JPS5827025A - Method and apparatus for analyzing vibration - Google Patents

Abstract

PURPOSE:To improve analysis processing efficiency, in the vibration analysis of structures, by combining the fundamental characteristics obtained as a static deformation mode and a natural vibration mode of the structure of a part of portion thereof, and further computing a frequency response as the natural vibration mode. CONSTITUTION:To a computer 11 which performs the vibration analysis of the structure, an input device 12 and diskd 13 and 14 as memory devices are connected. A display device 15 and a plotter 16 and a line printer 17 as recording devices are provided. In the disk 13, the dimensions such as the sizes and material quality of the structures of the parts or portions constituting a machine are stored. In the disk 14, the following programs are stored: a program which computes the static deformation mode and the natural vibration modes as the fundamental characteristics for every part by using the dimensions of each part stored in the disk 13; a program which combines the fundamental characteristics of the individual parts and computes the vibration characteistics of the entire machine; and a program which displays and rcords the result of the computation. By using said method and device, the fundamental characteristics of the parts and the vibration characteristics of the machine can be efficiently analyzed.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a vibration analysis method and a vibration analysis apparatus for analyzing vibration characteristics of a machine.

When developing a new machine or making a model change, it is customary in many cases to go through a prototyping process. That is, after designing a machine based on a new concept, parts are manufactured, assembled, and various tests are performed. The content of the test covers a wide range of areas, including performance, functionality, and reliability. If the test results are satisfactory, the prototype will be completed. Conversely, if the test results are not satisfactory, the parts are improved and the test is conducted again. This operation is repeated until the various test results satisfy their respective target values. Prototyping is rarely achieved in one go; rather, it is often the case that improvements are made and repeated tests are conducted. If satisfactory test results are obtained, the specifications and specifications in that case are determined to be appropriate values, and then the production of the final parts begins.

In particular, economical design is being strongly promoted in recent machines.
Along with this, ensuring reliability has become even more important than before. Specific measures for economic design include:
While making the machine more compact or using thinner structural members to save on the amount of materials used, the problem with reliability is that the machine becomes susceptible to vibration.

Therefore, the reliability of the machine against vibrations, that is, the dynamic reliability, is one of the most important items to be confirmed through trial production, and thorough vibration measurements and studies are performed through trial production.

Even in the case of prototypes intended to ensure dynamic reliability, vibration tests are conducted after assembling the parts to determine the vibration amplitude.

Until vibration characteristics such as natural frequency 9 and frequency response characteristics satisfy target values, improvements, assemblies, and tests of parts are repeated 7. In particular, if the prototype is large-scale or small but has a complicated shape, it will require multi-point vibration measurement, which may require a large-scale vibration measurement device or require a large amount of expense and man-hours. be forced to spend. The result is inconveniences such as an increase in the cost of human resources and a delay in the development period.

Furthermore, when developing a new machine or making a model change to a machine, vibration analysis is often performed at the design stage to ensure reliability after the machine is installed. Recently, with advances in computers and numerical analysis methods, it has become increasingly common to use calculations to predict machine vibrations and to ensure machine reliability at the design stage. However, when aiming for economical design by increasing the capacity of a single machine, the structural scale of the machine naturally increases, and even if a computer is used, a huge amount of calculation time is spent on vibration analysis, or the calculation scale is too large. I have often experienced situations where it is impossible to analyze because it is too thick. The reason for this is that, as seen in conventional analysis methods such as the finite element method, transfer matrix, and IJ Socs method, the machines to be analyzed are handled as a group, resulting in a very large calculation scale. As a result, the smooth progress of design work was significantly impaired, such as increased design costs and uncertainty about ensuring dynamic reliability.

SUMMARY OF THE INVENTION The object of the present invention is to provide a vibration solution method and a vibration analysis device that help eliminate the above-mentioned drawbacks regarding vibration testing and vibration analysis of machines.

