JP2008145277A - Device and method for random vibration prediction of panel by dynamic mass technique - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform vibration prediction with prediction errors smaller than those in conventional two techniques of NASA technique and impedance technique, about random vibration of each device mounted on a panel without changing the prediction technique. <P>SOLUTION: The method of predicting the random vibration of an excited panel predicts the vibration on the assumption that the mass of the mounted device is uniformly distributed over a flat plate using the NASA technique about the panel on which devices other than the object device are mounted. An object device effect coefficient exhibiting attenuation effect of vibration due to the object device is then calculated on the assumption that the object device is an elastomer. The response of the panel on which the object device is mounted is calculated by multiplying the object device effect coefficient acquired on the assumption that the object device is the elastomer by the vibration prediction results of the panel on which the devices other than the object device are mounted. The vibration of the panel is precisely predicted without changing the prediction technique. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an apparatus and method for predicting random vibration when an acoustic load is applied to a panel constituting an artificial satellite in the field of artificial satellite design analysis.

Each spacecraft equipment is exposed to a severe high-frequency random vibration environment due to acoustic excitation of 130 dB or more when the rocket is launched. For this reason, it is necessary to design the on-board equipment using the random vibration level of each on-board equipment as a flight environment condition. Since these random vibration conditions are high-frequency responses of 2 kHz or less, prediction is usually performed by statistical energy analysis (SEA) (Non-patent Document 1).
Conventionally, the NASA method (Non-patent Document 2) assumes that the mass of the on-board equipment is uniformly distributed throughout the flat plate, and the impedance technique (Non-Patent Document 2) assumes that the on-board equipment acts on the satellite structure panel as a mass 3) etc., the vibration prediction of the satellite structure panel having the onboard equipment has been performed by statistical energy analysis.

Here, a method for predicting vibration of a panel on which a device is mounted by statistical energy analysis will be described.
The response of a flat plate not equipped with a device that is vibrated from both sides by a diffuse sound field can be predicted by the following equation by doubling the acoustic radiation efficiency on one side using a two-element SEA model of a diffuse sound field and a flat plate structure. .
(A1)
here,
<a ^2>: time and space root mean squared acceleration of the plate
<p ² >: Time-space mean square of square diffuse sound pressure ρ ₀ : Air density c ₀ : Air sound speed S: Plate area n ₂ : Plate mode density η ₂ : Plate loss coefficient σ _rad : Plate radiation Efficiency M: The mass of the flat plate.

(i) NASA Glenn Research Center method (Non-Patent Document 2)
The NASA method was developed at the NASA Glenn Research Center, assuming that the modal density and critical frequency of the flat plate are unchanged regardless of the presence or absence of the mounted device, and the device mass is uniformly applied to the flat plate. Assume that Acceleration when performing double-sided acoustic excitation with the device mounted is
(A2)
It becomes. Here, M is the panel mass, M _c is mounted equipment mass, the <a ^2> _L is the acceleration when the equipment there. The mode density n ₂ and the radiation efficiency σ _rad are calculated from the surface density when no equipment is mounted.

(ii) Impedance method (Non-patent Document 3)
The impedance method is a method using a partial structure synthesis method. As shown in FIG. 10, it is assumed that the mounted device m is coupled to the structure p that receives the external force F _d via the interface i. At this time, the force at the interface is F _i . Let Z _ii ^p and Z _ii ^m denote the mechanical impedance at i when p and m are not coupled under unconstrained conditions. If the transmission impedance of the external force application points d and i is Z _id ^p , the speeds of p and m at i are given by the following equation from the principle of superposition.
(A3)
(A4)

Since the speeds of p and m are the same at the interface point, equation (A5) can be obtained by equalizing equations (A3) and (A4).
(A5)

Next, let X _i0 ^p be the speed of p in i when there is no device m, and X _i0 ^p can be written by the following equation.
(A6)
Substituting F _i obtained by substituting equation (A6) into equation (A5) into equation (A3),
(A7)
It becomes. Expression (A7) is an expression that correlates the speed when p and m are combined with the speed when they are not combined.

When the structure p is a flat panel with no curvature and a high frequency where vibration is sufficiently diffused is considered, the impedance in the equation (A7) matches the infinite plate impedance. That is,
(A8)
It is. Here, m ^Λ is the panel surface density, D is the bending rigidity, M is the mass, and n is the mode density.

