For a new type of postearthquake temporary prefabricated lightweight steel structure proposed in this paper, mainly composed of steel frame, prefabricated hanger slabs, prefabricated hanger columns, reinforced concrete superposed slabs, etc., parameters of dynamic property for the structure, including natural frequency, vibration mode, damping ratio, etc., are determined by the test method. For prefabricated hanger columns and prefabricated hanger slabs, they are all produced with construction waste in factory and assembled onsite, which can form exterior walls. The united method, based on forced vibration method and ambient random vibration method, can quickly obtain accurate natural frequencies of the fullscale twostory experimental model. In this paper, damping oscillatory method is used to obtain damping ratio which can be determined only by the test method. In order to analyse the modal of the experimental model, a finite element model for the fullscale twostory experimental model is established, where the weight of prefabricated hanger slabs is assumed to be supported by prefabricated hanger columns, and the stiffness of prefabricated hanger columns is also increased. In addition, the connections between lightweight steel frame and prefabricated hanger columns are regarded as flexible connection. Comparing natural frequencies obtained from the finite element method with that obtained from the test method, magnification factor of stiffness for prefabricated hanger column is determined. In the analysis of modal for the fullscale twostory experimental model, the results show that the experimental model satisfies the requirement of design for seismic performance.
Prefabricated lightweight steel structures, which are fabricated in factor and assembled onsite, have many advantages, such as relatively better construction quality, faster construction speed, and so on [
Prefabricated lightweight steel structure. (a) Steel frame. (b) Exterior walls: (i) prefabricated hanger slab and (ii) prefabricated hanger column.
Sketch of floorslab. (a) Floorslab: (i) hotrolled equilateral angle steel and (ii) reinforced concrete superposed slab. (b) Fine aggregate concrete.
For the conventional lightweight steel structure, Xu et al. [
For the new type of postearthquake temporary prefabricated lightweight steel structure to be widely used in the rural residencies especially situated in high seismic zones, the seismic performance of the structure should be investigated. Before investigating the seismic performance of the structure, the dynamic properties, including natural frequency, vibration mode, damping ratio, etc., should be first studied with experiment method and the finite element method in this paper. Therefore, the research on dynamic properties of the structure can provide basis for the subsequent research on seismic performance in the future.
To accurately obtain the dynamic properties of the new type of prefabricated lightweight steel structure, a fullscale twostory experimental model is built (Figure
Fullscale twostory experimental model: (i) ground beam and (ii) prefabricated lightweight steel structure.
The detailed dimension of experimental model. (a) Plan for first floor. (b) Plan for second floor. (c) Elevation for experimental model. Unit: mm.
In the experimental model, the column (5600 mm in length) is a hotrolled Hshaped steel column (HW 125 × 125 × 6.5 × 9.0 mm) and the beam (1950 mm in length) is also a hotrolled Hshaped steel beam (HW 125 × 125 × 6.5 × 9.0 mm). The columns and beams can be assembled by welding onsite, which use Q235B steel (yield stress value and ultimate stress value are 235 MPa and 355 MPa, respectively). In order to make the columns firmly embedded in ground beams whose dimension is 150 mm in height and 120 mm in width, four flanges shaped like triangle are welded with column at the bottom of each column. When the steel frame is finished, hotrolled equilateral angle steel (∠40 × 40 × 5 mm) is used as secondary beam, which also uses Q235B steel, connecting with beams by welding (Figure
Prefabricated hanger columns with a distance of 600 mm are fixed with the beams by semirigid connection, whose dimension is 100 mm in width and 100 mm thickness, with 2000 Kg/m^{3} in density. In order to improve the strength of prefabricated hanger columns, steel bar with 16 mm in diameter is placed in them, as shown in Figure
Sketch of prefabricated hanger column. (a) The dimension of prefabricated hanger column. (b) The dimension of hanger on prefabricated hanger column. Unit: mm.
Sketch of prefabricated hanger slab. Unit: mm.
Connection between (i) prefabricated hanger slab and (ii) prefabricated hanger column.
In order to make the exterior walls meet the requirement of heat preservation, firstly, expanded polystyrene foam board with 16 kg/m^{3} in density and 20 mm thickness is pasted on the inner surface of the exterior wall. And then the mineral wool board with 100 mm thickness is pasted on the surface of expanded polystyrene foam board. In addition, thermal insulation board with 30 mm thickness is pasted on the surface of mineral wool board.
Moreover, for the sloping roof, it is placed on the roof truss made of hotrolled steel channel (100 × 48 × 5.3 mm), which uses Q235B steel. Roof slab (Figure
Installing roof slab. Aluminium plate with 1.5 mm thickness is pasted on the surface of roof slab, and slab joints as well as lap joint are filled with polyurethane foamable adhesive.
Simulating live load. (a) At floorslab of second floor. (b) At roof truss.
In the test of dynamic property, acceleration transducers (Figure
Acceleration transducer. The arrows indicate the direction of vibration which can be measured by acceleration transducer.
Due to the symmetry of the experimental model, torsional vibration cannot be considered in the test. Therefore, the translational vibration is only considered in the test, and acceleration transducers should be placed on the symmetrical axis of plane of the experimental model. For the bottom of the first floor, acceleration transducers should be placed on the ground beams near the exterior walls. In addition, the direction of vibration on the symmetrical axes of plan of the experimental model, measured by acceleration transducers, should be perpendicular to each other, as shown in Figure
Arrangement of acceleration transducers. (a) At bottom of first floor. (b) At bottom of second floor. (c) At top of second floor.
The forced vibration method and ambient random vibration method are often used to obtain the natural frequencies [
Collecting fluctuating signals. (a) Signal collector. (b) Fluctuating signals.
Based on the peak value of fluctuating signals, the approximate natural frequencies can be determined. Next, the forced vibration method is used to obtain accurate natural frequencies of the model. In forced vibration method, the natural frequencies obtained from ambient random vibration method are input to signal generator which can make vibration exciter vibrate and also can make the structure vibrate and are adjusted to make the structure resonate. The detailed process is shown in Figure
Process of dynamic property test with forced vibration method.
In this paper, the vibration exciters are placed on the beams situated on the top of first floor and second floor, as shown in Figure
Arrangement of vibration exciter. (a) Vibration exciter. (b) On top of first floor: (i) beam and (ii) acceleration transducer. (c) On top of second floor.
In test of dynamic property, when the experimental model resonates, excited by vibration exciter under natural frequencies, the resonance curve for the experimental model can be received by acceleration transducer. By means of the resonance curve, the mode of vibration can be further obtained. In order to obtain the curve of damping oscillatory received by acceleration transducers, vibration exciters are shut off when the experimental model resonates. By means of curve of damping oscillatory, damping ratio obtained only by the test method can be determined.
If fluctuating signal is assumed to be stationary white noise with bandlimited, power spectrum for fluctuating signal is constant [
Peak values of autopower spectrums for fluctuating signals obtained from all acceleration transducers placed on the experiment model are all approximately equal.
When the experimental model resonates, the values of coherence function for fluctuating signals obtained from all acceleration transducers are maximum.
When the experimental model resonates, phase angles for fluctuating signals obtained from all acceleration transducers placed on experiment model are all approximately equal or the difference between phase angles is about 180°.
Based on autopower spectrums for fluctuating signal obtained from all acceleration transducers placed on the experimental model and crosspower spectrums for fluctuating signals obtained from acceleration transducer notated 1 and 2, natural frequencies of the experimental model in
Natural frequencies obtained with the ambient random vibration method. (a) First order in
Based on the natural frequencies obtained with ambient random vibration method, the accurate natural frequencies of the experimental model in
Natural frequency obtained with the forced vibration method. (a) First order in
In order to compare the natural frequencies obtained with ambient random vibration method with those obtained with the forced vibration method, all natural frequencies are shown in Table
Natural frequencies obtained from two methods.
Vibration mode  Natural frequency in 
Natural frequency in  