The present invention first focuses on parts or substructures constituting a machine.
The basic characteristics of a structure are calculated or measured as the natural vibration mode and the static deformation mode when a static external force is applied, and then the basic characteristics of each part (or partial structure) are combined (synthesized). This invention realizes a vibration analysis method and a vibration analysis device that calculate the vibration characteristics of the entire machine.

An embodiment of the vibration analysis method according to the present invention will be described with reference to FIGS. 1 to 6. FIG. 1 shows the procedure for performing vibration analysis of a machine according to the present invention. Figure 2~
FIG. 6 is a diagram illustrating each content of the present invention in principle, using a beam fixed at both ends as an example of the object of analysis instead of a complicated machine for the purpose of simplifying the explanation.

As shown in FIGS. 2 and 3, it is assumed that a beam 1 fixed at both ends to be analyzed consists of partial structures 2 and 3 as cantilever beams. It is assumed that the cantilever beams 2 and 3 are rigidly connected by welding or the like at both end points (boundary points) 4 and 5, and as a result constitute the beam 1 fixed at both ends.

An embodiment of this vibration analysis method will be described in accordance with the work procedure shown in FIG. 1 while using FIGS. 2 to 6.

(A) First, two types of static deformation modes are determined for the partial structure before assembly. The principle of how to find it is shown in Figure 4. One is to apply a static force to the boundary points and calculate the unit displacement X = = l at boundary points 4 and 5, as shown in the upper part of Figure 4. This is the transformation mode when .

CB) Another static deformation mode is the deformation when a static moment is applied to the boundary points to generate unit local displacement q = 1 at boundary points 4 and 5, as shown in the lower part of Figure 44. mode. This static deformation mode is determined for all parts or all partial structures that make up the machine.

(Next, for the parts or partial structures that are still in the state before assembly, fix conditions are given to each boundary point, and the natural vibration mode at that time is determined. This natural vibration mode is used to configure the machine. Calculate all parts or all partial structures.

■ (a) ~ (The machine was assembled by combining (synthesizing) the basic characteristics (static deformation mode and natural vibration mode) of all substructures obtained under the conditions such as 0. Calculation is performed to find the natural vibration mode assuming that .The principle of this calculation will be described later, but in the present invention, this method is referred to as a mode synthesis method or mode synthesis calculation.

When calculating this mode synthesis, coordinate transformation is performed to match the cohesive relationship between each part or substructure.
Combining (synthesizing) the basic characteristics of each part or substructure.

[F] Perform calculations to determine the frequency response of the machine based on the natural vibration mode of the machine to be analyzed obtained as a result of the 0-term mode synthesis calculation. The calculation principle for determining the frequency response from the natural vibration modes is clear from the references and can be easily achieved.

[F] Based on the calculation results of the natural vibration mode in the term, perform calculations to obtain the transient response of the machine. The calculation principle for determining the transient response from the natural vibration mode is also clear from the reference literature.

References include J, 13athe, E, I, Wilson, translated by Kikuchi: Numerical calculation of the finite element method, pages 345-386 (Science and Technology Publishing, published September 1979). ) The calculation principle for deriving the natural vibration mode of the machine from the basic characteristics (static deformation mode and natural vibration mode) is shown. In the present invention, this method is abbreviated as the keyed synthesis method.

It is assumed that a machine consists of a finite number of parts or a finite number of partial structures. The static stiffness equation can be written as follows.

In equation (1), B is a boundary displacement (displacement at a point where it connects to another part), and ■ is a symbol representing internal displacement. [k]
(r), [01(r), and ff1(r) are the rigidity of the component (or partial structure) r, the IJ lux displacement vector, and the external force vector, respectively.

The static deformation mode [φCIr) of the aforementioned part (or partial structure) is expressed as f f 1(r) in equation (1).
By setting −fo 1, [φCXr)=−(k”l)−′(r)CkIB](r
) -...-(21) This static deformation mode [φC)(r) is a matrix. [φ
Each column of C'Xr) is the amount of change in internal displacement when the displacement of each corresponding boundary point is changed by a unit amount.

