JPH02134531A - Measurement of characteristic vector of vibration - Google Patents

Abstract

PURPOSE:To make it possible to obtain an angular displacement component by an excitation test using only a vibration detector by differentiating the interpolation function of the displacement component of the characteristic vector of vibration which is measured at a discontinuous measuring point, and obtaining the angular displacement component. CONSTITUTION:Vibration detectors are provided at a plurality of places on a material to be measured. The interpolation curve of the maximum value of the displacement components of the characteristic vectors of the vibrations which are obtained with said vibration detectors is a continuous curve. Therefore, the displacement component at an arbitrary point is obtained as the function of the direction where the vibration detector is provided. Then, the interpolation curve for every natural frequency is differentiated, and the interpolation curve for angular displacement is prepared. The distance between measuring points is inputted on the interpolation curve of the angular displacement, and the angular displacement at the measuring point is obtained. When the angular displacement component is obtained in this way and when the data of the displacement components for about 10 points are obtained between nodes in a vibration mode, the error between the value of the angular displacement component obtained by differentiating the interpolation curve and the value of the true angular displacement component is within 2%.

Description

[Detailed Description of the Invention] [Field of Industrial Application] This invention performs functional interpolation of the eigenvectors of the displacement components of a structure obtained at discontinuous measurement points in experimental mode analysis.
The present invention relates to a method of calculating an eigenvector of an angular displacement component from this and obtaining an eigenvector containing both the displacement component and the angular displacement component.

[Conventional technology]

In the experimental mode analysis, as shown in Fig. 5, an excitation force with a clear frequency spectrum is applied to the structure 1 using an excitation means 3 such as an impulse hammer shown or an exciter not shown, and a predetermined excitation force is applied to the structure 1. A vibration detector 2 is attached to a plurality of measuring points 5, and the vibration response of the structure I is measured as a vibration response signal 6 which is a function of the vibration frequency, and this vibration response signal 6 and the excitation force signal 7 are used in an experiment. The signal is input to the mode analyzer 4 and a frequency response function (transfer function), which is the ratio between the excitation force and the vibration response, is measured. From this measured frequency response function,
Modal parameters that determine the dynamic characteristics of the structure 1, such as the natural frequency, damping ratio, and eigenvectors corresponding to vibration modes as illustrated in FIG. 6, are identified.

[Problem to be solved by the invention]

The modal parameters obtained through the experimental modal analysis described above are important values in evaluating the dynamic characteristics of structures, but they are not only the target of evaluation; It has also been used in numerical calculations to predict how the characteristics will change when the This is generally called structural change simulation.

In the experimental mode analysis, as described later, a displacement component in the vibration direction and an angular displacement component around each part in a plane parallel to the vibration direction are required. However, with the detectors used during vibration tests, generally only the vibration information in the displacement direction can be obtained.A vibration detector that can measure angular displacement, which is a rotational component around the measurement point in a plane parallel to the vibration direction Currently, it is not used because it has problems with accuracy.

For this reason, information can only be obtained from the displacement component as an eigenvector that can be identified as a modal parameter, and when simulating structural changes,
A problem has arisen in that it is not possible to predict the mode when a moment acts on an arbitrary point.

Furthermore, it is currently being considered to combine data obtained by experimental modal analysis with data obtained by the finite element method. Actually, at each point of the structure, there are three degrees of freedom in three mutually perpendicular displacement directions Y li Y *, Y s and an angular displacement direction θ1, as shown in FIG. θ2. There are 6 degrees of freedom in total, 3 degrees of freedom θ. Pure numerical calculation using the finite element method provides information on these six degrees of freedom, whereas experimental modal analysis provides information on only three degrees of freedom in the displacement direction.
There is also the problem that sufficient coupling with the finite element method cannot be defined.

The purpose of this invention is to provide a method for obtaining data on angular displacement (rotation) components based on data on eigenvectors that contain only displacement components obtained through experimental mode analysis. do.

[Means to solve the problem]

This invention measures the displacement component of the eigenvector of vibration directly or indirectly using vibration detectors installed at multiple locations in the direction intersecting the excitation direction of the structure, and each maximum value of the displacement component measurement value at these multiple locations. is interpolated in the direction in which the vibration detector is installed, and the displacement component of the eigenvector of the imaging is obtained from the value of the interpolated curve for any point in the direction in which the vibration detector is installed, and from the slope of the interpolated curve at that arbitrary point. This is to obtain the angular displacement component of the eigenvector of vibration. [Operation] Since the interpolation curve of each maximum value of the displacement component of the eigenvector of vibration obtained by vibration detectors installed at multiple locations on the object to be measured is a continuous curve, The displacement component at any point can be obtained as a function of the distance in the direction in which the vibration detector is provided. Since the angular displacement component corresponds to the slope of the interpolation curve at the above point, the angular displacement component can be obtained by determining the slope of the interpolation curve. Since the function form of the interpolated curve is given, the slope can be found by differentiating the interpolated curve.

〔Example〕

FIG. 1 is a flowchart of an embodiment of the method of the invention. By performing experimental mode analysis, at m measurement points, the eigenvectors (mode shapes) that generate vibration modes as shown in Figure 6 for each natural frequency of n1lff ranging from the fundamental mode to higher-order modes can be determined. Identified. If this eigenvector is measured with a vibration detector that can only measure the displacement direction, the vector of the displacement component will be detected.