Ambient random vibration method  Forced vibration method  Ambient random vibration method  Forced vibration method  
Firstorder  16.632  16.724  11.046  10.986 
Secondorder  49.415  48.339  33.845  32.684 
In test of dynamic property, when the experimental model resonates, based on the fast Fourier transformation of fluctuating signals obtained from acceleration transducers placed on the locations which are on the same vertical position of the experimental model, amplitudefrequency curves of frequency response function for acceleration transducers can be determined with the software of uTekMa which can record and analyse the fluctuating signals. Based on amplitudefrequency curves, the ratio of peak values of fluctuating signals obtained at the natural frequency can be determined, which is equal to the ratio of coordinate values of vibration mode at the same natural frequency. In addition, positive and negative sign of coordinate values can be determined according to the phase angles of crosspower spectrums for fluctuating signals obtained at the natural frequency. Therefore, the vibration modes at natural frequencies in
Vibration mode obtained with software uTekMa. (a) First order in
As can be seen from Figures
Damping ratio of the experimental model can be determined only with the test method. Both the halfpower point method and damping oscillatory method can be used to obtain damping ratio [
Curve of damping oscillatory.
In Figure
Curve of amplitude oscillatory.
Based on the curve of amplitude oscillatory and equation (
Damping ratio of the experimental model (%).
In 
In  