Next, assuming that the mounted device m is a rigid body, its impedance is expressed by equation (A9).
(A9)

Thus, it is possible to determine the acceleration <a ^2> _L when combined mounting device from the acceleration <a ^2> ₀ unbound state (A10) by the formula.
(A10)

NASA's method may result in an excess of 20 dB or more for devices with large mass and low response. Moreover, although the impedance method can be predicted for individual devices, since the on-board device is assumed to be a mass having a rigid mass, the prediction result tends to be too low at high frequencies. Therefore, conventionally, it was necessary to use these two methods properly depending on the frequency and device characteristics.
However, since there is no selection criterion for the two prediction methods, one method has been selected empirically from the two methods.

Lyon, R.H. and De Jong, R.G., Theory and Application of Statistical Energy Analysis (1995), Butterworth-Heinemann, New York McNelis, Mark E., A modified VAPEPS Method for Predicting Vibroacoustic Response of Unreinforced Mass Loaded Honeycomb Panels, NASA-TM-101467 (1989), p3 Ando, S., Shi, Q., the Prediction of Random Acoustic Vibration of Equipment Mounted on Honeycomb Panel, 5th ESA Aerospace Environmental Testing Symposium, Belgium (2005-6)

An object of the present invention is to perform vibration prediction with a small prediction error for random vibration of each device mounted on a panel.
Another object of the present invention is to perform random vibration prediction with a smaller prediction error than the conventional NASA method and impedance method without switching the prediction method.

In the present invention, a dynamic mass technique that focuses on the dynamic mass characteristics of the target on-board equipment is used.
The technique of the present invention is a combination of the impedance technique and the NASA technique. That is, it is assumed that the mounted devices other than the analysis target are uniformly distributed on the structure panel by the NASA method. Then, the mass of the target device to be analyzed is represented by dynamic mass, and a change in the vibration of the panel when the target device is mounted is given by an impedance method.
In the impedance method, mechanical resistance (F / V) representing the relationship between force (F) and velocity (V) was substituted into equation (A7) indicating the response relationship before and after mounting. In the present invention, “Apparent mass, dynamic inertia (F / A)” representing the relationship between force (F) and acceleration (A) is substituted.

The dynamic mass M￣ of the elastic body can be written by the following equation.
(1)
Here, M is the static mass of the elastic body, and m _ek and ζ _k are the effective mass and damping coefficient ratio of the k-th mode in the boundary condition where the elastic body is fixed at the coupling point (effective mass definition point), respectively. . Let ω _{k be} the natural frequency of the k-th mode and ω be the angular frequency. r _k is r _k = ω / ω _k , which is the normalized frequency.

Next, FIG. 1 illustrates the dynamic mass of an elastic body and a mass point. The static mass of the mass point is indicated by a dotted line. The static mass of the mass point is constant regardless of the frequency, and is the same value as the static mass with a frequency of 0 Hz. The dynamic mass of the elastic body is indicated by a solid line. Point A in the figure represents the dynamic mass at the primary natural frequency f ₀ . Since the dynamic mass is large at the frequency f ₀ , as can be seen from the equation (A7), the response at the device attachment point is greatly attenuated by the presence of the device. Further, point B in FIG. 1 is a primary resonance frequency, and the dynamic mass becomes small at this frequency, so that the response attenuation effect by the device at the device attachment point is low. As described above, the dynamic mass of the elastic body takes the same value as the static mass at the frequency of the primary natural frequency f ₀ or less without resonance, and at the frequency of the primary natural frequency f ₀ or more, the dynamic mass is the vibration. As the number increases, peaks and valleys appear alternately and decrease.

When considering a prediction method based on statistical energy analysis (SEA), it is necessary to obtain a frequency average of dynamic mass that varies with frequency. As for the frequency average, as will be described later, the following expression is obtained as an approximate solution of the frequency average of Expression (1) by Monte Carlo simulation.
(2-1)
Here, f ₀ is the primary natural frequency of the elastic body (the target device), and f is the frequency.