Now, regarding the above-mentioned natural vibration mode, boundary displacement is defined as the natural vibration mode of free vibration for any boundary condition (completely fixed or free condition). Generally, when a part (or partial structure) is a continuous elastic body, there are theoretically an infinite number of natural vibration modes, but in this solution, a finite number of natural vibration modes up to the P order are considered. The matrix in which these P natural vibration modes are arranged in a row is [
Here, [φ](r) will be referred to as the natural vibration mode.

In the mode synthesis method, the generalized coordinate vector (p”1(
Using r) and (qN)(r), the displacement vector (II 1(r) of the part (or partial structure) is divided into boundary displacement and internal displacement and expressed as follows.

However, [IB] in equation (3) is a unit matrix corresponding to the boundary displacement.

From equation (3), (u BJ(r)=I p Bl(r)+[φB)(
r) (q N1(r) -------・(4) is derived, but in general [φB](r) = CO,], so I u ' 1(r) - (p Bl(r) This relationship is a very useful property when creating calculation programs.

If we transform equation (4), we get (pBl(r) = (uBl(r) - [φJr)fqN)
(r)...-(51.

The following equation is further derived from equation (3).

(u')(r)=[φC](r)(pBl(r)+[φ
■Xr)(qN)(r) ・+61 Substituting the relationship in equation (5) to (p B)(r) on the right side of equation (6), the following equation is obtained.

(IJ ■) (r) − [φC) (r) (uB) (r) +
[φ”E(qN)(r)−17) Here, CφNH=[φ” 1r)−[φC](r)[φBIr
) ---・-181. From equation (7), the internal displacement vector (tJ ■1 (rl is the boundary displacement vector (1
1B) (r) and the generalized coordinate vector (q N) (r) corresponding to the above-mentioned natural vibration mode [φ] (r). Therefore, equation (3) can be rewritten as follows.

Equation (9) is the final equation expressing the basic characteristics of the part (or partial structure), and is the basic equation of the mode synthesis method. The relationship obtained from equation (9) is calculated as (qB)(
r) = (tJ Bl(r) This is a very important property when creating a program. In other words, at the boundary point (connection point) of a part (or substructure), (tJBl(r)
, and (q N)(r) is not involved. Therefore, it is easy to combine the basic characteristics of each part (or partial structure) to determine the vibration characteristics of the entire machine system. This combination method is exactly the same as the conventional superposition method of the finite element method.

The equation of motion of each component (or partial structure) r in the mode synthesis method using Equation (9) is as follows.

CM: ] (r) ('q ] (Kyo CK: Xr) (ql (
r) - (Fl(r) -...-QQI Here, dot represents time differentiation, and T is a symbol indicating matrix transposition. [m] (r), Ck
)(r), (f 1(r) is the discretized mass matrix stiffness matrix and external force vector of the part (, S, u substructure) r. [N](r) and (
q )(r) is a symbol defined as follows in equation (9).

When the operating equations of the parts (or partial structures) in the mode synthesis method expressed by 200) are combined (superimposed) for the entire machine system, the following is obtained.

CM] C) + [K] (q) - (F) ・・・・・・・・・
...0(a)here,(q),CM,,[:K),(F
) are the generalized coordinate vector, mass matrix, stiffness matrix, and external force vector of the entire machine system, respectively, which are mode-synthesized.

The eigenvalue problem for finding the natural frequency and natural vibration mode of the machine is as follows, if (F')-(0) (q)=fφ)el"1 is set in equation (14).

[K] (φ) = ω2 [M] (φ) ・・・・・・・・・
...(ω and (φ) satisfying Equation 151 (+51) can be calculated as the natural frequency and natural vibration mode of the machine, respectively. The above are the equations related to the mode synthesis method.

