Self-Excited Acoustical System for Stress Measurement in Mass Rocks

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1 JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL Pages Self-Excited Acoustical System for Stress Measurement in Mass Rocks Janusz Kwasniewski 1, Yury Kravtsov 2, Ireneusz Dominik 1, Lech Dorobczynski 2 and Krzysztof Lalik 1 1 AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics Krakow, Poland kwa_j@agh.edu.pl, dominik@agh.edu.pl, klalik@agh.edu.pl 2 Maritime University of Szczecin, Faculty of Marine Engineering, Szczecin, Poland, y.kravtsov@am.szczecin.pl, l.dorobczynski@am.szczecin.pl ABSTRACT The paper is devoted to theoretical end experimental studies of the lowfrequency Self-excited Acoustical System (SAS), which allows monitoring stress changes in various elastic media including metals, concrete and mass rocks. The main principle of the SAS system is using a vibration exciter and vibration receiver placed on a sample with a positive feedback, which causes the excitation of the system. Stress changes manifest themselves in small but detectable variations of resonance frequency which can be used to indirectly measure stress changes in the material. In the paper the considerations concerning working frequency of SAS were performed. It was suggested that in the case of stress variation in mass rock monitoring, the low frequency (even infrasound) band should be selected, in contrast to the stress monitoring in columns of marble or concrete, where frequencies from an acoustic band should be used. Computer simulations conducted in the MATLAB-Simulink environment were based on the research performed in the laboratories. They focused on finding a relationship between the compressing force and velocity of sound in a specimen made of concrete. Results of the simulations allowed to state that the frequency of self-excited oscillations of simulated SAS change linearly with the pressing force. In the next step the laboratory experiments were carried out. The impact on stress measurement parameters such as: the position of sensors, actuator, and the influence of geometrical shape and dimensions of the sample. A sample of sandstone compressed in a frame by a hydraulic press was used in the study. The results proved the applicability of the design system. Additionally, the new possible applications of SAS were suggested, such as monitoring stress variations of stresses in mass rock, particularly in the active seismic zones. Keywords: autodyne effect, self-excited systems, stress variation measurement 1. INTRODUCTION Autodyne systems developed by Armstrong [1] are widely applied in radio engineering [2,3] and for monitoring changes in tested objects [4,5]. In mechanics and geophysics autodyne systems are used much more rarely [6]. The present paper describes the Self-excited Acoustic System (SAS) of an autodyne type that measures stress changes in elastic media. Preliminary publications on similar systems were published in [7,8]. The experimental confirmation of stress variation monitoring in elastic media with the use of the SAS was described in [9, 11]. This system has been patented recently [1]. The systems which are used nowadays to monitor and analyse the state of construction elements are based on simple strain gauges or by visual methods including vision systems [12]. Vol. 32 No

2 Self-Excited Acoustical System for Stress Measurement in Mass Rocks The paper is presented in a way that basic properties of the system are described in Section 2 which also contains basic equations describing the SAS system. A characteristic feature of SAS is that oscillation frequency changes when stress is applied, as is analyzed in Section 3, which also contains considerations on working frequency selection as well as the dependence between delay time and mass rock layer thickness. Section 3 contains also an estimation of the SAS sensitivity to stress changes. The laboratory test description and experimental results can be found in Section 4 and 5. New applications of SAS are described in Section 6, whereas Section 7 presents the use of SAS in monitoring of other parameters, influencing sound velocity. Section 8 contains final summary and conclusions. 2. BASIC PROPERTIES OF SAS Let us consider a self-excited acoustical system, presented in figure 1, which consists of: piezoelectric detector PD, amplifier-limiter A-L, pass-band filter F, piezoelectric exciter PE, delaying element DE, frequency meter FM. Figure 1. Basic scheme of self-excited acoustical system Input of A-L is a harmonic signal described by amplitude U, frequency ω and phase angle ϕ u : ut () = U cos( ωt+ φu). (1) Output signal v(t) of non-linear A-L contains the basic frequency as well as higher harmonics: vt () = F ()cos( v ωt+ φ1) + F ( v)cos( 2ωt+ φ2) (2) Amplitudes of harmonic components depend on the amplitude of input signal u. The first component of the sum (2) is of utmost importance: v () t = F ( v)cos( ωt + φ ). (3) Due to elimination of higher harmonic frequencies, signal v is transmitted by pass-band filter F, thus, the filter on the output limiter cleans the spectrum of acoustical oscillations from higher harmonics. A further evolution of an acoustical wave in an elastic medium obeys linear wave equations. Please note that typical acoustic power in SAS is no more, than 1 W, which guarantees the weakness of nonlinear processes in elastic medium. The equation of phase balance permits to determine frequency of self oscillations which can be expressed as: ωτ arg G( jω ) = 2π n, (4) ωτ Φ( ω ) = 2π n (5) 134 JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL

3 Janusz Kwasniewski, Yury Kravtsov, Ireneusz Dominik, Lech Dorobczynski and Krzysztof Lalik where: ω frequency of self-oscillations G(jω) transfer function of filter τ delay time of delay element n natural number whereas the following equation of amplitude balance: U = k F () v G ( 1 jω ) (6) makes it possible to find the necessary gain factor k of element A-L and the amplitude of self-oscillations. 3. ANALYSIS OF SAS SENSITIVITY The pass band of resonant circuit of Q factor Dw = (ω ω /2Q, ω + ω /2Q) can cover the frequencies ω n corresponding with the different values of index n. To avoid generation of multiple frequencies, the following inequality has to be fulfilled: ω ω (7) n+ 1 ωn> Q Using the estimation : π ω 2 n (8) n τ we have: 1 ω > then: Q > ωτ. (9). τ Q In such conditions frequency can be determined as follows: ωτ = 2π n (1) Deriving (1) with stress σ as the independent variable we obtain: dω 1 dω 1 dτ, or: =. (11) σ τ ω d + τ = d dσ ω dσ τ dσ Formula (11) is a basic relation to determine stress variation using SAS. Phase component ϕ(ω) in (5) can be approximated as: Φ( ω ) Φ( ω ) d ( ω ω ) ( ) ( ) (12) dω = 2Q ω ω ω T ω ω where T = 2Q/ω o denotes time constant of resonant circuit. Substituting (12) with (5) we have: ωτ + T( ω ω ) = 2π n (13) and: dω (14) σ τ ω d ( + T ) + τ = d dσ As a result we obtain: 1 dω 1 dτ = (15) ω dσ ( τ + T) dσ where 1/τ component was changed into 1/(τ+T). Usually T << τ and for this reason derivative dω/dσ in (15) is almost equal to (11). Equation (14) makes possible to estimate the sensitivity of variation in frequency caused by variation in temperature Θ: dω ω τ Θ + T T d ( ) d dθ = Vol. 32 No

4 Self-Excited Acoustical System for Stress Measurement in Mass Rocks which allows to write: dω ω (16) Θ = T d d τ + T dθ Consequently, the sensitivity of variation in frequency caused by variation in temperature is T/(τ+T) times lower than the sensitivity of variation in resonant frequency caused by variation in temperature. A basic feature of SAS is dependence between variation in delay in wave propagation time between the exciter and receiver, caused by variation in stresses in an elastic propagation environment. Delay time is not only dependent on the distance exciter - receiver, but also on the depth, at which the receiver is situated. Let us assume that depth is marked by h and the mean value of mass-rock density is marked by γ, which is shown in figure 2. Figure 2. Model of mass-rock Compressing force F is proportional to dimension x: F(x)=g γ S x, and compressing stress σ is determined as: Fx σ( x)= ( ) = g γ x (17) S According to research results, which were performed at the AGH University of Science and Technology [14], dependence between sound propagation velocity v and stress σ in an elastic medium can be expressed by a linear function: v( σ) = Aσ + v (18) Connecting (17) and (18), we obtain dependence between local velocity of wave propagation v and the current co-ordinate x: vx ( )= A g γ x+ v = m x+ v (19) On the other hand, wave propagation time d through layer of thickness dx is equal to: dx dx dx vx ( )= dτ = = dτ vx ( ) m x+v (2) Hence, total propagation time from level to level denoted as h will be equal to: h dx m h = = = ln + ln = 1 ln m x+ v m +1 v τ d τ α[ ( m h v ) ( v ) ] (21) instead of a simplified formula τ = x/v, implied by the assumption of constant propagation velocity v. 136 JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL

5 Janusz Kwasniewski, Yury Kravtsov, Ireneusz Dominik, Lech Dorobczynski and Krzysztof Lalik Frequency of self-oscillations is a primarily determined feature of an elastic element as well as by the features of a pass-band. Limitations of the upper and lower frequency concerning SAS working frequency should be considered. The upper limitation is caused by frequency-dependent attenuation of an acoustic wave in the propagation area. Partially, it can be compensated by an increase of the amplifier gain factor but it can cause system susceptibility to external interference. The lower limitation results from geometrical dimensions and the supply power of the exciter. In order to estimate the SAS system sensitivity, computer simulations conducted in MATLAB-Simulink environment were performed on the basis of the research performed in laboratories of the AGH University of Science and Technology in Krakow. It focused on finding a relationship between compressing force and velocity of sound in a specimen made of concrete [9]. Figure 3. Dependence between velocity of sound and pressing force in concrete The obtained linear regressive model has the following form: v = a F + v, where: F compressing force expressed in kn, v sound velocity expressed in m/s. The values of coefficients a and v are as follows: a = m/ns, v = m/s. The obtained results are presented in figure 3. The simulation was performed for the specimen length L=.45 m. The parameters of the model built in Simulink, according to scheme in figure 1 were as below: static characteristic of the limiter was described by a formula y=k arctan (x) gain factor of amplifier was assumed as K=25 The band pass filter consisted of two sections, each of them described by transfer function: ω ms G () s = 2 2 Qs + ω s + Qω ff 1 2 where: ωm = 2 π ff 1 2; Q= and f 1 = 47 Hz, f 2 = 48 Hz are f2 f1 respectively lower and upper cut-off frequencies of the filter. The self-excited oscillations obtained during the simulation were recorded. The resonant frequency f depending on delay time τ was determined. The obtained values of resonant frequency f depend on compressing force F are presented in Table 1. m m (22) Vol. 32 No

6 Self-Excited Acoustical System for Stress Measurement in Mass Rocks Table 1. Simulation results F [kn] τ [ms] f [Hz] On the basis of the previous data, the system sensitivity factor, expressed by: f S = (24) F can be estimated with the use of the least squares method as: S =.43 Hz/kN (25) 4. LABORATORY STAND During our preliminary research at the Department of Process Control at the AGH University of Science and Technology the Self-excited Acoustical System was developed. A diagram of the system is shown in figure 4, where an amplifier, shaker (E) and receiver (R) are formed in a feedback loop. The shaker (E) was fixed to a stone bar. The bar was placed into a testing machine to create a load. On the beam s surface four accelerometers were fixed: three of them on the same surface as the shaker and the last one directly on the opposite side. As a result of positive feedback, there is a bilateral interaction between the control device and the vibrating system, which allows the self-oscillating system to control its own energy balance. As a result, despite loss of energy in the system, oscillations have a periodic and non-fading character. Many examples of selfoscillating phenomena are known. These include: vibrations of cutting tools, turbine blade vibration, vibration of aircraft wings, vibration of bridge suspension, which may cause a destruction of the bridge, such as the Tacoma Bridge, etc. In such cases we try to eliminate vibrations. Figure 4. Self- oscillation Acoustical System diagram, where E shaker and R receiver The system was intended to measure a stress change in elastic mechanical structures, construction and rock masses. The purpose of this study was to determine whether or not the system can be used for real objects such as bridges, dams, buildings, mines, etc. The sensitivity of this system, for small and large 138 JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL

7 Janusz Kwasniewski, Yury Kravtsov, Ireneusz Dominik, Lech Dorobczynski and Krzysztof Lalik deformations, is higher than the sensitivity of other measurement systems (especially open systems). Tests on a single sample of sandstone were performed. The impact on stress measurement parameters such as: the position of sensors, actuator, and the influence of geometrical shape and dimensions of the sample. A sample of sandstone compressed in a frame by a hydraulic press was used in the study. In addition, the system was equipped with a force sensor to calculate compressive stress in the beam in real time. Figure 5. Diagram of deployment of emitters on sandstone Accelerations were measured by three accelerometers for three reasons: - to determine what impact the distance from the emitter to the receivers has on the results and the position of resonance, - to make sure where the sensor is not located in a resonance node, which would result in incorrect test results, - to designate the velocity of wave propagation in the material with correlation methods. The study was conducted in three configurations of the position of the emitter (E). For a sandstone sample with the rectangular cross-section of 6x7 emitting and receiving devices were mounted in the configuration shown in figure EXPERIMENTAL RESULTS The SAS is designed for measurements of stress in elastic structures including rocks as well as mines, bridges, dams, buildings, etc. Therefore it is necessary to create a universal procedure to detect the changes in the strain in the objects mentioned above. The designers decided to use first the system to conduct tests in the open loop [9]. The sample, charged with various varied compressive forces, was initially given the chirp signal emitted in the frequency range of 1 Hz 2 khz. This allowed to obtain the amplitude - frequency characteristics of the structure with visible resonances. Figure 6 presents the movement of the first resonance peak believed to be related to the change of stress in the sample. Variation of resonant frequency due to changes of compressing force equals to 9 Hz. For the closed loop system, which is shown in figure 7, the frequency change at the same load change is as large as 45 Hz. In addition, the amplitude of vibration is 2 3 times greater than in the open loop system, which makes them more visible and easier to identify. Thus our experiments have demonstrated an opportunity to detect stress changes in elastic geophysical objects: marble, sandstone and also concrete by means of a self-oscillating acoustical system (SAS). We hope that a similar system might be helpful for stress change detection in rock mass and mines as well as civil engineering objects i.e. bridges, dams and buildings. Vol. 32 No