Next, equation (2-1) is used as the frequency-averaged dynamic mass of the mounted device. In the impedance method described above, elasticity is already considered in the structure p on which the device is mounted. For this reason, the dynamic mass obtained by taking the frequency average only for the mounted equipment is used. That is, replaced in the formula (A10), the onboard equipment mass M _c with the following equation.
(2-2)

  Furthermore, it is assumed that the mass other than the analysis target device, which was ignored in the impedance method, is uniformly distributed throughout the panel by the NASA method. In other words, the vibration when a device other than the analysis target device is mounted is obtained by the NASA method, and the vibration when the analysis target device is mounted is analyzed using the dynamic mass obtained by taking the frequency average of the target device. .

In this case, the total mass including the panel and the mounted device is M _tot , the device mass to be analyzed is M _c , and the mass of only the panel is M _p . In the formula (A10) for determining the acceleration by the impedance technique, using equation (2-2) as the mass M _c of the mounting device. Response <a ^2> _L of the analysis target device,

(3)
(Four)
It becomes.

In Equation (3), the mass is (M _tot -M _c ), assuming that the mass of devices other than the analysis target device is uniformly distributed throughout the panel using the NASA method. Because.
According to the equation (2-2), the equation (4) is divided into a case where the frequency is f <f _{0 and} a case where f ≧ f ₀ , and the target device influence coefficient g (ω ). The coefficient g (ω) is a term indicating a vibration reduction (attenuation) effect at the device attachment point due to the mounting of the target device, and is referred to as a target device influence coefficient in this specification.
Here, ω = 2πf and ω ₀ = 2πf ₀ .
By equation (3), vibration responses can be obtained individually for a plurality of devices having different masses and primary natural frequencies mounted on the same panel.

1 aspect of this invention is an apparatus which estimates the random vibration when the panel which mounts an apparatus is vibrated,
A storage device, an arithmetic device, an input device, and an output device;
The storage device
A program storage unit for storing the calculation formula;
A data storage unit for storing data of the panel and the mounted device;
A calculation result storage unit that stores a calculation result calculated by the calculation formula,
The arithmetic unit is:
NASA method calculation unit for calculating the vibration response of the panel mounted with a device other than the target device, assuming that the mass of the mounted device is uniformly distributed in the panel body,
A target device influence coefficient calculating unit that handles the target device as an elastic body and calculates a target device influence coefficient indicating a vibration reduction effect by mounting the target device;
The vibration of the target device is calculated by multiplying the vibration response of the panel mounted with the mounted device other than the target device calculated by the NASA method calculation unit by the target device influence coefficient calculated by the target device influence coefficient calculation unit. A predicted value calculation unit for calculating a predicted value,
It is a vibration prediction device that accurately predicts vibration of the target device.

  It is preferable that the target device influence coefficient calculation unit calculates a predicted vibration value using the dynamic mass of the target device.

  In a range where the frequency of the target device is smaller than the primary natural frequency of the target device, the dynamic mass of the target device is the same value as the static mass, and the frequency of the target device is higher than the primary natural frequency of the mounted device. In a large range, the predicted vibration value can be calculated assuming that the dynamic mass of the target device gradually decreases as the frequency of the target device increases.

The dynamic mass,
Where M _c is the dynamic mass, f ₀ is the primary natural frequency of the elastic body (the target device), f is the frequency,
As described above, the target device influence coefficient of the target device can be calculated.

Another aspect of the present invention is a method for predicting random vibration when a panel on which a device is mounted is vibrated,
a) For a panel with equipment other than the target equipment, calculate the vibration assuming that the mass of the equipment is evenly distributed on the panel,
b) Treat the target device as an elastic body, calculate the target device influence coefficient indicating the vibration reduction effect by mounting the target device,
c) A step of calculating a predicted vibration value of the target device by multiplying the result of calculating the vibration of the panel on which the device other than the target device is mounted in step a) by the target device influence coefficient obtained in step b). This is a vibration prediction method for accurately predicting the vibration of a panel provided with.

Conventionally, when predicting random vibration of a device attached to a panel, it has been necessary to switch the prediction method depending on the frequency and device characteristics.
In the present invention, random vibration can be predicted without switching the prediction method by using the dynamic mass method focusing on the dynamic mass characteristics of the device. In addition, it is possible to predict random vibration with higher accuracy than the two conventional methods.
Therefore, it is possible to contribute to design efficiency and cost reduction.

Embodiments of the present invention will be described below.
An acoustic vibration test was conducted on nine actual satellites (the total number of onboard equipment was 385). In addition, vibration prediction was performed by the dynamic mass method, NASA method, and impedance method of the present invention, and the vibration test result was compared with the vibration prediction result.

