This paper deals with the vibration analysis of adjacent structures controlled by a magnetorheological (MR) damper and with the discussion of a numerical procedure for identification and definition of a reliable finite element model. The paper describes an extensive experimental campaign investigating the dynamic response, through shaking table tests, of a tridimensional fourstory structure and a twostory structure connected by an MR device. Several base excitations and intensity levels are considered. The structures were tested in nonconnected and connected configuration, with the MR damper operating in passive or semiactive mode. Moreover, the paper illustrates a procedure for the structural identification and the definition of a reliable numerical model valid for adjacent structures connected by MR dampers. The procedure is applied in the original nonconnected configuration, which represents a linear system, and then in the connected configuration, which represents a nonlinear system due to the MR damper. In the end, the updated finite element model is reliable and suitable for all the considered configurations and the mass, damping, and stiffness matrices are derived. The experimental and numerical responses are compared and the results confirm the effectiveness of the identification procedure and the validation of the finite element model.
Different control techniques are available for structural protection against dynamic actions [
Some theoretical studies exist in which structural control is effectively applied to adjacent structures by means of passive viscoelastic [
Concerning the experimental studies, most of them focus on passive devices [
Another crucial role, when dealing with these features, is played by the identification of these types of structures. In fact, when the mechanical characteristics are known, it is possible to determine if damage occurred in the structure, especially after significant events. In literature, there are examples of identification on controlled structures [
In this respect, the present paper deals with the vibration analysis of adjacent structures controlled by a magnetorheological (MR) damper and with the discussion of a numerical procedure for the identification and definition of a reliable finite element model (FEM). The tridimensional physical model consists of a fourstory structure and a twostory structure connected at the second level by the control device, with the possibility of acting in passive or in semiactive mode. Another paper by the authors in [
In the end, an updated finite element model, reliable and suitable for all the examined configurations, is obtained and the mass, damping, and stiffness matrices for a secondorder formulation are supplied.
The paper is organized as follows. Section
The tridimensional physical model consists of a pair of structures (a 4story and a 2story one) of different heights, Figure
Tridimensional physical model mounted on the shaking table with MR damper at the second story.
Dimensions of the adjacent structures and MR damper numerical model: (a) elevations; (b) plan, with model’s degrees of freedom; (c) device numerical model.
Instrumentation setup: location and direction.
An MR damper is installed at the second level between the structures. The device uses the typical property of controllable magnetorheological fluids: when exposed to a magnetic field, it can change in milliseconds its characteristics from a linear viscous fluid to a semisolid state. The literature reports many applications of MR dampers in several engineering fields, including mechanics, aerospace and robotic [
Shaking table tests are conducted utilizing an MTS shaking table available at the ENEA Casaccia Laboratory. The main nominal characteristics of the shaking table are frequency range 0–50 Hz, peak acceleration 3 g, maximum displacement ±125 mm, maximum velocity ±0.5 m/s, and maximum overturning moment about 300 kNm.
The structures and the shaking table are instrumented with accelerometers and displacement transducers, Figure
Accelerometers (PCP Piezotronics 3701G3FA3G): 2 are installed in
Laser displacement transducers (Microeplison Optoncdl LD1605200): sensors d1 and d2 are assigned to measure relative displacement of the first two levels of structure A, while sensors d3 and d4 are used to measure relative displacement between the structures.
Linear Variable displacement transducers LVDT (Micro Epsilon WDS300P60SRU): sensors d5 and d6 measure interstory displacement for the third and fourth levels of structure A.
A load cell (piezoelectric HBM, 500 Kg) measures the MR damper control force.
Data achieved are acquired at 500 Hz, using an MTS 469D system.
The physical model is tested under several base excitation time histories at several intensity levels.
A white noise input at low Peak Ground Acceleration (PGA), 0.05–0.1 g, and a sine sweep sinusoidal input at frequencies increasing between 1 and 25 Hz at 0.1 g are used to dynamically characterize the system. Natural seismic inputs of El Centro, Hachinohe, Kobe, and Northridge earthquakes are used to evaluate the performance of the control strategy [
Considering the geometrical scaling factors, a time scaling factor,
Different configurations for the adjacent structures have been considered:
Nonconnected configuration (NC);
Connected configuration (CC): rigid (RC), passive (PC), and semiactive (SAC).
A general procedure for structural identification and for the definition of a reliable numerical model for adjacent structures connected by MR dampers is proposed making use of the experimental results. Since the approach presented is general, it can be used even for different kinds of control devices.
The method follows three steps: (i) the vibration analysis of the system, (ii) the identification of a firstorder modal model (frequencies, damping ratios, and complex eigenvectors), and (iii) the definition of an accurate finite element model (and of the secondorder model) by means of an updating procedure.
The procedure is applied at a first stage in the original nonconnected configuration and then in the connected configuration. In the end, an updated finite element model, reliable and suitable for all the examined configurations, is obtained and the mass, damping, and stiffness matrices for a secondorder formulation can be supplied.
In the experimentation, the structures were excited with a monodirectional input along the
The ERA/OKID algorithm [
The equations of motion for the
Equations (
Storing the eigenvalues in the
Equations (
For each structure, the considered DOFs at each level are the center of mass translation
It is known that an MR damper subjected to harmonic excitation at a given level of input voltage manifests viscoplastic behavior [
For MR devices, the parameter which can be directly regulated in order to change the control force intensity is the input voltage (
In the nonconnected configuration, the adjacent structures move independently. The section is organized following the three steps described in Section
Among all the records achieved by sensors represented in Figure
The first test examined is the sine sweep at PGA 0.1 g with a frequency range of 1–25 Hz and a sweep rate of 0.20 Hz/sec. By considering the acceleration recorded by sensors a1–a5 installed on structure A in the
Nonconnected (NC) configuration, acceleration measured by sensors a1–a8. Sine sweep frequency test PGA 0.1 g.
The identification procedure has been performed to obtain modal parameters for the structures.
Figures
Nonconnected (NC) configuration, identified frequency response functions: (a) sensors a1–a8 versus ground acceleration
As a matter of fact, the results obtained by observing the identified FRFs suggest a fundamentally planar dynamic behavior for the structures: acceleration recorded in the
Once the
Nonconnected (NC) configuration. Structures A and B identified frequencies and damping factors versus PGA.
Mode  1  2  3  4  1  2  3  4 

