CN114912302B - Method for acquiring modal density of stiffened plate based on modal space sampling algorithm - Google Patents
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Abstract
The invention relates to a method for acquiring modal density of a stiffened plate based on a modal space sampling algorithm, which comprises the following steps: evaluating the maximum modal range of the non-reinforced flat plate structure in a modal space according to the upper frequency limit; calculating the modal number of the non-reinforced flat plate structure in a selected frequency range; determining sampling points according to the modal quantity; calculating wave numbers of each sampling point in the X direction and the Y direction based on four-side constraint of the stiffened plate, determining natural frequency according to the relation between half wavelength and spacing of reinforcing ribs, and determining the modal quantity of the stiffened plate; calculating the modal total number of the stiffened plate based on the modal number of the stiffened plate; and calculating the modal density of the stiffened plate based on the modal total number of the stiffened plate. The method does not need means such as test and the like in the whole process, and the calculation efficiency of the modal density of the stiffened plate is improved.
Description
Technical Field
The invention relates to the technical field of statistical energy analysis, in particular to a method for acquiring modal density of a stiffened plate based on a modal space sampling algorithm.
Background
The stiffened plate is a common structural form in the industrial fields of aerospace, shipbuilding, automation and the like. When solving the vibration problem of the reinforced plate structure, the statistical energy analysis method is the most effective method, and the modal density is an important index of the method. At present, no theoretical analytical solution exists for the modal density of the stiffened plate, and different experts and scholars need to consume huge manpower, financial resources and calculation time for calculation through a test method and a finite element numerical calculation method.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for acquiring the modal density of a stiffened plate based on a modal space sampling algorithm, which can improve the calculation efficiency.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method for acquiring the modal density of the stiffened plate based on the modal space sampling algorithm comprises the following steps:
(1) Evaluating the maximum modal range of the non-reinforced flat plate structure in a modal space according to the upper frequency limit;
(2) Calculating the modal quantity of the non-reinforced flat plate structure in a selected frequency range;
(3) Determining sampling points according to the modal quantity;
(4) Calculating wave numbers of each sampling point in the X direction and the Y direction based on four-side constraint of the stiffened plate, determining natural frequency according to the relation between half wavelength and spacing of reinforcing ribs, and determining the modal quantity of the stiffened plate;
(5) Calculating the modal total number of the stiffened plates based on the modal number of the stiffened plates;
(6) And calculating the modal density of the stiffened plate based on the modal total number of the stiffened plate.
The step (3) is specifically as follows: when the modal quantity is smaller than or equal to a threshold value K, all the modal quantities are used as sampling points to participate in subsequent calculation; and when the mode number is larger than a threshold value K, sampling according to the sampling point number K, and participating the sampling point in subsequent calculation.
When the wave numbers of each sampling point in the X direction and the Y direction are calculated based on the four-edge constraint of the stiffened plate in the step (4), the mode shape function of the stiffened plate is as follows:
wherein
and
respectively represents the coordinate values of the stiffened plate in the X direction and the Y direction,
the number of the vibration mode harmonics of the stiffened plate along the X direction,
the vibration mode harmonic number of the stiffened plate along the Y direction,
the length of the side of the stiffened plate in the X direction,
the length of the side of the stiffened plate in the Y direction,
the number of waves in the X direction is,
the wave number in the Y direction.
The determining the natural frequency according to the relationship between the half wavelength and the distance between the reinforcing ribs in the step (4) specifically comprises the following steps:
and (3) determining the properties of the stiffened plate:
when the half wavelength is larger than the distance between the reinforcing ribs, the mass stiffness of the reinforcing ribs is distributed in the whole flat plate structure, and the stiffened plate is equivalent to an orthogonal anisotropic plate; when the half wavelength is smaller than the reinforcement distance, the reinforcement rib is regarded as a rigid boundary, and the stiffened plate is divided into a plurality of lattices by the reinforcement rib;
a natural frequency calculation step:
when the half wavelength in the X direction and the half wavelength in the Y direction are both larger than the distance between the reinforcing ribs, the reinforcing ribs in the two directions are equally spread, and the natural frequency is equal to the length of the side
And
orthogonal anisotropy of the plate count, number of lattices
；
When only the half wavelength in the Y direction is larger than the distance between the reinforcing ribs, the reinforcing ribs only parallel to the Y direction are evenly spread, and the natural frequency is equal to the length of the side
And
tablet count, number of cells
；
When only the half wavelength in the X direction is larger than the distance between the reinforcing ribs, the reinforcing ribs only parallel to the X direction are evenly spread, and the natural frequency is equal to the length of the side
And
tablet count, number of cells
；
When the half-wave length in the X direction and the half-wave length in the Y direction are both smaller than the distance between the reinforcing ribs, the reinforcing ribs in the two directions are not evenly spread, and the natural frequency is equal to the side length
And
tablet count, number of cells
；
Wherein,
the length of the side of the stiffened plate in the X direction,
the length of the side of the stiffened plate in the Y direction,
the distance between the reinforcing ribs parallel to the X direction,
the distance between the reinforcing ribs is parallel to the Y direction.