The frequency design rule for random vibration by acoustic excitation of the on-board equipment is 20Hz to 2kHz. Further, it is stipulated in the satellite machine design standard that the primary natural frequency f ₀ of the on-board equipment is 120 Hz or more. In the prediction method of the present invention, f ₀ of all the mounted devices is 100 Hz. In addition, since SEA used in the prediction method can be applied at the secondary natural frequency or higher, the vibration prediction was performed at the secondary natural frequency or higher of the satellite structure panel.
Vibration prediction at the attachment point of each on-board equipment was performed for each on-board equipment on each actual satellite by the prediction method of the present invention, the NASA technique, and the impedance method. Moreover, the vibration experiment of each mounted apparatus was conducted and the vibration at the attachment point of each mounted apparatus was measured. For each installed device, the vibration prediction results and vibration test results were compared, and the prediction errors of the three prediction methods were calculated.

Octave means double, and octave band (1/1 octave band) means a frequency range in which the higher frequency f _{2 in} the frequency band is twice the lower frequency f ₁ , that is, f ₂ / It is a range of two frequencies where f ₁ = 2. On the other hand, the ^1/3 octave band is two frequency ranges in which f ₂ / f ₁ = 2 ^1/3 = 1.25. These frequency bands are represented by a center frequency f ₀ = √ (f ₁ f ₂ ), which is a geometric mean of f ₂ and f ₁ .

When the prediction result at the 1/3 octave center frequency ω _i is L _p (ω _i ) (dB) and the acoustic test result is L _m (ω _i ) (dB), the prediction error e ￣ (ω _i ) (dB) Is defined as:
(Five)
here,
_{L p (ω i) = 10} × log 10 (<a 2> L / a 0 2), a 0 = 1.0m / s 2
It is.

FIG. 2 shows the result of calculating the prediction error at each frequency and calculating the average prediction error at the center frequency of 1/3 octave band from 100 Hz to 2000 Hz for each on-board device using Equation (5).
From FIG. 2, it can be seen that the vibration prediction result using the dynamic mass method of the present invention has a smaller prediction error than the prediction result using the impedance method and NASA method in 160 Hz to 1250 Hz, which is the main band of the on-board equipment. Above 1250 Hz, the NASA method has a smaller prediction error than the dynamic mass method of the present invention, but the difference is about 3 dB at the maximum. Moreover, although the impedance method tends to have a large prediction error in the high frequency band, it can be seen that the dynamic mass method of the present invention does not have such a problem.
From the above, it was shown that the dynamic mass method of the present invention has a smaller prediction error than the conventional impedance method and the NASA method, and it is not necessary to selectively use the prediction method in an important frequency band.

Block Diagram FIG . 3 is a block diagram of an apparatus for automatically selecting the panel vibration prediction method of the present invention. The apparatus includes a central processing unit 20, an arithmetic unit 21, a storage device 28, an input device 32, and an output device 33.

The storage device 28 includes a program storage unit 29, a data storage unit 30, and a calculation result storage unit 31.
The program storage unit 29 of the storage device 28 stores calculation formulas such as formulas (A1) to (A10) and formulas (1) to (4). The data storage unit 30 stores data such as panel dimensions, mass, device mass, and the like input from the input device 32. The calculation result storage unit 31 stores vibration prediction results and the like that have been calculated by the arithmetic unit 22 using the expressions (A1) to (A10) and the expressions (1) to (4).

The arithmetic device 21 includes a NASA technique calculation unit 22, a target device influence coefficient calculation unit 23, and a predicted value calculation unit 24.
The NASA method calculation unit 22 calculates the vibration response of the panel when a device other than the target device is mounted by the NASA method using the equation (A2).
The target device influence coefficient calculation unit 23 calls the equation (4) from the program storage unit 29 according to the command of the central processing unit 20, and according to the equation (4), classifies according to whether ω is smaller than ω ₀ , Calculate the coefficient g (ω).
The predicted value calculation unit 24 calls the equation (3) from the program storage unit 29 according to the instruction of the central processing unit 20, and the target device influence coefficient g obtained by using the equation (4) in the target device influence coefficient calculation unit 23. Substituting (ω) into equation (3), the predicted value of vibration of the target device is calculated.