PGA  Frequency (Hz)  Damping factor (%)  




0.05 g  2.73  8.22  13.30  17.08  0.70  0.65  0.67  0.85 
0.10 g  2.70  8.15  13.18  16.85  2.29  1.05  0.98  1.12 
0.30 g  2.54  7.95  12.90  16.54  6.80  1.86  1.75  2.57 




0.05 g  5.28  14.49  19.70  0.38  0.35  0.32  
0.10 g  5.25  14.43  19.66  0.75  0.53  0.41  
0.30 g  5.10  14.30  19.40  2.53  0.82  0.62 
PGA level influences damping ratio as well. Considering all the identified modes, it is possible to state that damping ratios increase by increasing PGA. Besides, it is possible to notice that the modal characteristics identified for structure A are more influenced by the PGA level than those identified for structure B. For the sake of exemplification, let us observe the damping ratio of the first mode. For structure A, it increases from 0.70% at 0.05 g to 6.80% at 0.3 g; for structure B, it increases from 0.38% to 2.53%.
Seismic eigenvectors, estimated with (
Structure A identified seismic eigenvectors, white noise test at 0.1 g; Kobe test PGA 0.3 g.
Mode  1  2  3  4  1  2  3  4 

Location 

 


Test white noise PGA 0.10 g  
a1  −0.33  −0.34  −0.21  −0.05  −0.15  −0.10  0.006  0.016 
a2  −0.80  −0.39  0.08  0.09  −0.38  −0.12  −0.002  −0.023 
a3  −1.00  0.01  0.17  −0.08  −0.48  0.00  −0.004  0.020 
a4  −1.18  0.38  −0.14  0.03  −0.57  0.11  0.003  −0.009 
a5  −1.27  0.34  −0.14  0.04  −0.61  0.10  0.004  −0.010 
a6  0.02  −0.08  −0.01  0.00  0.01  −0.02  0.000  −0.001 


Test Kobe PGA 0.30 g  
a1  −0.35  −0.29  −0.20  −0.02  −0.07  −0.30  −0.14  −0.01 
a2  −0.86  −0.36  0.08  0.03  −0.16  −0.37  0.06  0.02 
a3  −1.06  0.02  0.15  −0.04  −0.20  0.06  0.10  0.00 
a4  −1.24  0.36  −0.14  0.01  −0.23  0.40  −0.09  0.04 
a5  −1.34  0.30  −0.13  0.02  −0.25  0.29  −0.09  0.01 
a6  0.02  −0.10  −0.01  0.01  0.00  −0.16  −0.01  0.00 
Structure B identified seismic eigenvectors, white noise test at 0.1 g; Kobe test PGA 0.3 g.
Mode  1  2  3  1  2  3 

