odd numbered (diagonal) buttresses; thus a vertical displacement restraint is applied to the dome in the analytical model at the location of the diagonal buttresses. Also, the examination of the influence of the adjacent domes on each other is studied by mounting the accelerometers on the apices of the eight domes adjacent to the center dome. For the frequency range and the excitation levels of this study, the negligible dynamic contribution of the adjacent domes is observed; therefore, modeling a single dome is considered adequate for this particular structure.

Verification of the Linearly Elastic Behavior

Although masonry is known to have nonlinear and inelastic behavior over a wide range of load, under service load conditions masonry structures can be safely assumed to behave linearly. The validity of this assumption can be verified by investigating the uniqueness of the FRF for different excitation levels, and the reciprocity between different data points.

In theory, a linearly elastic structure exhibits reciprocity. That is an excitation at point A causes the same response at point B as the response at A produced by an excitation at B. When applied to experimental data described herein, a very good agreement between measurements is observed with an average deviation of 3%, as seen in Figure 10 for point 7 and point 9.

The linearity of the system behavior can also be verified by making use of the fact that for a linear system the response is proportional to its excitation. Hence, provided that the system is linear, different excitation levels should deliver an identical FRF. As illustrated in Figure 11, the magnitude FRF shows almost no variation for excitation levels of 100 lb and 230 lb; other than an improvement in the coherence function for low frequencies. The improved coherence is explained by a higher signal to noise ratio for the larger load.

Conclusions and Recommendations

Given that the test variables are selected correctly, acquiring high-quality data is possible even when dealing with a challenging material like masonry. The selection of these variables can be assisted by analytical simulations in the early stages of the research. Reconnaissance visits and preliminary tests may reveal the specifics of the system and alleviate the development of the in-situ test plan.

Based on the experience gained through this study, accelerometers that can cover a measurement range of ±5 g and frequency range of 0-500 Hz are well suited for low amplitude testing on existing masonry vaults. When doubly curved structures are tested, mounting the transducers normal to the vibration surface ease the challenges related to mounting, thus this should be considered during the FE model development. During the tests described herein, modeling clay proved itself to provide satisfactory coupling between the vibration surface and transducer, for temperatures below 40° C. Taping the cables on the dome shell is observed to be effective in securing the bond of the transducers to the vibration surface, and in reducing the strain on the cables.

The present study adopts a test plan that has a circumferential resolution of eight points and a meridional resolution of four points. This test scheme clearly captured 8 bending modes, but failed to identify any axisymmetric modes. It is probable that due to the complexity of the structural system, the domes discussed herein do not exhibit axisymmetric modes. The possibility that the axisymmetric modes are present but highly dominated by the bending modes is also credible. A further experimental study is necessary to clarify this argument.

The impact hammer is found the most suitable when testing on masonry vaults due to its portability and applicability on curved surfaces. The hammer size and input force level is selected based on the intensity of the noise and ambient vibration in the test environment and the size and mass of the structure to be tested. In this study, the masonry vaults weighting 10000 kg are satisfactorily excited by an impact hammer with a peak 22 kN force capacity. Because of the high signal to noise ratio (60 db), high coherence functions and clear mode shapes are obtained.

Precision in the accelerometer and excitation placement is essential, especially when identification of higher order modes is attempted. It has been experienced that misplacing the impulse or response transducers, even by a couple of inches, may cause exciting and capturing entirely different modes. When acquiring driving point data, the hammer blows are located at the same distance from corresponding accelerometers (10 cm).

The existence of the hammer operator on the dome shell introduces additional non-proportional damping and unknown reaction forces, and thus degrades the coherence function. When possible, it is preferable to keep the hammer swinger on adjacent structural elements, e.g. surcharge, buttress. However, when this is not possible, the reduction in coherence is moderate.

Adjusting the time frame instead of using exponential window is preferable when testing on masonry vaulted systems, which have several clustered modes and inherent high damping. The additional damping that an exponential window would introduce gives opportunities to the high frequency modes to dominate the less significant peaks in the FRF.

As in any other test case, application of experimental modal analysis to a masonry double curved system, like historic domes and vaults, has particulars and unique practicalities. The challenges encountered and lessons learned during the study can be extrapolated to future studies on monumental civil structures.

Acknowledgements

The authors gratefully acknowledge the support of the National Center for Preservation Technology and Training. The authors also wish to acknowledge George Webb of the NY State Education Office for the opportunity to test in the building. Special thanks to Corinna Fisher for her assistance in editing the manuscript.

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