Introduction

Nowadays, almost every communication method is wireless. Telecommunication towers form one of the most essential components of any telecom network, thus it is not only used by cell phone providers for phone calls and internet but also used by police and ambulance to obtain their wireless communications and provide a quality service. Studies have been carried over the years to study the effect of different dynamic loads such as wind, ice loading and seismic loadings. Although, it was clear that only few studies carried out the experimental investigations either from existing structures or applied to scale models in wind tunnels or shacking tables [1,2,3]. Also, it was found that vibration measurements to full scale structures would lead to enhancing the accuracy of finite element model through calibration with its measured properties. That technique has been applied into large civil structures such as bridges [4,5,6,7], dams, high rise buildings [8], towers [1,2,3, 9,10,11,12,13,14], and monuments [15,16,17]. In context of ongoing consulting project for assessment of telecommunication towers across Egypt, the project is implied in structures and metallic constructions research institute, Housing and Building National Research Center (HBRC); the 50 m height self-supporting tower was selected to perform a full structural seismic study using AVT techniques and FE model analysis. In this paper, the identification of natural frequencies and their corresponding mode shapes through measuring the ambient response of a full scale self-support tower was performed. The ambient vibration testing (AVT) is considered an output- only response technique for dynamic test method. Moreover, AVT test method has the advantage of being a cost effective, because there is no need for the structure to be excited using special instruments. Therefore, AVT is considered as an effective non-destructive test and being harmless to the tested structure [18]

Structural parameters were used to produce the global modes interpreting the experimentally identified peaks in the spectral analysis. The modal behavior was investigated in the range 0–20.50 Hz. The first fundamental natural frequency of the self-support tower was identified at 0.5704 Hz. A verification based on the measurements has been carried using ANSYS and it shows good agreement between the experimental results and the finite element model. Furthermore, a study on the effect of seismic loads on the tower was conducted using 1995 Gulf of Aqaba earthquake time history records.

The self-supported tower

The tower was constructed back in 1985 in Ismalia, Egypt. The tower components are shown in Fig. 1. The geometrical properties were measured in the field using a vernier and a metal thickness detector. The tower is a 50 m steel tower is an equilateral triangle in plan of size 3.23 m and at top 0.28 m, as shown in Fig. 2. The lower part of the tower starting at the ground level consists of 3 main legs of steel hollow pipe cross sections with dimensions of diameter 76 mm and 5.5 mm thickness. These leg members are interconnected by bolted connections. Steel angles cross section with dimensions of 45 × 45 × 3.5 mm thickness are used as bracing connecting the main legs. The tower is supported on a reinforced concrete foundation under each leg.

Fig. 1
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The components of self-supported tower

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Fig. 2
figure 2

Geometric Properties of the self-supported tower

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Insitu ambient vibration test (AVT)

The ambient dynamic response was measured using the following:

  1. (a)

    Eighteen uniaxial piezoelectric accelerometers (PCB Model 393B04) of high sensitivity. The sensitivity of each accelerometer was determined using a calibrator exciter of type 4294 manufactured by Brüel & Kjær, the sensitivity of each is 1000 mV/g, a measurement range of ± 5 g and frequency range 0.06 to 450 Hz.

  2. (b)

    PULSE analyzer type 3650/B manufactured by Brüel & Kjær.

  3. (c)

    PULSE LAN-XI analyzer with dynamic range of 160 dB manufactured by Brüel & Kjær, which has real-time capabilities for FFT analysis, order tracking and time data recording on multi channels.

  4. (d)

    A notebook with LAN interface.

  5. (e)

    IDA-based data acquisition front-end hardware with eighteen input channels.

The test grid consists of twenty six locations on the main legs of the tower as shown in (Table 1). Ten reference accelerometers and eight roving accelerometers were used to measure 26 DOF at the test points. Horizontal acceleration was recorded in orthogonal axes (X-axis and Y-axis) at the main legs of the tower as shown in (Table 1) and Fig. 3 shows the direction of measurements on different levels. Two data setups were executed to identify the natural frequencies of the tower under the effect of the surrounding wind and ambient conditions. In all cases, the sampling frequency on site was 512 Hz and total duration of 300 s was selected for each setup.