Location 

 


Test white noise PGA 0.10 g  
a7  0.70  0.30  0.02  0.001  −0.05  0.26 
a8  1.22  −0.21  0.02  0.003  0.03  0.41 


Test Kobe PGA 0.30 g  
a7  0.66  0.23  0.01  0.03  −0.01  0.25 
a8  1.18  −0.16  0.01  0.07  −0.01  0.37 
By observing the identified values, it is possible to make the following considerations:
Seismic eigenvectors were evaluated through (
Comparing the seismic eigenvectors in
Seismic eigenvectors components corresponding to sensors a1–a5 have higher values when compared to the components relating to sensor a6.
Seismic eigenvectors in
Compared to those in
Seismic eigenvectors in
Once modal parameters have been identified (frequencies, damping ratios, and seismic eigenvectors), the FE model can be defined and, then, the secondorder model representation can be provided. The model should be suitable for the NC configuration, as well as for the controlled configuration. Considering that in the controlled configuration the tests have been performed with relative higher PGA levels (greater or equal to 0.3 g) than in the NC configuration, the modal quantities identified for the Kobe test with 0.3 g will be used in the further analysis.
The structures shown in Figure
Since not all the parameters involved in the model are considered exactly defined, some of them are considered variable and a model updating procedure is applied to select their optimal values. By perturbing the values assumed for the parameters that are uncertain, a more representative model is obtained.
Columns, beams, and bracings are modeled with threedimensional beam elements. Geometry and masses are considered known, Figures
In addition, connections between columns and other structural components are bolted. In order to consider this aspect, different Young’s moduli
The procedure of model updating is based on the minimization of the following error function [
It is important to underline that using seismic eigenvectors is possible in order to directly relate the identified components and the calculated ones. In fact, seismic eigenvectors, differently from natural eigenvectors, are not related to the system representation and do not depend on any assumed normalization, but they are only related to the system properties [
The optimal values for the uncertain parameters (
Concerning the identified frequencies and seismic eigenvectors, the values related to base excitation in the
Table
Initial and updated values of FE model parameters.










Structure A  
Initial value  1.0 ⋅ 10^{6}  1.0 ⋅ 10^{6}  1.0 ⋅ 10^{6}  1.0 ⋅ 10^{6}  2.0 ⋅ 10^{11}  2.0 ⋅ 10^{11}  2.0 ⋅ 10^{11}  2.0 ⋅ 10^{11} 
Updated value  4.3 ⋅ 10^{6}  3.2 ⋅ 10^{6}  4.5 ⋅ 10^{6}  3.3 ⋅ 10^{6}  1.8 ⋅ 10^{11}  1.9 ⋅ 10^{11}  2.9 ⋅ 10^{11}  2.3 ⋅ 10^{11} 
Structure B  
Initial value  1.0 ⋅ 10^{5}  1.0 ⋅ 10^{5}  1.0 ⋅ 10^{5}  1.0 ⋅ 10^{5}  2.0 ⋅ 10^{11}  2.0 ⋅ 10^{11}  —  — 
Updated value  4.5 ⋅ 10^{5}  3.8 ⋅ 10^{5}  4.3 ⋅ 10^{5}  4.1 ⋅ 10^{5}  2.2 ⋅ 10^{11}  2.6 ⋅ 10^{11}  —  — 
Initial and updated FE model frequencies.
Initial value  Updated value  Identified value  Initial error (%)  Updated error (%)  

Structure A  

2.64  2.59  2.54  3.94  0.79 

7.70  7.94  7.95  3.14  0.38 

12.19  12.66  12.90  5.50  1.01 

15.21  16.80  16.54  8.04  1.09 
Structure B  

4.84  5.07  5.10  4.51  0.60 

12.80  14.30  14.30  10.48  0.00 
Structure A and B FE model seismic eigenvectors.
Mode  1  2  3  4 