The mode number of the stiffened plate determined in the step (4) is specifically as follows: and judging whether the natural frequency is in the selected frequency range, if so, recording the mode, and determining the mode number of the stiffened plate according to the grid number.
The step (5) is specifically as follows: and dividing the modal number of the stiffened plate by a sampling coefficient to obtain the modal total number of the stiffened plate, wherein the sampling coefficient is the ratio of the number of the sampling points to the modal number.
The step (6) is specifically as follows: and dividing the modal total number of the stiffened plate by the selected frequency range to obtain the modal density of the stiffened plate.
Advantageous effects
Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects: according to the method, sampling calculation is carried out based on the modal space, the stiffened plate is subjected to equivalent treatment by flattening the quality and rigidity of the stiffened rib into the flat plate, so that the modal density of the stiffened plate can be quickly calculated, the whole process does not need means such as test and the like, and the modal density result of the stiffened plate structure can be quickly and effectively obtained under the conditions of high frequency and large modal quantity.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The embodiment of the invention relates to a method for acquiring modal density of a stiffened plate based on a modal space sampling algorithm, which comprises the following steps as shown in figure 1:
step 1, evaluating the maximum modal range of a non-reinforced flat plate structure in a modal space according to the upper limit of frequency;
step 2, calculating the modal number of the non-reinforced flat plate structure in a selected frequency range;
step 3, determining sampling points according to the modal quantity;
step 4, calculating wave numbers of each sampling point in the X direction and the Y direction based on four-side constraint of the stiffened plate, determining natural frequency according to the relation between half wavelength and spacing of reinforcing ribs, and determining the mode number of the stiffened plate;
step 5, calculating the modal total number of the stiffened plate based on the modal number of the stiffened plate;
and 6, calculating the modal density of the stiffened plate based on the modal total number of the stiffened plate.
Wherein, the step 3 is specifically as follows: when the mode number is smaller than or equal to a threshold value K, taking all the mode numbers as sampling points to participate in subsequent calculation; and when the mode number is larger than a threshold value K, sampling according to the sampling point number K, and participating the sampling point in subsequent calculation. In the embodiment, the threshold K =200, that is, when the calculated number of modes does not exceed 200, sampling is not performed, and all the number of modes are used as sampling points to participate in subsequent cycle calculation; and if the calculated number of the modes exceeds 200, sampling according to the sampling point number of 200. In the present embodiment, sampling is performed in the Y direction, and the sampling interval is set to 2 × the number of modes divided by 200 and then rounded.
In step 4, under the condition of four-side constraint of the stiffened plate, the mode shape function of the stiffened plate is as follows:
wherein,
and
respectively showing coordinate values of the stiffened plate in the X direction and the Y direction,
the number of the vibration mode harmonics of the stiffened plate along the X direction,
the vibration mode harmonic number of the stiffened plate along the Y direction,
the length of the side of the stiffened plate in the X direction,
the length of the side of the stiffened plate in the Y direction,
is the wave number in the X direction,
the wave number in the Y direction.
When the half wavelength of the bending traveling wave in the stiffened plate is larger than the spacing between the reinforcing ribs, the mass rigidity of the reinforcing ribs can be distributed in the whole flat plate structure, and the stiffened plate is equivalent to an orthotropic plate. Described in wavenumber form as:
wherein
the distance between the reinforcing ribs parallel to the X direction,
the distance between the reinforcing ribs is parallel to the Y direction.
When the half wavelength is smaller than the distance between the reinforcing ribs, the reinforcing ribs are regarded as rigid boundaries, the reinforcing rib plates are divided into small lattices by the reinforcing ribs, and at the moment, the mode number needs to be multiplied by the number of the small lattices.
When the natural frequency is calculated, firstly, the mode vibration type function of the stiffened plate is adopted, the wave number is calculated based on sampling points, then, the half wavelength is compared with the distance between reinforcing ribs, and the natural frequency is calculated according to different conditions, specifically as follows:
when in use
When the length of the half wavelength in the X direction and the Y direction is larger than the distance between the reinforcing ribs, the reinforcing ribs in the two directions are evenly spread, and the natural frequency is equal to the length of the side
And
orthogonal anisotropy of the plate count, number of lattices
；
When in use
When the length of the edge is equal to the length of the reinforcing ribs, the half wavelength in the Y direction is larger than the spacing of the reinforcing ribs, the reinforcing ribs only parallel to the Y direction are evenly spread, and the natural frequency is equal to the length of the edge
And
tablet count, number of cells
；
When in use
When the frequency is higher than the frequency, the half wavelength in the X direction is larger than the distance between the reinforcing ribs, at the moment, the reinforcing ribs only parallel to the X direction are evenly spread, and the natural frequency is equal to the side length
And
tablet count, number of cells
；
When in use
When the frequency is higher than the frequency range, the half-wave length in the X direction and the half-wave length in the Y direction are smaller than the distance between the reinforcing ribs, the reinforcing ribs in the two directions are not evenly spread, and the natural frequency is equal to the side length
And
tablet counting, number of cells
。
If the calculated natural frequency is in the analyzed bandwidth frequency range, the mode is counted, and the number is counted according to the number of small lattices
And (4) adding in a superposition mode.
