CN104636556A - Vibration response calculating method of limited baseboard structure connected at any angle - Google Patents
Vibration response calculating method of limited baseboard structure connected at any angle Download PDFInfo
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- CN104636556A CN104636556A CN201510069017.7A CN201510069017A CN104636556A CN 104636556 A CN104636556 A CN 104636556A CN 201510069017 A CN201510069017 A CN 201510069017A CN 104636556 A CN104636556 A CN 104636556A
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Abstract
The invention discloses a vibration response calculating method of a limited baseboard structure connected at any angle. The vibration response calculating method comprises the following steps: taking a joint and a force stimulating place as a border, and classifying the limited baseboard structure connected at any angle into multiple sub-structures; obtaining the structural parameter and stimulation parameter of a connecting plate structure, wherein the structural parameter includes geological dimension and material property parameter of multiple sub-structures; the stimulation parameter includes amplitude and distribution position of the stimulating force; structuring a wave solution form of the displacement and the inner force of the sub-structure under a local pairing coordinate system according to the obtained structural parameter and the external stimulation parameter; according to the wave solution form and the continuous conditions of the sub-structures at the force stimulating place, the border and the joint, establishing a coupling vibration governing equation of the whole plate structural model; according to the coupling vibration governing equation, solving and obtaining the vibration response and power flow of the limited baseboard structure connected at any angle.
Description
Technical field
The present invention relates to structural vibration response technical field, be specially into the quantitative calculation method of the finite size plate structure vibratory response of arbitrarily angled connection.
Background technology
Become the finite size plate structure form of arbitrarily angled connection, as " L " template, T-shape plate and box-structure etc., have a wide range of applications in engineering.When connecting board structure is subject to dynamic excitation, the vibration wave that vibration produces is delivered to structural attachments can there is waveform conversion, and then transmits to other minor structures, thus causes total to be vibrated.Therefore the vibration characteristics studied in connecting board structure has important engineering significance to the vibration mechanism verifying engineering structure.
Researcher adopted Fluctuation Method to analyze the Vibrational power flow analysis of L-type plate structure in the past.Generally L-type plate is divided into three regions, considers the condition of continuity of junction, boundary condition, set up the vibration control equation of total, and then obtain the vibratory response of position, thus computational accuracy is higher.But for the finite size plate structure of arbitrarily angled connection, the method needs to define more displacement solution unknowm coefficient, increase the increase that can cause exponent arithmetic simultaneously due to the condition of continuity, the decline of computational accuracy may be caused.Therefore, in the urgent need to a kind of calculated amount suitably, precision is higher, and can be calculated to be the quantitative calculation method of the finite size plate structure vibratory response of arbitrarily angled connection in broadband.
Summary of the invention
For solving the rising of existing method with analysis frequency, the increase of model subsystem, the deficiency that calculated amount is larger, computational accuracy is lower, the present invention proposes a kind of computing method being specified to the finite size plate structure vibratory response of arbitrarily angled connection.
The technical solution adopted for the present invention to solve the technical problems is:
There is provided a kind of become the quantitative calculation method of finite size plate structure vibratory response of arbitrarily angled connection, comprise the following steps:
Step 1: with junction and power excitation place for border, is divided into multiple minor structure by becoming the finite size plate structure of arbitrarily angled connection;
Step 2: the structural parameters and the excitation parameters that obtain connecting board structure, described structural parameters comprise physical dimension and the material characteristic parameter of multiple minor structure; Excitation parameters comprises amplitude and the distributing position of exciting force;
Step 3: according to the structural parameters obtained and external excitation parameter, builds displacement and the Wave Solutions form of internal force under the dual coordinates system of local of minor structure;
Step 4: according to Wave Solutions form and the minor structure condition of continuity in power excitation place, boundary and junction, set up the coupled vibrations governing equation of whole plate structure model;
Step 5: solve the vibratory response of finite size plate structure and poower flow that obtain into arbitrarily angled connection according to coupled vibrations governing equation.
In method of the present invention, described Wave Solutions form comprise minor structure its local dual coordinates system in displacement state vector expression and internal force status vector expression.
In method of the present invention, step 4 specifically comprises the following steps:
According to the condition of continuity of minor structure in power excitation place, boundary and junction, set up the vibration wave transitive relation of multiple junction;
Set up the coupled vibrations governing equation of total model, the transfer matrix of all vibration wave transitive relations is integrated together, obtain the overall transformation relation d=Sa+s of coupling plate structure, wherein d and a represents the unknown wave amplitude vectors leaving ripple and arrival ripple all in coupling plate structure respectively, S is the exact transfer matrix method of coupling plate structure, and s is the wave source vector because the existence of external excitation produces.