Location 




a1  −0.44  −0.33  −0.21  −0.02 
a2  −0.85  −0.29  0.10  0.03 
a3  −1.08  0.02  0.14  −0.04 
a4  −1.25  0.35  −0.12  0.02 
a5  −1.25  0.35  −0.12  0.02 


a7  0.77  0.23  
a8  1.17  −0.16 
The updated FE model seems feasible; it is therefore possible to obtain the stiffness matrices to be used in the secondorder model. Tables
Structure A stiffness matrix (⋅10^{5}) N/m.
6.17  −0.71  0.00  −3.25  0.36  0.00  0.17  0.01  0.00  0.04  −0.05  0.00 
−0.71  174.38  0.00  −1.10  −94.81  0.00  0.53  5.81  0.00  1.66  8.84  0.00 
0.00  0.00  16.03  0.00  0.00  −8.60  0.00  0.00  0.43  0.00  0.00  0.73 
−3.25  −1.10  0.00  7.67  1.12  0.00  −4.77  −0.40  0.00  0.26  0.00  0.00 
0.36  −94.81  0.00  1.12  173.94  0.00  −0.01  −100.25  0.00  −1.46  15.13  0.00 
0.00  0.00  −8.60  0.00  0.00  16.33  0.00  0.00  −9.38  0.00  0.00  1.22 
0.17  0.53  0.00  −4.77  −0.01  0.00  8.14  −0.59  0.00  −3.54  0.34  0.00 
0.01  5.81  0.00  −0.40  −100.25  0.00  −0.59  172.42  0.00  0.96  −79.37  0.00 
0.00  0.00  0.43  0.00  0.00  −9.38  0.00  0.00  16.33  0.00  0.00  −7.52 
0.04  1.66  0.00  0.26  −1.46  0.00  −3.54  0.96  0.00  3.22  −0.31  0.00 
−0.05  8.84  0.00  0.00  15.13  0.00  0.34  −79.37  0.00  −0.31  52.01  0.00 
0.00  0.00  0.73  0.00  0.00  1.22  0.00  0.00  −7.52  0.00  0.00  5.29 
Structure B stiffness matrix B (⋅10^{5}) N/m.
7.73  −1.04  −0.01  −4.20  0.38  0.00 
−1.04  174.93  0.10  1.46  −74.49  −0.04 
−0.01  0.10  16.51  0.00  −0.04  −7.27 
−4.20  1.46  0.00  4.02  −0.43  0.00 
0.38  −74.49  −0.04  −0.43  59.70  0.03 
0.00  −0.04  −7.27  0.00  0.03  6.05 
Tables
Structure A FE model frequencies and excited masses.
Mode  1  2  3  4  5  6  7  8  9  10  11  12 

Frequency (Hz)  2.56  6.52  7.98  8.18  12.77  16.72  22.34  32.59  39.65  50.40  61.15  79.08 
% dir 
90.02  0.00  7.68  0.02  2.18  0.09  0.00  0.00  0.00  0.00  0.00  0.00 
% dir 
0.01  0.00  0.49  75.87  0.00  0.00  0.00  20.18  0.00  0.00  2.99  0.47 
% Rot.  0.00  80.73  0.00  0.00  0.00  0.00  17.24  0.00  2.78  0.37  0.00  0.00 
Structure B FE model frequencies and excited masses.
Mode  1  2  3  4  5  6 