Damping ratio  1.0397  0.8211  1.2985  0.2889 
As can be seen from Table
In this section, a finite element model is established with 3D software SAP2000, as shown in Figures
Finite element model. (a) In plan of
In the finite element model, modulus of elasticity for the beam and column used in the steel frame is 2.06 × 10^{6} Mpa. Modulus of elasticity for prefabricated hanger column is 2.55 × 10^{4} Mpa. The moment of inertia for beam and column is
In order to obtain the suitable magnification factor of stiffness for prefabricated hanger column, the magnification factor is set to be 1.0, 1.1, and 1.2, respectively. Natural frequencies for the finite element model can be determined with the eigenvector method, as shown in Table
Natural frequencies obtained with the finite element method.
Vibration mode  Natural frequency in 
Natural frequency in  

Magnification factor of stiffness for prefabricated hanger column  
1.0  1.1  1.2  1.0  1.1  1.2  
First order  10.5626  12.8751  16.9137  8.0154  9.9852  11.0617 
Second order  33.2546  40.2262  44.0106  22.4567  26.7878  33.7984 
As can be seen from Table
Frequency obtained with the forced vibration method and finite element method (Hz).
Vibration mode  Forced vibration method  Finite element method  Difference  

In 
First order  16.724  16.9137  −1.13% 
Second order  48.339  44.0106  8.95%  


In 
First order  10.986  11.0617  −0.69% 
Second order  32.684  33.7984  −3.41% 
Based on the finite element method, vibration modes of experiment model in
Vibration modes obtained with the forced vibration method and finite element method. (a) First order in
As can be seen from Figures
Based on the finite element model with magnification factor of stiffness for prefabricated hanger column 1.2, the improved Ritz vector method is used to obtain the modal for the experimental model. In addition, the method of defining weight including dead load, live load, additional weight, etc., is used in the dynamic analysis of the finite element model. In the finite element model, the number of vibration mode is 3 and frequency deviation is not considered.
Moreover, the participation mass ratios for the experimental model can be determined according to the finite element analysis, as shown in Table
Participation mass ratio for different modals.
Modal  Frequency (Hz)  Period (s)  UX 
UY  UZ  RX  RY  RZ 

First order  11.062  0.091  0  0.78  0  0.91  0  0.240 
Second order  15.578  0.064  0.73  0  0  0  0.81  0.220 
Third order  18.612  0.054  0  0  0  0  0  0.300 
Modal for the experimental model. (a) Firstorder modal. (b) Secondorder modal. (c) Thirdorder modal.
For the finite element model, the modal mainly depends on UX, UY, and RZ [
The period of thirdorder modal is 0.054 s, i.e.,
In this paper, the dynamic property of a new type of postearthquake temporary prefabricated lightweight steel structure is studied with the test method and finite element method, and the following results are given below:
The united method, proposed based on the forced vibration method and ambient random vibration method, can be used to quickly obtain accurate natural frequencies of the experimental model.
For firstorder vibration mode, damping ratio decreases with increasing of natural frequency, and damping ratio in
When the magnification factor of stiffness for prefabricated hanger column is the value of 1.2 in the finite element model, natural frequencies obtained with the finite element method are in good agreement with that obtained with the test method.
For the experimental model, due to
All the data in this paper are obtained from tests and numerical analysis in this study, and no other data in the literature are used to support this study.
The authors declare that there are no potential conflicts of interest with respect to the research, authorship, and publication of this article.
This study was financially supported by a project of Shandong Province Higher Educational Science and Technology Program (grant no. J17KB059) and Doctoral Scientific Fund Project of Weifang University (grant no. 2017BS14).