The input device 32 is a known input device such as a keyboard, and is used to input the area and circumference of the panel and the area and circumference of all the mounted devices.
The output device 33 is a known display device such as a display, or a printing device such as a printer, and displays or prints out a panel random vibration prediction result.

Flowchart 4 is a flow chart of a method of vibration predicted panel by dynamic weighing method of the present invention.
In this method, in step S01, the input device 32 inputs data necessary for calculation such as panel size, mass, and total weight of all mounted devices.
In step S02, the central processing unit 20 commands the start of prediction of the mounted device j.
In step S03, the input device 32, inputs the mass M _cj primary natural frequency omega ₀ of the mounting device j.

In step S04, the mass M _cj of the target mounted device is subtracted from the total mass M _{tot of the} panel, and the response of the panel having the mass M _tot −M _cj is calculated by the NASA method using equation (A2).
In step S05, the central processing unit 20 commands the start of vibration prediction at the frequency ω _i .
In step S06, it is determined whether or not the primary natural frequency ω ₀ of the mounted device j is greater than ω _i . If ω ₀ is equal to or smaller than ω _i , the process proceeds to step S07, and the target device vibration g (ω) when ω _i > ω ₀ is calculated by equation (4).
Next, the process proceeds to step S08, where g (ω) is multiplied by the NASA method result obtained by equation (A2) in step S04, and the vibration predicted value at frequency ω _i is obtained by equation (3) and calculated. Store in the result storage unit 31.

If ω ₀ is larger than ω _{i in} step S06, the process proceeds to step S09, and g (ω) in the case of ω _i <ω ₀ is calculated by equation (4).
Next, the process proceeds to step S10, where g (ω) is multiplied by the result obtained by the NASA method obtained in step S04, and a vibration predicted value at the frequency ω _i is obtained by equation (3) and stored in the calculation result storage unit 31. To do.

The process proceeds from step S08 or step S10 to step S11. In step S11, it is determined whether or not the calculation has been completed for all frequencies. If not completed, i = i + 1 is set in step S12, the process returns to step S05, and the predicted calculation of vibration at the next frequency ω (i + 1) is performed for the mounted device j.
If the calculation of the predicted vibration values at all frequencies is completed in step S11, the process proceeds to the next step S13.

In step S13, it is determined whether or not the prediction of all the mounted devices that need prediction is completed. If not finished, j = j + 1 is set in step S14, the process returns to step S02, and the prediction of the next mounted device j + 1 is started.
In step S13, when prediction of all the mounted devices is completed, the process proceeds to the next step S15.
In step S15, the predicted vibration value stored in the calculation result storage unit 31 is output to the output device 33. The output can be displayed on a display or printed out by a printer.

Two vibration prediction methods, the NASA method and the impedance method, are incorporated in an acoustic vibration analysis system such as an artificial satellite (JANET, JAXA Acoustic Analysis Network System). A device in which the dynamic mass prediction method according to the present invention was added to the JANET system was created.
Fig. 5 shows a schematic diagram of the JANET system. Using this apparatus, a predicted value of vibration was obtained and compared with the experimental result of vibration.

  FIG. 6 shows a schematic diagram of the satellite vibration experiment apparatus 41. A panel 42 equipped with a satellite or equipment is placed in an experimental apparatus, and high-frequency acoustic vibration is applied with high sound pressure. For example, the acoustic vibration is 140 dB and the frequency is 11 kHz or less. The vibration response of the panel equipped with the equipment at this time is measured.

FIG. 7 shows an experiment of acoustic vibration at a 1/3 octave center frequency when the mounted device A1 (mass 22 kg) was mounted on the panel as Example 1 of the present invention, and the vibration of the mounted device A1 was measured. . In addition, vibration prediction was performed on the mounted device A1 using the dynamic mass method, the NASA method, and the impedance method of the present invention at a 1/3 octave center frequency. The result which compared the vibration prediction result and the vibration experiment result is shown.
The prediction result by the impedance method is close to the vibration experiment result near the frequency of 200 Hz, but becomes farther from the vibration experiment result as the frequency increases. The prediction result by the NASA method is close to the vibration experiment result near the frequency of 2000 Hz, but is far from the vibration experiment result at a lower frequency. It can be seen that the prediction result by the dynamic mass method of the present invention is close to the vibration experiment result over the entire frequency range of 200 Hz to 2000 Hz.