Frequency (Hz)  5.07  14.30  20.69  21.66  42.52  64.11 
% dir 
95.85  4.15  0.00  0.00  0.00  0.00 
% dir 
0.01  0.04  0.00  89.51  0.00  10.45 
% Rot.  0.00  0.00  91.14  0.00  8.90  0.00 
In the connected configuration structures interact reciprocally, influenced by the control action of the MR damper installed between them. It is important to underline that, in this configuration, since the MR damper is a nonlinear device, the whole system is nonlinear.
The section is organized following the three steps described in Section
The measurements considered in this configuration are acceleration recorded by sensors a1–a8, relative displacement between structures at the second level,
When the adjacent structures are connected through the MR damper, the wellfunctioning of the entire control system must be previously checked. MR damper can operate between passive and semiactive mode at different voltage levels, reacting with a nonlinear control force when subjected to relative displacement. The signals measured to make the control algorithm work correctly are acquired by means of the acquisition board and then processed in a PC. A code implemented with LabView software applies the control law after interpreting the signals and then modulates the input voltage through the device actuator. The results obtained enabled confirming the validation of the passive and semiactive control system and of the entire control process. Considerations about the control aspects and the effectiveness of the control strategy can be found in [
The first test examined is the sine sweep at PGA 0.1 g with the MR damper working at 0 V (minimum voltage). Acceleration and control force time histories are shown in Figure
Passive connected (PC) configuration, acceleration measured by sensors a1–a8 and control force, voltage level (a) 0 V and (b) 2.5 V. Sine sweep frequency test PGA 0.1 g.
In general, the dynamic amplifications of both structures are less evident if compared with the NC configuration, Figure
The acceleration and the control force time histories achieved for sine sweep base acceleration at PGA 0.1 g with MR damper working at 2.5 V (maximum voltage), are reported in Figure
Experimental results of the white noise test at 0.05 g with control device working at 2.5 V are also considered to better explain the dynamic behavior in the passive configuration. It was observed that, in such a configuration, the MR damper does not develop significant dissipation, due to the low bidirectional base excitation level, to the high values of the control force
Figure
Rigid connected (RC) configuration, identified frequency response functions. Ground acceleration
Figures
In case of natural earthquake input, the experimental response of the structures subjected to El Centro test at 0.6 g is reported. An elaboration of the acceleration responses in the frequency domain has been carried out also when the device operates in passive or semiactive mode. However, since in this case the controlled system behaves as nonlinear, pseudo frequency response functions (PFRFs)
Passive connected (PC) configuration, experimental pseudo frequency response functions. Ground acceleration
Semiactive connected (SAC) configuration, experimental pseudo frequency response functions. Ground acceleration
Figure
Experimental frequency response functions. Ground acceleration
By comparing experimental FRF related to NC and RC cases and experimental PFRFs related to semiactive cases, similar results (not reported for the sake of brevity) are obtained.
Similar aspects are confirmed also by observing responses time histories and other earthquake inputs; the results are therefore not reported for the sake of brevity.
As a matter of fact, the modification of dynamic behavior depends on seismic action type, on the PGA value, and on the intensity of the control force (i.e., voltage level).
In order to obtain modal and physical system parameters in the connected case, the identification procedure described has been utilized and applied with reference to the case in which the connection can be regarded as rigid. The identified firstorder modal models in terms of frequencies, damping ratios, and seismic eigenvectors are obtained.
Table
Identified natural frequencies and damping ratios in the nonconnected (NC) and rigid connected (RC) configuration; white noise test PGA 0.1 g.
Mode  Structure A (NC)  Structure B (NC)  Connected structure (RC)  

Frequency (Hz)  Damping (%)  Frequency (Hz)  Damping (%)  Frequency (Hz)  Damping (%)  
1  2.70  2.29  5.25  0.75  3.18  2.35 
2  8.15  1.05  14.43  0.53  7.26  2.45 
3  13.18  0.98  19.66  0.41  8.63  1.91 
4  16.85  1.12  13.53  1.11  
5  15.78  1.19  
6  19.94  0.69  
7  23.70  2.52 
The identified frequencies obtained in the RC configuration are then compared with the ones obtained in the NC configuration with the same input and PGA. It is confirmed what was observed in the vibration analysis: the rigid connection modifies the dynamic response of the system. The first frequency of the coupled structures is higher than structure A’s uncoupled frequency and lower than the uncoupled one of structure B. The other frequencies, instead, are all lower than the corresponding ones for the uncoupled structures. It is interesting to underline that resonance frequencies obtained with the rigid connection are very close to the ones observed in passive and semiactive cases. Instead, damping ratios in the RC configuration are generally greater than the corresponding ones for the two unconnected structures, especially with reference to structure B.
Figures
Identified seismic eigenvectors: (a) nonconnected (NC) and (b) rigid connected (RC) configuration. White noise test PGA 0.05 g.
The numerical model of the adjacent structures linked by the MR damper is here defined. The FE model developed in Section
In order to obtain a rigid connection,
At first, the FE model with the rigid connection is discussed. The natural frequencies and excited masses percentages of the FE model in the rigid connection configuration are reported in Table
Rigid connected (RC) configuration FE model natural frequencies and excited masses.
Mode  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17 