Table 1 Test grid details
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Fig. 3
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Direction of measurements at different levels

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Signal processing

The signal data were recorded using PULSE labshop [19] afterwards the signal processing was carried using ARTeMIS extractor [20]. The spectral density matrices are evaluated at discrete equally spaced frequency lines in the range between zero (DC) frequency and Nyquist frequency. This is considered a radix-2 number because of the use of Fast Fourier Transform (FFT). The Hanning window function is the window which is used by default. Also, the overlap between two data segments is taken 66.67%. Moreover, the overlap that is presented in order to reimburse the information loss due to tapering of the data segments that happens due to the data segments being multiplied by the window function. In the case of the self-support tower, the frequency lines were 2048 in order to have enough averages to minimize the noise on the estimated spectral densities. The frequency resolution used 0.01 Hz. The frequency resolution was expected to be sufficient to resolve any closely detected natural frequencies. Also, the used signal processing algorithms are explained as follows [9]:

Fast Fourier transform (FFT)

The fast Fourier transform (FFT) is a quick (computationally efficient) method to calculate the discrete Fourier transform (DFT), The DFT of a discrete-time signal x (nT) is

$$X\left[k\right]={\sum }_{n=0}^{N-1}X\left[n\right]exp\left(-\frac{i2\pi kn}{N}\right)={\sum }_{n=0}^{N-1}X\left[n\right]W\left(\genfrac{}{}{0pt}{}{nk}{N}\right)$$
(1)

where the sampling period T is insinuated in X[n], X[k] is the kth harmonic (k = 0...N−1), x[n] is the nth input sample (n  = 0...N−1) Also, N is the frame length, and WN is shorthand for exp (−i2π/N). For a radix-2 FFT, N must be a power or base of 2 [21].

Cross power spectrum

The fast Fourier transform (FFT) is s a quick (computationally efficient) way to calculate the discrete Fourier transform (DFT), The DFT of a discrete-time signal x (nT) is.

Cross-power spectrum between two signals y(t) and x(t), it is the product of the Fourier transform of the first signal with the complex conjugate of the Fourier transform of the second signal:

$${\text{Gy x}}\left( f \right) \, = {\text{ Y}}\left( f \right){\text{ X}}\left( f \right)*$$
(2)

where both Y(ƒ) and X(ƒ) are Fourier transforms obtained from the functions y(t) and x(t), and * denotes the complex conjugation.

Auto power spectrum

Auto power spectrum is a spectrum obtained by multiplying X(ƒ) by its own conjugate X*(ƒ). Gxx(ƒ) is real and positive at all frequencies.

Coherence

Auto power spectrum is a spectrum obtained by multiplying X(ƒ) by its own conjugate X*(ƒ). Gxx(ƒ) is real and positive at all frequencies.

It is computed as the ratio of the magnitude squared of the cross power spectrum divided by the product of the input and output auto power spectrums as follows:

$$\gamma ^{2} \left( w \right) = \frac{{\left| {G_{x} ~Y~\left( f \right)} \right|^{2} }}{{\left| {G_{{XX}} ~~\left( f \right)^{{*~}} G_{{YY}} ~\left( f \right)} \right|}}$$
(3)

The coherence function is real valued having values between zero and one. For output only measurements, coherence function is a very important function because it is expected that the coherence would take high values at resonance frequencies, as a strong vibration pattern exist and a high signal to noise ratio is found.

Identification of modal properties

The measurement data were recorded in the range of 0–512 Hz. However, only the frequency band from 0 to 20.50 Hz was studied in this analysis. Typical coherence functions between spectra at the levels of 42.70 and 48.80 m for X and Y directions as shown in Fig. 4. Good correlation is revealed between spectra at this specified range. The resonant peaks of the spectra in the lower frequency range represent the global modes of the whole tower, which are of main concern for the purpose of the model calibration. The identification of natural frequency was performed using peak picking method. It is based on the fact that the frequency response function goes through an extreme value around the natural frequency. In the context of output- only response vibration measurements, the frequency response function is replaced by the auto spectra and cross spectra of the output-only data [22]. The method leads to reliable estimates provided that the basic assumptions of low damping and well separated modes are satisfied.

Fig. 4
figure 4

Results of signal processing

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Inspection of all average spectral estimates of ASD and CSD allowed to identify the values of natural frequencies successfully as shown in Fig. 4. The spectra of acceleration in the X & Y directions showed the resonant frequencies (spectral peaks) at 0.5704, 1.884, 4.068 and 7.567 Hz. Beside identified torsion modes at 10.1231 and 14.7127 Hz. Both of the EFDD and SSI techniques were used, both of them produced very close results for the modal frequencies analyzed from 0 to 20.50 Hz as shown in Tables 2 and 3.