In Fig. 5, when determining the natural vibration mode as a basic characteristic of a part or substructure, a fixed condition is given to the boundary points. The solution shown in Figure 1 holds true even in mode.

The effects of adopting the embodiment shown in FIG. 1 are as follows.

0) In order to carry out vibration analysis of a machine in two stages: first determining the basic characteristics of the parts or substructures, and then combining them to determine the vibration characteristics of the entire machine, it is necessary to measure each characteristic.・It has the advantage of reducing the scale of calculations and making it easier to perform vibration analysis of large-scale machines.

(b) For vibration analysis of machines in which multiple identical parts or substructures are arranged periodically, it is only necessary to obtain the basic characteristics of one part or substructure. It is possible to streamline the vibration analysis of various types of machines.

(c) As a result of finding the basic characteristics of the part or partial structure (static deformation mode and natural vibration mode) and the natural vibration mode of the machine, by comparing them, you can quickly solve vibration problems with the machine. It becomes easy to catch the problem and find countermeasures.

Figure 7 shows another embodiment of the present invention in which the starting point of vibration analysis is to obtain all the basic characteristics (static deformation mode and natural vibration mode) of the parts or substructures constituting the machine through actual measurements. . If the basic characteristics of a part or substructure are measured many times and there are variations or there are few measurement points, use the least squares method to express the static deformation mode or natural vibration mode of the part or substructure. It is also possible to obtain an approximate function and use the result for synthetic calculations.

According to the embodiment shown in FIG. 7, the following effects can be expected.

(b) The basic properties of a part or substructure (the static deformation mode and the natural vibration morton) are determined by actual measurement as the starting point for analysis. It is possible to improve the accuracy of machine vibration prediction.

(b) The vibration characteristics of assembled machines can be predicted based on the basic characteristics (static deformation mode and natural vibration mode) of parts or substructures, so it is possible to measure vibrations after assembling the machine. Particularly in the case of large-scale machines, the work of assembling the machine and measuring the vibration of the machine after assembly requires a huge amount of man-hours, so these tasks can be omitted. The fact that this can be omitted has the effect of significantly reducing the development costs for machines in the prototype stage and the costs required for inspection for machines in the production stage.

(c) The effect of being able to omit machine vibration testing is not only in saving man hours. That is, according to the present invention, since the measurement work is limited to structurally small components or substructures, a small-scale measuring device is sufficient, which also has the effect of preventing the introduction of expensive large-scale measuring devices. .

2) If the results of vibration testing on a machine do not yield satisfactory vibration characteristics, it is a matter of course that improvement measures must be taken. In such cases, if you tabulate the modified part (or substructure) and measure its basic characteristics, you can use the already measured data to measure the basic properties of other parts (or substructures). Therefore, it is easy to predict the vibration of a machine assuming that a modified part has been installed. In other words, it is possible to limit the work related to improving the vibration characteristics of the machine to a minimum of creating a parts list and measuring, and the work related to vibration testing can be streamlined.

Next, still another embodiment of the present invention is shown in FIG. The example shown in Fig. 8 calculates the basic characteristics (static deformation mode and natural vibration mode) of all the parts that make up the machine, and then combines the basic characteristics of each part obtained by calculation to create the entire machine. This is a method for calculating vibration characteristics.

The basic characteristics of the parts in the embodiment shown in FIG. 8 are calculated using the finite element method or transfer matrix method, which is well known in the field of vibration analysis.

Since this method processes all work by calculation, it is possible to predict the vibration of the machine assuming the completion of surface machining at the design stage prior to machine surface machining. The ability to predict vibrations even without the physical presence of the machine means that effective designs can be made to ensure reliability. In other words, as a result of being able to easily carry out so-called parameter surveys, which investigate how the vibrations of a machine will occur when the dimensions of parts are changed in various ways, it is possible to prevent design defects and to avoid artifacts in defective products. Demonstrates the effect of preventing.