Frequency (Hz)  3.19  7.25  8.48  9.33  11.40  13.54  15.86  16.46  22.08  32.29  32.94  47.35  58.37  62.10  64.98  74.44  80.03 
% 
85.08  12.65  0.00  0.00  0.01  1.20  0.26  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00 
% 
0.01  0.03  51.18  0.00  0.00  0.01  0.00  0.00  29.49  0.00  13.50  0.00  0.00  2.02  3.44  0.00  0.33 
% Rot  0.00  0.00  0.00  43.58  0.00  0.00  0.00  41.06  0.00  9.35  0.00  4.28  1.53  0.00  0.00  0.22  0.00 
In passive or semiactive mode, the numerical FE model having the same parameters assumed in (
In the optimization procedure, time histories and maximumminimum responses are collected in the following vectors:
The error functions between the measured and the calculated values (overlined quantities) are defined as follows:
The diagonal terms of weighting matrix for the time history and the maximum and minimum responses are defined as follows:
The value of
Figures
Passive connected configuration (PC), experimental versus FEM 4th floor structure A and 2nd floor structure B acceleration
Passive connected (PC) configuration, experimental versus FEM forcedisplacement, loop voltage level 0 V. Kobe test PGA 0.5 g.
Finally, the FE model is utilized to reproduce the experimental data in semiactive modality. The MR device works between two input voltages, in accordance with an ON–OFF control law; as an example, here the case 0–1.5 V is reported. The model reproduces the experimental acceleration for both structures in a quite precise way, Figure
Semiactive connected (SAC) configuration, 0–1.5 V, experimental versus FEM 4th floor structure A and 2nd floor structure B acceleration
Semiactive connected (SAC) configuration, 0–1.5 V, experimental versus FEM forcedisplacement loop. Kobe test PGA 0.5 g.
Even if the system showed a substantially planar behavior, so far, a threedimensional model was adopted. In fact, the asymmetry of the physical model and the light degree of coupling highlighted for some modes were considered. Nevertheless, by analyzing the recorded base acceleration, sensors
Experimental data and the identified modal and physical parameters suggested that structural responses in the
The paper illustrated the vibration analysis of adjacent structures controlled by a MR damper and the discussion of a numerical procedure for identification and definition of a reliable finite element model. The tridimensional physical model consisted of a fourstory structure and a twostory structure connected at the second level by the control device with the possibility of acting in passive or in semiactive mode. On the one hand, the results of an extensive experimental campaign carried out using shaking table tests, devoted to investigate the dynamic behavior of the uncoupled and coupled structures utilizing a wide variety of base excitations at several intensities, have been presented. On the other hand, a procedure for the structural identification and the definition of a reliable numerical model for adjacent structures connected by an MR damper making use of experimental results has been illustrated. Specific conclusions of the study in the nonconnected and connected configuration are summarized as follows.
The vibration analysis detected a different dynamic behavior between the two frames. Four natural frequencies for structure A and three for structure B were observed. Frequencies, damping ratios, and seismic eigenvectors of the firstorder modal model were identified at different PGA levels. The light shifts observed in the values of the frequencies and damping ratios suggested a modest nonlinear structural behavior. An accurate 3D FE model of the two uncoupled structures has been obtained; by comparing experimental and numerical data, the achievement of a good agreement in both the time and frequencies domains was observed.
The vibration analysis detected that the connection modified the dynamic structural behavior compared to the nonconnected configuration in a wide range of frequencies. For both structures, the fundamental frequencies were shifted and the observed vibratory modes were almost the same. The connected configuration with the device working at 2.5 V can be regarded in some cases as a rigid connection. In this situation, the system has been considered to behave linearly and the dynamic characteristics were studied considering experimental frequency response functions. The structures identification with rigid connection gave frequencies, damping ratios, and seismic eigenvectors. The dynamic characteristics of the FE model of the two structures with a rigid connection were compared with the identified ones observing a very good accordance. When the device operated in passive and semiactive mode, it emerged that the dynamics of the system only changed in terms of dynamic amplifications, but the resonance frequencies remained unchanged, situated among the frequencies observed in the NC and RC cases.
A modified BoucWen element was chosen to model the MR damper and the parameters were updated to reproduce the experimental outcomes. The coupled FE model was determined putting the updated MR damper model together with the one previously defined for the uncoupled structures. The complete FE model was capable of efficiently reproducing the dynamics of the adjacent structures rigidly, passively, or semiactively connected, by adequately setting the MR device parameters.
As a conclusion, when dealing with the characterization of structures equipped with control devices, the results of this paper confirm the possibility of considering, in a first stage, the uncoupled structures and then defining an updated FE model. In a second stage, a suitable model for the control device can be considered; in the end, a finetuning with the experimental response of the mechanical parameters can be made and it should be assembled with the model defined for the uncoupled structures.
The knowledge of modal characteristics and the availability of an updated model are fundamental matters for a structural monitoring program that could reveal any gradual decay due to aging in the integrity of the structures.
The authors declare that they have no competing interests.
The authors gratefully thank Dr. Giancarlo Fraraccio for the contribution he has made supporting this research work with numerical studies.