FIG. 8 shows a vibration prediction result when another mounting device B (mass 35 kg) is mounted on another panel as Example 2 of the present invention. FIG. 9 shows a vibration prediction result when another mounting device C (mass 9 kg) is mounted on another panel as Example 3 of the present invention. Table 1 shows the conditions of the panels and mounted devices used in Examples 1 to 3.
7 to 9, the predicted vibration value calculated using the dynamic mass method of the present invention is compared with the case predicted using the NASA method and impedance method, regardless of the panel conditions and the mass of the target device. Thus, it can be seen that it is close to the vibration experiment result.

Table 1

(Verification of validity of frequency average value of dynamic mass)
In the following, it is verified by Monte Carlo simulation that the frequency average of dynamic mass shown in Equation (2-2) holds widely for elastic bodies.
(B-1)
Here, f ₀ is the primary natural frequency of the elastic body, and f is the frequency.

Consider a system of N degrees of freedom connected in series as shown in FIG. m _i (i = 1, 2,..., N) is the i-th mass, and k _i and c _i are the spring constant of the spring on the left side of the i-th mass and the damp pot damping coefficient, respectively.
In this N-degree-of-freedom system, the mass m ₁ is vibrated by the force f, and the acceleration U is observed at the vibration point. At this time, the dynamic mass of the N-degree-of-freedom system is
It is.

In order to confirm that the equations (2-2) and ((B-1)), which are frequency average values of dynamic masses, are satisfied for various structures, all the masses m _i and spring constants k _i Monte Carlo simulations were given, giving uniform random variables independent of each other. Table B-1 shows the conditions for Monte Carlo simulation. We generated 500 50-degree-of-freedom systems with random variables and calculated their dynamic masses. The attenuation was calculated by changing the attenuation coefficient ratio ζ to 1%, 5%, and 10%.

Table B-1 Monte Carlo simulation conditions
12 to 14 show dynamic mass calculation results when the damping coefficient ratio ζ is 1%, 5%, and 10%. The horizontal axis of the figure is the frequency normalized by the primary natural frequency at the time of base excitation of the N-degree-of-freedom system. The normalized frequency was calculated up to 70 with a step size of 0.2. The vertical axis in the figure represents the dynamic mass obtained by normalizing the dynamic mass with the total mass of the N-degree-of-freedom system. The following is considered from the calculation results of the dynamic mass.

1) FIGS. 12 to 14 show 500 N-degree-of-freedom dynamic masses overwritten. The higher the frequency, the greater the variation in the dynamic mass peak and valley frequency. This indicates that the higher the frequency, the more random the structure.
2) Regardless of the damping coefficient ratio, the dynamic mass fluctuates around the formula (B-1) when the normalized frequency is 1 or more.
3) As the damping coefficient ratio increases, the resonance peak is suppressed, so the dynamic mass is close to equation (B-1).
4) The dynamic mass peak at normalized frequency 1 is the resonance frequency when the excitation point of the N-degree-of-freedom system is fixed. The smaller the damping coefficient ratio, the larger the value is approximately 1 / (2ζ). .
From the above, it is considered that Equation (B-1) closely approximates the frequency average value of dynamic mass that varies with frequency.

Therefore, consider the frequency average of dynamic mass. With respect to the normalized frequency, a 1 / n octave band having a center frequency 2 ^{i / n} having a band interval [2 ^{i / n−1 / 2n} , 2 ^{i / n + 1 / 2n} ] is introduced, where i is an integer. For the dynamic mass of 500 N-degree-of-freedom systems when the damping coefficient ratio ζ is 1%, 5%, and 10%, 1/1 octave band frequency average and ensemble average (N-degree of freedom individual average) The result of having performed is shown in FIG. It can be seen that above the secondary natural frequency, the average value of dynamic mass is in good agreement with equation (B-1).
From the above Monte Carlo simulation results, it can be seen that Equation (B-1) gives a good approximation of the frequency average value of the dynamic mass of various actual structures.

INDUSTRIAL APPLICABILITY The present invention can be used for design and analysis related to random vibration of a panel in the space industry, particularly under the acoustic excitation of an artificial satellite.
In addition, it can be used to predict the vibration level of a structure in which equipment is mounted on a panel, even outside the space industry.