Furthermore, the advantage of the embodiment shown in FIG. 8 is added. When performing vibration analysis of a machine using the finite element method or transfer matrix method, conventional methods treat the machines to be analyzed as one unit for calculation purposes, which may seem convenient at first glance, but in reality, it is difficult to perform calculations. As the scale increases, even if a computer is used, it will take a huge amount of calculation time, or
Alternatively, calculations may become impossible on a small-scale computer.According to the embodiment shown in Fig. 8, the vibration characteristics of the entire machine are calculated in order to pre-calculate the basic i-characteristics of each component, which requires a small calculation scale. In this case, the amount of information used in the calculation can be compressed, so the calculation time can be reduced compared to conventional methods, and it is also possible to analyze large-scale machines that cannot be handled with conventional methods. becomes.

Also, according to the implementation of FIG. 8, it is integrated,
It is effective for vibration analysis of mechanical structures that cannot be actually divided. Examples of such mechanical structures include towers, tanks, casings, etc. For vibration analysis of this type of mechanical structure, the object to be analyzed is virtually divided into a finite number of substructures based on the design drawing, and the basic characteristics of each of the virtually divided substructures are calculated. , and by performing calculations that combine these, vibration analysis of the original mechanical structure can be achieved.

Furthermore, another embodiment of the present invention will be described based on FIG. The embodiment shown in FIG. 7 shows a method in which the basic characteristics (static deformation mode and natural vibration mode) of all parts or partial structures are obtained by actual measurement. Further, the embodiment shown in FIG. 8 is a method in which the basic characteristics of all parts or partial structures are determined by calculation. On the other hand, the method shown in FIG. 9 is a vibration analysis method that starts by actually measuring the basic characteristics of a certain part and calculating the basic characteristics of other parts.

For the sake of explanation, the two parts that make up the machine are given part number 2 as Z=1.2. -・", L, L+1.--, Z are attached. In this example, Z=1.2......, the basic characteristics of the L parts were determined by actual measurements, Z=L+1.L+2
This is a method of calculating the vibration characteristics of the machine by combining two types of basic characteristics, using the calculated basic characteristics for the parts of ゜..., Z. The arithmetic processing after determining the basic characteristics of each component by actual measurement and calculation is the same as the method explained in the embodiment of FIG.

Depending on the shape and configuration of the parts that make up the machine and the scale and performance of the measuring equipment, there are some parts where it is easier to actually measure the basic characteristics, and others where it is more convenient to rely on calculations. There is something. According to the principles of the present invention, machine vibration analysis can be achieved regardless of the means used to determine the basic characteristics of the parts. All you have to do is find the basic characteristics of. The flexibility of being able to analyze vibrations of machines regardless of the means for determining the basic characteristics of parts means that the present invention can be widely applied.

As a method for calculating the basic characteristics of a component, a method suitable for the vibration analysis of each component may be selected from among methods commonly used in conventional vibration analysis, such as the finite element method or the transfer matrix method.

Further, the embodiment shown in FIG. 9 is effective in improving the vibration characteristics of a machine. In other words, if the vibration characteristics of the machine determined by the method of the example shown in FIG. During the design phase of the change,
Since you can predict the effects after corrections, you can streamline the work for improvement. For modified parts, basic characteristics may be calculated based on the design drawings, and for other parts, basic characteristics already obtained through actual measurements may be used. If the vibration characteristics of the machine predicted in this way are not acceptable, it means that the modifications to the part in question were not appropriate, and the design can be changed again. In other words, according to the embodiment shown in FIG. 9, it is easy to find the appropriate specifications or specifications at the design stage when parts need to be modified, without having to make a table of the original part for which the design has been changed. It is possible to prevent the display of parts that may not be present.

