TWI220923B - A method for continuously measuring the damping ratio of structural systems - Google Patents

Abstract

The present patent is a method for measuring the damping ratio of a structural system that is under base excitations. The method is accomplished by processing the response signal with respect to that of the input. In other words, one is to measure the responses of the system, which is excited by an input sinusoidal signal. Once the response signal is obtained, it is modulated by two different reference signals. The first one is the row input signal, while the second one is the phase-shifted input signal. The proposed phase given here is 90 degrees. The two modulated output signals are then put into the low-pass filter separately and their dc values are the ones the present method required. Dividing the dc values each other to get the tangent value of the phase lag, which is due the system damping ratio, one is able to use the equation provided to calculate the required damping ratio. Because the present method is based on the phase angle of the steady-state responses, it can be adopted and displayed in real time. In addition, the current method does not require the system damping to be small and valid for a wide range of damping ratios.

Description

1220923 V. Description of the Invention (l) " ----- [Technical Field] This creation is a damping ratio detection method suitable for mechanical or civil structure systems, especially for systems that are excited by a base. Use this creation The measured signal can be continuously and instantly converted into the damping ratio of the system, so it can increase the relevant functions of the structure dynamic measurement instrument. ♦ Drama [Prior art] Most commonly used system damping measurement methods are mostly measured in a temporary way, for example, applying a shock to the system being measured to reduce the amplitude of the amplitude, or a logarithmic equivalent, so that Time t 丨 wash t evening screen; ^ \ With the method of music number < ti, the logarithmic decreasing factor 6 is 1 and t]: Kl) 5

δ (1) where Γ is the damping ratio coefficient of the system. That is, it is assumed that the system damping is very small, and it is calculated by ignoring the amplitude reduction process in 2 miles. Or divide the stiffness by the first term =, and then inversely derive the system damping ratio from the inverse ratio rA of U): (the field or the maximum amplitude), and obtain (2a) · 'Another type of method is to measure the domain, Expressed in the following way: The response of the J system is converted to the frequency (a) half-power or Q-value bandwidth eight ω and the ratio, or the approximate Hansby coefficient table of the system '-' ,,, ..., ' Frequency ωη of 1220923 Five 'invention description (2) (2b) (b) fit of frequency domain curve (fitti fit, (ϋ) circle of Nyquist diagram is desirable) (1) resonance section curve regardless of 疋It is assumed or applicable that the damping ratio of the system is much less than; t Disadvantages: (1) Most methods cannot measure and display the measurement system in real time; or (2) Control cannot select the maximum effect when it is extremely large. This creation = Ratio, so that it is the method, there is no familiarity with various methods of measuring the damping ratio measurement. 7 Disadvantages and limitations, a brand new [invention content and theoretical background] 6 members understand The theoretical background of this creation and its correctness, the following content explains the main derivation of this creation Process: Referring to the system of Figure 1, let a single-degree-of-freedom (SD0F) system act on the base (54) u (t), then its equation of motion can be expressed as: wz + c (i ~ / /) + k (z ~ //) = 0 (3) In the above formula, m represents the system mass (51), C represents the system damping (52), and k is the system stiffness (53). Therefore, the system response z (t ) (55) can be expressed as ζ (ί) l + j (2rc) a-r2) + / (2rC)

UeiQt = ZeK〇x ^ (4) If the base excitation u (t) (54) is a frequency Ω harmonic, or it is expressed in a complex formula

Page 9 1220923 5 Description of the invention (3) (5) u (t) = UeiQt ^ In the formula ... π. In addition, due to the existence of the version, the phase difference ρ tangent between the input excitation (54) and the system response γ55) can be expressed as (6) tM1 ^ = (i-r2) + (2rc7) The following parameter symbols have been used: (7-9) l4mk,% = ;, r " ~ where ζ of the formula (7) is the damping ratio of the measurement target. To further explain the background theory of this creation, Let the input signal (54) ❿ (10) w (i) = i / sia (Qf) then the steady-state response (55) of the system can be expressed as (11) z (t) = ZOύ (Ωί-φ). Therefore, if The system steady-state response (5 5) and the excitation signal (5 4) are multiplied by (60), or written as (12) g (t) = u (t) z (t) = Usin (pt) ήη ( α-φ) However, (13) The above formula can also be written as a factory using a triangle equation. C / 2 g (t) = —- [cos ^-cos (2Ωί-φ) [where rz is defined by (4) or

r 〇 -λιιζ (14) Z | _ (1 a r2) 2 + Gang \ Observe (13), the first term in the brackets is not a time-varying term, so if a low

Page 10 1220923 V. Description of the invention (4) Therefore, the low-pass filter (LPF, 61) passes it out (15)