The figure showing the dynamic mass of an elastic body and a mass point. The figure which shows 1/3 octave band center frequency and a prediction error. The block diagram of the vibration prediction apparatus of the panel by this invention. The flowchart of the vibration prediction method using the dynamic mass method by this invention. The block diagram of acoustic vibration analysis systems, such as an artificial satellite. Schematic of a satellite vibration experiment apparatus. The figure which shows the vibration prediction result and vibration experiment result by Example 1 of this invention. The figure which shows the vibration prediction result by Example 2 of this invention, and a vibration experiment result. The figure which shows the specification at the time of the vibration prediction result by Example 3 of this invention, a vibration experiment result, and a design. The conceptual diagram which shows the partial structure synthesis method. The conceptual diagram of the N degrees-of-freedom system connected in series. Dynamic mass calculation result when the damping coefficient ratio ζ is 1%. Dynamic mass calculation result when the damping coefficient ratio ζ is 5%. Dynamic mass calculation result when the damping coefficient ratio ζ is 10%. Calculation results of dynamic mass frequency and average between individuals.

Explanation of symbols

20 Central processing unit
21 Arithmetic unit
22 NASA Method Calculator
23 Target equipment influence coefficient calculator
24 Predicted value calculation section
28 Storage device
29 Program storage
30 Data storage
31 Calculation result storage
32 input devices
33 Output device
41 Vibration test equipment
42 Panel with equipment

Claims (8)

A device for predicting random vibration when a panel on which equipment is mounted is vibrated,
A storage device, an arithmetic device, an input device, and an output device;
The storage device
A program storage unit for storing the calculation formula;
A data storage unit for storing data of the panel and the mounted device;
A calculation result storage unit that stores a calculation result calculated by the calculation formula,
The arithmetic unit is:
NASA method calculation unit for calculating the vibration response of the panel mounted with a device other than the target device, assuming that the mass of the mounted device is uniformly distributed in the panel body,
A target device influence coefficient calculating unit that handles the target device as an elastic body and calculates a target device influence coefficient indicating a vibration reduction effect by mounting the target device;
The vibration of the target device is calculated by multiplying the vibration response of the panel mounted with the mounted device other than the target device calculated by the NASA method calculation unit by the target device influence coefficient calculated by the target device influence coefficient calculation unit. A predicted value calculation unit for calculating a predicted value,
A vibration prediction apparatus for accurately predicting vibration of the target device.   The vibration prediction apparatus according to claim 1, wherein the target device influence coefficient calculation unit calculates a predicted vibration value using a dynamic mass of the target device.   3. The vibration prediction apparatus according to claim 2, wherein the dynamic mass of the target device is the same value as the static mass in a range where the frequency of the target device is smaller than the primary natural frequency of the target device, In a range in which the frequency of the target device is larger than the primary natural frequency of the mounted device, the predicted vibration value is calculated by assuming that the dynamic mass of the target device gradually decreases as the frequency of the target device increases. The vibration prediction apparatus according to claim 3, wherein the dynamic mass of the target device is
Where M _c is the dynamic mass, f ₀ is the primary natural frequency of the elastic body (the target device), f is the frequency,
As an apparatus for calculating the target device influence coefficient of the target device. A method for predicting random vibration when a panel on which equipment is mounted is vibrated,
a) For a panel with equipment other than the target equipment, calculate the vibration assuming that the mass of the equipment is evenly distributed on the panel,
b) Treat the target device as an elastic body, calculate the target device influence coefficient indicating the vibration reduction effect by mounting the target device,
c) A step of calculating a predicted vibration value of the target device by multiplying the result of calculating the vibration of the panel on which the device other than the target device is mounted in step a) by the target device influence coefficient obtained in step b). When,
A vibration prediction method characterized by accurately predicting vibrations of a panel comprising: The vibration prediction method according to claim 5,
In the step b), the target device influence coefficient is obtained by using dynamic mass as the mass of the target device. The vibration prediction method according to claim 6,
In a range where the frequency of the target device is smaller than the primary natural frequency of the target device, the dynamic mass of the target device is the same value as the static mass, and the frequency of the target device is higher than the primary natural frequency of the mounted device. A method of calculating a predicted vibration value assuming that the dynamic mass of the target device gradually decreases as the frequency of the target device increases in a large range. The vibration prediction method according to claim 7, wherein the dynamic mass of the target device is
Where M _c is the dynamic mass, f ₀ is the primary natural frequency of the elastic body (the target device), f is the frequency,
As a method for calculating the target device influence coefficient of the target device.