In step 5, dividing the modal number of the stiffened plate by a sampling coefficient to obtain the modal total number of the stiffened plate, wherein the sampling coefficient is the ratio of the number of the sampling points to the modal number.
And 6, dividing the modal total number of the stiffened plate by the selected frequency range to obtain the modal density of the stiffened plate in the bandwidth.
It is not difficult to find that the method is based on modal space to perform sampling calculation, and performs equivalent treatment on the stiffened plate by spreading the quality and the rigidity of the stiffened plate into a flat plate, so that the modal density of the stiffened plate can be quickly calculated, and the modal density result of the stiffened plate structure can be quickly and effectively obtained under the conditions of high frequency and large modal quantity without means such as test and the like in the whole process.
Claims (5)
1. A stiffened plate modal density acquisition method based on a modal space sampling algorithm is characterized by comprising the following steps:
(1) Evaluating the maximum modal range of the non-reinforced flat plate structure in a modal space according to the upper frequency limit;
(2) Calculating the modal number of the non-reinforced flat plate structure in a selected frequency range;
(3) Determining sampling points according to the modal quantity;
(4) Calculating wave numbers of each sampling point in the X direction and the Y direction based on four-edge constraint of the stiffened plate, determining natural frequency according to the relation between half-wavelength and spacing of reinforcing ribs, and determining the modal number of the stiffened plate;
(5) Calculating the modal total number of the stiffened plate based on the modal number of the stiffened plate, specifically: dividing the modal number of the stiffened plate by a sampling coefficient to obtain the modal total number of the stiffened plate, wherein the sampling coefficient is the ratio of the number of the sampling points to the modal number;
(6) Calculating the modal density of the stiffened plate based on the modal total number of the stiffened plate, specifically: and dividing the modal total number of the stiffened plate by the selected frequency range to obtain the modal density of the stiffened plate.
2. The method for acquiring the modal density of the stiffened plate based on the modal space sampling algorithm according to claim 1, wherein the step (3) is specifically as follows: when the number of the modes is less than or equal to a threshold value K, taking all the modes as sampling points to participate in subsequent calculation; and when the mode number is larger than a threshold value K, sampling according to the sampling point number K, and participating the sampling point in subsequent calculation.
3. The method for acquiring modal density of a stiffened plate based on a modal space sampling algorithm according to claim 1, wherein when the wave number of each sampling point in the X direction and the Y direction is calculated based on four-edge constraint of the stiffened plate in the step (4), the modal shape function of the stiffened plate is as follows:
wherein
and
respectively represents the coordinate values of the stiffened plate in the X direction and the Y direction,
the number of the vibration mode harmonics of the stiffened plate along the X direction,
the vibration mode harmonic number of the stiffened plate along the Y direction,
the length of the side of the stiffened plate in the X direction,
the length of the side of the stiffened plate in the Y direction,
the number of waves in the X direction is,
the wave number in the Y direction.
4. The method for acquiring modal density of a stiffened plate based on a modal space sampling algorithm according to claim 1, wherein the determining the natural frequency according to the relationship between the half wavelength and the spacing between the reinforcing ribs in the step (4) specifically comprises:
and (3) determining the properties of the stiffened plate:
when the half wavelength is larger than the distance between the reinforcing ribs, the mass stiffness of the reinforcing ribs is distributed in the whole flat plate structure, and the stiffened plate is equivalent to an orthogonal anisotropic plate; when the half wavelength is smaller than the reinforcement spacing, the reinforcement is regarded as a rigid boundary, and the stiffened plate is divided into a plurality of lattices by the reinforcement;
a natural frequency calculation step:
when the half wavelength in the X direction and the half wavelength in the Y direction are both larger than the distance between the reinforcing ribs, the reinforcing ribs in the two directions are equally spread, and the natural frequency is equal to the length of the side
And
orthogonal anisotropy of the plate count, number of lattices
；
When only the half wavelength in the Y direction is larger than the distance between the reinforcing ribs, the reinforcing ribs only parallel to the Y direction are evenly spread, and the natural frequency is equal to the length of the side
And
tablet count, number of cells
；
When only the half wavelength in the X direction is larger than the distance between the reinforcing ribs, the reinforcing ribs only parallel to the X direction are evenly spread, and the natural frequency is equal to the length of the side
And
tablet counting, number of cells
；
When the half-wave length in the X direction and the half-wave length in the Y direction are both smaller than the distance between the reinforcing ribs, the reinforcing ribs in the two directions are not evenly spread, and the natural frequency is equal to the side length
And
tablet count, number of cells
；
Wherein,
the length of the side of the stiffened plate in the X direction,
the length of the side of the stiffened plate in the Y direction,
the distance between the reinforcing ribs parallel to the X direction,
the distance between the reinforcing ribs is parallel to the Y direction.
5. The method for acquiring the modal density of the stiffened plate based on the modal space sampling algorithm according to claim 4, wherein the determining the modal number of the stiffened plate in the step (4) is specifically as follows: and judging whether the natural frequency is in the selected frequency range, if so, recording the mode, and determining the mode number of the stiffened plate according to the grid number.
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