_IIlpF cosd n I I ·· I I in the above formula represents a time-invariant value after filtering. On the other hand, if the excitation signal (54) is subjected to product modulation, a quarter cycle or p / 2 phase shift (62) is performed as the first reference signal of the system response. According to the same product change (^, low-pass filtering (64) mode as above, we can obtain, (16), and g (〇 = u (i ~ r / 4) «z (i)

& _LPF Division of two signals (17) ⑽ 2 Therefore, from (15) and (17), and after comparing (6), (65) holds

G 2ζΓ (18) (i-n ^ (2rcy At the same time, the equation (18) can also be rearranged and the system damping ratio (, r2 ± ^ jr4 -4G2 (l-r2)

(19), 4rG Figure 2 illustrates the above calculation process and creative concept. In addition, because the system's damping ratio is a positive real value, the following formula must be established according to the choice of r:

Page 11 1220923 V. Description of the invention (5) 2 if r < l.〇 (20) J ^ TG 〇 > 10 Furthermore, observe the formula (18), when r—1.0 (ie, #, G ~ G Since ... a, the damping ratio Γ is very small), then

Come two. If G is small, G can be used for Q ίϊ: i is still applicable. In addition, according to the Fourier: number input shock wave can be viewed as any periodic wave, not necessarily harmonic [Embodiment] To organize the theoretical background, the implementation of this creation is mainly to test the system to a known The periodic harmonic is excited, and the sensor (71) is used to capture the input signal (54), refer to Figure 1. On the other hand, when the system under test is excited ((54), its response signal (55) , Can be captured by another sensor (72). Next, you can use software or circuit hardware to process according to Figure 2 or the method of this creation. Figure 3 and Figure 4 are the experimental signals during the development of this creation. The enlarged diagram of the example, in which Figure 3 is the signal via circuit 54 6061; Figure 4 is the same signal but processed by circuit 54_62_63. In addition, since the measurement method of this creation is performed in the time domain, it can be performed immediately Measurement, real-time display, Figure 5 illustrates the concept of real-time measurement in this creation. Assume that after time L, a measurement is performed at a certain time u, and according to the sampling speed A t of the experiment, as long as the next sampling time (12 27 ^ + ^ Ί ΙΗ Page 12 1220923 V. Description of the invention (6) △ t), according to this creation, the next cycle of measurement can be performed. That is, all the signal circuits of Figure 1 are completed every △ t, and the output is displayed on the screen. Therefore, this creation can achieve the measurement of the damping ratio continuously and in real time. However, the above mentioned are only examples of the best implementation of this creation and should not be used to limit the scope of this creation. = Patent 范 ® 作 之 均 # Variations and modifications should all be within the scope of this creative book ::: 'I would like to invite the reviewing committee to make a clear reference, and pray for your approval. It is a simple illustration of the 1220923 diagram. A block diagram of the damping ratio measurement process of this creation. Figure 2 A block diagram of signal processing of the damping ratio measurement method of this creation. Fig. 3 An enlarged schematic diagram of the signal processed by the circuit 5 4-6 0-61 in this embodiment of the creation. Figure 4 The enlarged schematic diagram of the signal processed by the circuit 54- 62-63 in this creative embodiment. Figure 5 The conceptual illustration of the implementation of the continuous measurement method in this creative embodiment. Figure No. Description: 50 Reference datum or fixed surface of the system 51 System mass 52 System damping 53 System stiffness 54 m Induced vibration signal 55 System output response signal 60 Product modulation processing 61 Low-pass filtering processing 62 Signal phase shift processing 63 Product modulation processing 64 Low-pass filtering 65 Signal multiplication and division Process 66 Calculate process 71 according to the formula provided by this creation 71 Sensor 72 Sensor Ω Input frequency g (t) of the excitation signal Signal after product modulation processing

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Claims (1)

1220923 VI. Scope of Patent Application [Patent Scope] 1. A method for measuring or detecting the damping ratio of a continuous measurement system, which excites the system with a sine wave or periodic wave signal, measures the response signal of the system, and then responds to the signal Perform product modulation with the excitation signal and the 90 ° phase-shifted excitation signal, respectively, and perform low-pass processing, respectively, extract the DC levels of the two signals after the product modulation, calculate the ratio, and substitute the following formula to calculate (R2 ± ”r4 4G2a — r2) The meanings of the symbols in the formula are: · ζ * · damping ratio of the system under test; Γ: ratio of the frequency of the excitation signal to the natural frequency of the system; G: product adjustment DC level ratio of variable signal. 2. The measurement or detection method of the damping ratio of the continuous measurement system, as described in item 1 of the scope of the patent application, can display the results immediately, which can achieve the function of instant measurement or monitoring. Page 15