Table 2 Modal results identified using EFDD and SSI
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Table 3 Comparison between identified bending mode shapes using ANSYS FEM and experimental
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Finite element model validation and seismic analysis

In order to verify the FE model, a 3D model was developed using the finite element software ANSYS. The model was updated using experimental modal results obtained by ARTeMIS extractor software. In order to form a 3D finite element model (FEM), the geometry of the tower was measured in site using a total station instrument. Moreover, for the material characteristics of all steel members a Young’s modulus of 200 GPa, a Poisson’s ratio of 0.3, and steel density of 7850 kg/m3. In addition to, the three legs of the tower are assumed to be restrained at the foundation level. In order to model the three main legs (vertical elements of the tower) BEAM4 element was chosen as well as the corresponding cross section (as described in Clause 2). As for the braces LINK8 element was chosen for its characteristics of carrying axial force both of tension and compression forces, their corresponding cross sections were represented in the model (as described in Clause 2). The dishes and antennas were represented as MASS21 and applied at their corresponding locations. The modal analysis of the updated FEM predicted the dynamic identity of the studied tower in terms of its modal frequencies and corresponding mode shapes. A comparison between the results of the FEM and the experimental results is shown in Table 3 and the comparison shows a good agreement between both results.

There is a crucial importance of maintaining the telecommunication services during the hazards. Due to seismic nature and activities by the red sea coast, structural performance of the existing towers is significant especially for the top part of the tower, where the antennas are attached. In order to study the seismic effect on the tower. Three generated seismic events were used 1995 Gulf of Aqaba, 1940 Imperial Valley and 1995 Kobe, Japan earthquakes time history records were applied to the model individually using time history analysis, the events were of magnitude Mw = 7.1 [23], 6.95 and 6.90 [24], respectively, and maximum acceleration during each event 0.896, 2.755 and 2.705 m/sec2, respectively. Generation of earthquakes been developed and applied as per [13]. Antenna supporting towers should comply with strict serviceability criteria. Seismic amplification may affect the top part of the tower where the antennas are attached and it should not result in any local permanent deformation after the earthquake.

The results of the maximum displacement at the top of the tower obtained from seismic loading due to the earthquakes are 0.091, 0.2964 and 0.3637 m, respectively. Also, the axial stresses obtained from the earthquakes are 0.0509, 0.2036 and 0.1918 t/cm2, respectively. Table 4 shows for each case displacement vs time and the axial stresses vs time.

Table 4 Identified displacement and axial stresses for different earthquakes
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Maximum displacement allowable as per Table (9.1), ECP-205 [25] is 0.1 m and the maximum axial compression stresses allowable as per ECP-205 is 0.9840 t/cm2 for the mast’s vertical legs of steel pipe section 75 × 5.5 mm. Therefore, the tower falls in the allowable limits for the axial stresses under the acting loads, while exceeding the allowable limits for displacement in case of 1940 Imperial Valley and 1995 Kobe, Japan earthquakes.

Conclusions

The paper presents an experimental and analytical dynamic study of an existing telecommunication tower using ambient vibrations. Being a very flexible steel structure, setting up the test grid and mounting the sensors along the height of the tower was a real challenge. To reach the test grid points of the tower very skillful trained engineer climbed the tower to gain access to different levels along the height of the tower while the tower was swinging. This reflects how valuable are the results of AVT as very few studies illustrate such complicated experimental work. Both of the EFDD and SSI techniques were utilized to perform experimental modal analysis. The experimental modal analysis was successful in identifying the natural frequencies and their corresponding mode shapes in the range 0–20.50 Hz. The dynamic modal behavior of the tower included bending and torsion modes.

The FE model in ANSYS was thoroughly updated to match the identified modal properties. 7 global modes were selected to tune with the results of experimental modal analysis. Good correlation between experimental and theoretical model enabled the updated model to provide reliable predictions to evaluate the structural performance of the tower under seismic loading. The accurate data concerning the geometrical, material properties, connections details and boundary conditions are essential to build an updated base line model representing the real dynamic behavior.

The seismic analysis of the tower under three selected seismic events was applied using time history analysis. The structural performance of the tower was predicted showing no strength deficiency under load patterns. In case of 1995 Gulf of Aqaba earthquake there is no influence on the structural integrity of the tower or the antenna serviceability criteria due to the motion of the top part of the tower, however in the case of 1940 Imperial Valley and 1995 Kobe, Japan earthquakes the maximum limit to displacement is exceeded and would require strengthening for the tower for such case in order to comply with the code limits. Accordingly the adopted plan in this study shown to be accurate and valid to assess the structural performance of lattice self-supporting towers under different structural loadings. The updated FE model can be extensively useful if the tower need to be investigated for adding larger or additional antenna and also for any future structural modifications.