Here, the position i1f X j which is m discontinuous measurement points
Displacement component of the eigenvector obtained for each coordinate point of (j・1....+m) y r (xj)+(t・1...
・+n) and the data of the position Xj of each measurement point, the displacement component data is interpolated by an interpolation function, and a continuous function y*-rt(X) of the eigenvector y that is a function of the position X of the measurement point is obtained. A spline function is most suitable as an interpolation function. The spline function is a continuous function expressed by a polynomial defined under the condition that all higher-order differential values are continuous in the positive and negative directions of each coordinate point.

As shown in Figure 2, the angular displacement component of the eigenvector is a component associated with rotation around the focused coordinate point in a plane parallel to the vibration direction, and is calculated as a spline function y =
It can be determined from the gradient at the coordinate point X of f (X). That is, the angular displacement component is equivalent to the value obtained by differentiating y = f (x). Therefore, the function θ-dy/dx, which is obtained by differentiating the eigenvector curve y-f (x) determined by the spline function, becomes a function indicating the angular displacement.

Therefore, as shown in the flowchart in Figure 1, the interpolation curve y table for each natural frequency -f t (X), (1-1°・
...+n), and obtain the interpolation curve θl-f' of angular displacement (
X).

(i・1....+n) is created.

Furthermore, input the distance between the measurement points into this angular displacement interpolation curve θm (χ), and calculate the angular displacement θi (Xi) at the measurement point X.
-f'r (xj), (j-1, -, m) are determined.

In this way, when finding the angular displacement component using the interpolation curve,
Naturally, this will involve errors. On the other hand, Figure 3 shows the relationship between the number of measurement points and the error when the displacement component in the y direction is interpolated using a spline function from node to node in the vibration mode. If there is displacement component data of about 10 points between the .

Further, FIG. 4 shows the results of comparing the natural frequencies and natural vectors (vibration modes) obtained by the method of the present invention and the finite element method for a cantilever beam with one end fixed.

In the finite element method, the angular displacement component of the displacement component of the eigenvector is calculated. Since only the displacement component can be obtained in the experimental modal analysis, only the displacement component of the eigenvector obtained by the finite element method is used to interpolate the angular displacement component and the angular displacement component calculated by the finite element method according to the flowchart above. A comparison is made with the angular displacement component. The results show that the difference in angular displacement between the above two methods is within 2%.

The results shown in FIGS. 3 and 4 prove that there is no practical problem even if the angular displacement component obtained by the interpolation curve is used in the simulation of structural changes or in combination with the finite element method.

〔Effect of the invention〕

According to the present invention, the angular displacement component is also obtained by differentiating the interpolation function of the displacement component of the eigenvector of vibration measured at discontinuous measurement points, which has not been possible until now through experimental modal analysis. The angular displacement component can be determined by a vibration test using only a conventional vibration detector. In addition, by applying an interpolation curve, eigenvectors other than measurement points (
It also has the advantage of being able to determine displacement components and angular displacement components.

[Brief explanation of the drawing]

Fig. 1 is a flowchart showing the procedure for calculating the angular displacement component in an embodiment of the present invention, Fig. 2 is an explanatory diagram showing the relationship between the displacement component of the eigenvector and the angular displacement component, and Fig. 3 is the error between the number of measurement points and the angular displacement component. Fig. 4 is a graph showing the relationship between angular displacement and angular displacement obtained by the method of the embodiment of this invention and the angular displacement obtained by the finite element method. Fig. 5 is a graph showing the relationship between An explanatory diagram showing the overview, Fig. 6 is an explanatory diagram showing the relationship between the vibration mode obtained by experimental mode analysis and the displacement component of the eigenvector, and Fig. 7 shows the degrees of freedom that can be measured by experimental mode analysis and the actual degrees of freedom. It is a perspective explanatory view. 1: Structure, 2: Vibration detector, 3: Excitation means, 4: Experimental mode analysis device, 5: Measurement point, y: Displacement component, θ: Angular displacement component. 5: Eigen° pect, displacement component θ: Eigenvector angle change χ: Measurement distance Distance n: Number of modes m: Number of measurement points Figure 3 'y' = f(x) Figure 2 MODE . N-8,23H2 MODE. 2FN 5E5.99H2 No. 411 Procedural amendment ("ゞ3 1. Indication of the incident Patent application 1977-2g'7'7t) 1, title of the invention & %, n fixed page 2 + 1/sheet) established 3. Name of address related to the case of the person making the amendment

Claims (1)

[Claims] 1) Measure the displacement component of the eigenvector of vibration directly or indirectly using vibration detectors installed at multiple measurement points in the direction intersecting the excitation direction of the structure, and measure the displacement component at these multiple locations. Interpolate each maximum value in the direction of the vibration detector, and calculate the displacement component of the vibration eigenvector from the value of the interpolated curve for any point in the direction of the vibration detector, and calculate the slope of the interpolated curve at that arbitrary point. A vibration eigenvector measurement method characterized by obtaining an angular displacement component of the vibration eigenvector from .