8 Self-Excited Acoustical System for Stress Measurement in Mass Rocks Figure 6. Selected and expanded resonance peaks related to the changes of stress Figure 7. Selected and expanded resonance peaks of the closed loop system related to the changes of stress 6. POSSIBLE APPLICATIONS OF SAS The main application of SAS is recording stress changes in an elastic medium. The first SAS experiments [9] have dealt with a sandstone bar of the length of about 1 m. A typical frequency of self-excited oscillation in these experiments was within the band of Hz (Fig. 7). A frequency shift was observed also in metal constructions supporting industrial weighing scales. Figure 8. Positions of sound transducer T, receiver R and feedback line F on high chimney, exposed to wind force 14 JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL

9 Janusz Kwasniewski, Yury Kravtsov, Ireneusz Dominik, Lech Dorobczynski and Krzysztof Lalik Figure 9. Positions of sound transducer T, receiver R and feedback line F in case of mines monitoring A significantly lower frequency, about 1-1 Hz, should be recommended for larger objects as chimneys, high buildings, bridges and so on, as discussed above. High objects like chimneys are exposed to the force created by wind, as shown in figure 8. Transducer T is installed near the earth, and receiver R is placed on the top of chimney. Feedback is realised through a conductor along the chimney. Choice of the SAS frequency depends first of all on sound absorption in the chimney s body. β is an absorption coefficient and K is an amplification coefficient of the signal transmitted through the feedback line. Self excitation is possible if K exp( β L)>1, when L is of the chimney s height. As a rule, absorption factor γ increases with frequency so the working frequency should be chosen in a lowfrequency band f = 1 1 Hz. In this case SAS allows for observation of chimney deformation with sufficiently low frequencies. Similar phenomena can be observed also in masts and high buildings. The SAS system application for stress monitoring in mines is of special interest. In this case we should deal with sufficiently lower frequencies, comparable with 1 Hz, because waves of higher frequencies propagate with larger absorption. Position of SAS elements is shown in figure 9. Transducer T is installed on the earth s surface, whereas receiver R is placed at the depth H of.5-1. km. When mass-rock experiences deformations, frequency of self-oscillation is changing, indicating some perturbations in a mine. Optimisation of a working frequency requires not only numerical modelling, but also experimental testing. An experimental scheme, presented in figure 9, can be used also to solve the challenging problem of monitoring stress changes in deep mass-rocks in order to forecast possible earthquakes. One more subject for SAS application is weighing loose materials e.g. sand, cement or grain, as is shown in figure 1. Figure 1. Positions of sound transducer T, receiver R and feedback line F in the case of loose materials weighing Figure 11. Positions of SAS components on the bridge pillars Vol. 32 No

10 Self-Excited Acoustical System for Stress Measurement in Mass Rocks A possible application of SAS to stress variation monitoring in the structure of bridges is illustrated in figure 11: when a heavy truck is moving over the bridge, all pillars supporting the bridge span experience additional stress. Finally, the possibility of stress monitoring in a ship hull, what is shown in figure 12, is also worth mentioning. Figure 12. Position of SAS components destined to monitor 2D distribution of stresses Figure 13. SAS monitoring the variations of groundwater level Transducer T excites sound waves, propagating them in directions of receivers R 1 and R 2. Traces T R1 and T R2 are placed orthogonally to each other on the ship hull. By measuring stress changes along lines T R1 and T R2 we obtain an opportunity to monitor 2D distribution of stresses in the presence of large waves on the sea s surface. 7. MONITORING OTHER PARAMETERS INFLUENCING SOUND VELOCITY In principle, frequency of the SAS generator depends not only on stress change, but also on other parameters, influencing sound velocity. One of these parameters is temperature of an elastic medium. When sound velocity depends on temperature, v = v(θ), increment of frequency ω is proportional to temperature shift Θ: ω = K Θ Θ Θ (26) where coefficient K Θ characterises sensitivity of frequency to temperature changes. The role of temperature variations becomes insignificant, when increment ω Θ is lesser than frequency shift ω σ due to stress change: ω Θ << ω σ (27) In contrast, when ω Θ >> ω Θ, the temperature change becomes the main factor determining frequency variations. It means that in such cases SAS may serve as a kind of thermometer. One more factor, influencing sound velocity, is the amount of liquid in an elastic medium. In this case frequency change can indicate changes in liquid content (level) 142 JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL

11 Janusz Kwasniewski, Yury Kravtsov, Ireneusz Dominik, Lech Dorobczynski and Krzysztof Lalik in an elastic media. The system which registers the level of groundwater, is shown in figure 13. Low frequency sound source is placed on the ground surface, whereas the receiver is sunk into the ground. A feedback line connects the receiver with the source and provides oscillations in SAS. The frequency of oscillations depends on the amount of water in the ground. The systems of this kind can be helpful also for measuring oil level in oil-bearing fields. SUMMARY The paper describes properties of the self-oscillating system of an autodyne type. The systems of this type converts sound velocity changes in an elastic medium into self-excited frequency changes. The main factor influencing sound velocity change is stress change in an elastic medium. The paper presents experimental evidence of this effect in sandstone samples, in concrete and in metal. SAS provides various applications for elastic media monitoring. In particular, SAS allows for monitoring stress changes in mines, in chimneys, masts, high buildings as well as bridge pillars and in ships hulls. SAS can be helpful under certain conditions for recording temperature changes and the level of liquids in elastic media. Further research will focus on applying smart filters based on the FPGA technology. The whole set of filters, ranging from classical to advanced filters, based on artificial neural networks, will be considered. The embedded filter will select an operating frequency bandwidth of the SAS system. It will also allow the system to eliminate some disturbances created by other working devices, which is especially important in the industry. ACKNOWLEDGEMENT The authors are grateful to Polish Ministry of Science and Higher Education for financial support in frame of grant No N N REFERENCES [1] Armstrong E.H., Some recent developments of regenerative circuits, 1922, Proceedings of the Institute of Radio Engineers, Vol. 1, No. 8, pp [2] Blaney T.G., Infrared and Millimeter Waves, Vol. 3, Part 2., NY Acad. Press, 198 [3] Shestopalov P., Physical Foundations of the Millimeter and Submillimeter Waves Technique, Vol 2, VSP, Zeist, Netherlands, 1997 [4] Jankowski J., Weighs and weighing. (in Polish), 1983, Warsaw, WNT [5] Gallo M. and Melcher D., Elektrischer Massen und Kraftmesser (in German), patent , 1973, Federal Institute of Intellectual Property, Bern [6] Gustkiewicz J., Kanciruk A. and Stanislawski L., Some advancements in soil strain measurement methods with special reference to mining subsidence, 1985, Amsterdam, Elsevier Science Publishers, B. V. [7] Bobrowski Z., Chmiel J., Dorobczynski L. and Kravtsov Y., An application of string tensiometer in variable stress measurement in ships hull (in Polish), 24, Szczecin, Proceedings of Maritime University in Szczecin 1 (74), ISSN , pp [8] Bobrowski Z., Chmiel J., Dorobczynski L. and Kravtsov Y., Ultrasonic system destined to measurement of variable stress in ship s hull (in Polish), 24, Szczecin, Proceedings of Maritime University in Szczecin 1 (74), Poland, ISSN , pp Vol. 32 No

12 Self-Excited Acoustical System for Stress Measurement in Mass Rocks [9] Kwasniewski J., Dominik I., Konieczny J., Sakeb A. and Lalik K., Application of self-excited acoustical system for stress changes measurement in sandstone bar., 211, Warsaw, Journal of Theoretical and Applied Mechanics, ISSN , Vol. 49, No. 4., pp [1] Kwaśniewski J., Kravtsov Y., Dominik I. and Dorobczynski L., Method for monitoring of stress changes in elastic systems and mass rocks, patent application P , 211, Warsaw, Polish Patent Office [11] Kwaśniewski J., Dominik I. and Lalik K., Application of self-oscillating system for stress measurement in metal, Journal of Vibroengineering, ISSN , Vol. 14, 212. [12] Sioma A., The rope wear analysis with the use of 3D vision system. Control Engineering, ISSN 1-849, 213, Vol. 6, No. 5, pp JOURNAL OF LOW FREQUENCY NOISE, VIBRATION AND ACTIVE CONTROL