The embodiment shown in FIG. 7 shows a case in which the basic characteristics of a component are determined by actual measurement, and the embodiment shown in FIG. 8 shows a case in which the basic characteristics of a component are determined by calculation. In contrast to these methods, FIG. 10 shows a method according to another embodiment of the present invention in which the static deformation mode is calculated and the natural vibration mode is actually measured as a means for determining the basic characteristics of the component. Further, FIG. 11 shows a method of yet another embodiment in which the static deformation mode is determined by actual measurement and the natural vibration mode is determined by calculation, contrary to the method shown in FIG. 10. This method is useful when you want to perform vibration analysis of a machine based on actual measurement data for each component as much as possible, but only one of the basic characteristics of the component can be measured due to the equipment you have. It is effective as a means of coping. The vibration analysis method of the present invention includes all methods of determining the basic characteristics of a component, regardless of the means used to determine them.

When looking at the main parts of a machine, it is often the case that the machine itself consists of multiple parts. An example of a main component made by assembling a plurality of components is a casing for a rotating machine, which is made up of an upper lid and a lower lid. The present invention can be applied to such an analysis target, and the analysis target of the present invention includes not only a complete machine but also a partial structure of a machine consisting of a plurality of parts.

FIG. 12 shows a vibration analysis device that is based on the vibration analysis method of the present invention and is capable of consistently performing various tasks using a computer.

11 is computer, 12-17 is computer 1
1 is a peripheral device connected to 1, 12 is an input device, and 13 is a peripheral device connected to 1.
．． 14 is a disk as a storage device, 15 is a CRT as a display device, and 16.17 is a plotter and a line printer as recording devices.

The disk 13 stores specifications such as dimensions and materials of parts (or partial structures) that constitute the machine. The disk 14 is a program for calculating the basic characteristics (static deformation mode and natural vibration mode) of each part using the specifications of each part stored in the disk 13, and a program that synthesizes the basic characteristics of each part and calculates the machine. It contains a program to calculate the overall vibration characteristics and a program to display and record the calculation results.

If the vibration analysis device shown in FIG. 12 is used, the vibration characteristics of the machine can be calculated based on the specifications of the parts. In particular, it has the advantage of being able to efficiently and consistently calculate the basic characteristics of parts and the vibration characteristics of the machine from the specifications of the parts on the drawings using a single computer.

Figure 13 shows a vibration analysis device also according to the present invention, which includes a measuring device that detects the basic characteristics of parts (static deformation mode and natural vibration mode) and also measures the vibration characteristics of the machine based on the detected data. It is a system that performs calculations and processing consistently.

18 is a displacement pickup for detecting the static deformation mode of the component, 19 is a vibration pickup for detecting the natural vibration mode of the member, and 2o and 21 are amplifiers for the pickups 18 and 19, respectively. Reference numeral 22 is a data input device whose main element is an A-D converter, and displacement signals and vibration signals detected regarding the parts are captured via the data input device and computer 23 to a disk 24 as a storage device for data files. It will be done. 25 is also a disk as a storage device, which is used for various data processing described later.
It is used to store calculation and display programs. 26, 27 and 28 are respectively computer 23
The included CRT, plotter, and line printer.

There are three main programs stored on the disk 25 as shown below.

■ A data processing program that calculates the static deformation mode and natural vibration mode of each part based on multi-point measurement data about the part.

■ A synthetic calculation program that calculates the vibration characteristics of the entire machine by combining the static deformation mode and natural vibration mode of each part.

■ A program to display and record the basic characteristics of each part and the vibration characteristics of the entire machine.

In the device shown in Figure 13, one displacement pickup and one vibration pickup are used to measure the basic characteristics of the component, but it is easy to arrange multiple pickups to increase measurement efficiency. Therefore, the present invention does not depend on the scale of the measurement system. 4 According to the embodiment shown in FIG. 13, in one set of systems,
A major advantage is that it is possible to carry out the whole process from measuring parts to predicting the vibration characteristics of the machine.

[Brief explanation of drawings]

FIG. 1 is a flowchart showing a vibration analysis method for a structure which is an embodiment of the present invention, and FIGS. 2 to 6 are explanatory diagrams each illustrating a beam as an analysis object and providing a detailed explanation of the present invention.
7 to 11 are flowcharts showing vibration analysis methods for structures according to other embodiments of the present invention, and FIGS. 12 and 13 are configurations showing a vibration analysis apparatus for structures to which the present invention is applied. It is a diagram. Representative Patent Attorney Akio Takahashi Figure 7 Figure 8 Figure 9 Figure 1O Figure 11 Figure 12

Claims (1)

[Claims] 1. In vibration analysis of a structure consisting of multiple parts or partial structures, the basic characteristics of the parts or partial structures are first determined as static deformation modes and natural vibration modes, and then the parts or partial structures are determined as static deformation modes and natural vibration modes. Alternatively, the vibration characteristics of the structure are calculated as a natural vibration mode by combining the basic characteristics obtained for each partial structure, and the frequency response and transient response of the structure are further calculated using the vibration mode of the structure. A vibration analysis method for structures characterized by the following. 2. In claim 1, when determining the natural vibration mode of a certain part (or partial structure), the part (or partial structure) is coupled with another part (or partial structure), A vibration analysis method characterized by determining connected boundary points under fixed conditions and calculating handling characteristics of a structure based on the natural vibration modes thus obtained. 3. Claims In the first term of the range, when determining the natural vibration mode of a certain part (or substructure), the boundary point where the part (or substructure) is held or connected to another part (or substructure) A vibration analysis method characterized by calculating the vibration characteristics of a structure based on the natural vibration mode obtained under conditions of mechanical freedom. 4. Claim 1 In the vibration analysis method described in Section 1, the static deformation mode of a part (or substructure) is the static deformation mode when a unit displacement is applied to the boundary point where the part is held or connected to another part. , and a static deformation mode when a unit angular displacement is given to the same boundary point, and the vibration characteristics of a structure are calculated using both static deformation modes. 5. In the vibration analysis method set forth in claim 1 or 2 or 3 or 4, the basic characteristics (static deformation mode and natural vibration mode) of all parts (or partial structures) A vibration analysis method characterized by calculating the vibration characteristics of the entire structure by calculating the vibration characteristics of the entire structure by calculating the basic characteristics of all the actually measured parts (or partial structures).6. In the vibration analysis method in Scope 5, after actually measuring the static deformation mode and natural vibration mode of a component or substructure, the static deformation mode and natural vibration mode are calculated using the least squares method based on the measured data. A vibration analysis method characterized by calculating the vibration characteristics of a structure by determining approximate functions and finally combining all the approximate functions representing the basic characteristics of each part or external structure. 7. Claims In the vibration analysis method described in Section 1, the basic characteristics (static deformation mode and natural vibration mode) of all parts or substructures constituting the structure are calculated, and all calculated parts or substructures are A vibration analysis method, characterized in that the vibration characteristics of the entire structure are predicted by calculation by combining the basic characteristics of The basic characteristics (static deformation mode and natural vibration mode) of □ other parts (
A vibration analysis method characterized by calculating the basic characteristics of a partial structure (or partial structure) and predicting the vibration characteristics of the entire structure by combining the basic characteristics of all parts obtained through actual measurements or calculations. . 9. In the vibration analysis method according to claim 1, the static deformation mode of the component or partial structure is determined by actual measurement,
A vibration analysis method characterized by calculating the natural vibration mode. 10. In the vibration analysis method of claim 1,
A vibration analysis method characterized by calculating the static deformation mode of a component or partial structure and determining the natural vibration mode by actual measurement. 11. A storage device for storing specifications of parts or substructures constituting a structure, means for calculating static deformation modes and natural vibration modes that are the basic characteristics of the parts or substructures, and parts or parts. A vibration analysis characterized by comprising: a calculation device comprising means for calculating the vibration characteristics of the entire structure by combining basic characteristics of each structure; and a display device for displaying these specifications and the calculated vibration characteristics. Device.