Present invention also offers a kind of become the quantitative computing system of finite size plate structure vibratory response of arbitrarily angled connection, it is characterized in that, comprising:
Minor structure divides module, for junction and power excitation place for border, be divided into multiple minor structure by becoming the finite size plate structure of arbitrarily angled connection;
Parameter acquisition module, for obtaining structural parameters and the excitation parameters of connecting board structure, described structural parameters comprise physical dimension and the material characteristic parameter of multiple minor structure; Excitation parameters comprises amplitude and the distributing position of exciting force;
Wave Solutions form builds module, for according to the structural parameters obtained and external excitation parameter, builds displacement and the Wave Solutions form of internal force under the dual coordinates system of local of minor structure;
Coupled vibrations governing equation sets up module, for according to Wave Solutions form and the minor structure condition of continuity in power excitation place, boundary and junction, sets up the coupled vibrations governing equation of whole plate structure model;
Computing module, for solving the vibratory response of finite size plate structure and poower flow that obtain into arbitrarily angled connection according to coupled vibrations governing equation.
In system of the present invention, described Wave Solutions form comprise minor structure its local dual coordinates system in displacement state vector expression and internal force status vector expression.
In system of the present invention, described coupled vibrations governing equation is set up module and is specifically comprised:
Vibration wave transitive relation sets up module, for according to the condition of continuity of minor structure in power excitation place, boundary and junction, sets up the vibration wave transitive relation of multiple junction;
Establishing equation module, for the transfer matrix of all vibration wave transitive relations is integrated together, obtain the overall transformation relation d=Sa+s of coupling plate structure, wherein d and a represents the unknown wave amplitude vectors leaving ripple and arrival ripple all in coupling plate structure respectively, S is the exact transfer matrix method of coupling plate structure, and s is the wave source vector because the existence of external excitation produces.
The beneficial effect that the present invention produces is: fluction analysis method combines with local dual coordinates system by the present invention, provide a kind of become the quantitative calculation method of finite size plate structure vibratory response of arbitrarily angled connection, computing is simple and easy, is easy to realization.The foundation of kinetic model is carried out based on analytical method, and this semi-analytic method effectively can improve counting yield, not limit by calculating frequency band.The method, by setting up local dual coordinates system, avoids the numerical error that exponent arithmetic brings.
Accompanying drawing explanation
Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:
Fig. 1: the program flow diagram of the inventive method.
Fig. 2: the structural representation being the finite size plate structure becoming arbitrarily angled connection in one embodiment of the invention.
Fig. 3: be into displacement comparison diagram in the finite size plate structure of arbitrarily angled connection.
Fig. 4: be into shearing comparison diagram in the finite size plate structure of arbitrarily angled connection.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.
The quantitative calculation method of the finite size plate structure vibratory response of the arbitrarily angled connection of one-tenth of the embodiment of the present invention, as shown in Figure 1, comprises the following steps:
Step S1, with junction and power excitation place for border, be divided into a series of minor structure IJ, JK by becoming the finite size plate structure of arbitrarily angled connection
Step S2, the structural parameters obtaining connecting board structure and external excitation parameter, described structural parameters comprise the physical dimension, material characteristic parameter etc. of the minor structure of plate; Excitation parameters comprises the amplitude f of exciting force
0and distributing position (x
0, y
0), can F=f be expressed as
0δ (x-x
0) δ (y-y
0) e
i ω t, i represents imaginary number, and ω is circular frequency, and t is time variable.
Step S3, according to raw data input, build the displacement of minor structure and the Wave Solutions form of internal force under the dual coordinates system of local, for plate IJ, the displacement state vector expression in its IJ local coordinate system is
internal force status vector expression is
Wherein
for corresponding to the motion vector under the n-th joint mode,
For phasing matrix, Y
n=diag{sink
yy cosk
yy sink
yy sink
yy cosk
yy} is mode in the y-direction, is diagonal matrix, A
n δ, D
n δfor corresponding to the displacement coefficient matrix arriving ripple and leave ripple, a
nand d
nbe respectively and arrive ripple and leave wave-wave width coefficient.
Step S4, according to the condition of continuity of structure in power excitation place, boundary and junction, set up a series of junction I, J, K ... vibration wave transitive relation, d
sIGN=S
sIGNa
sIGN, SIGN=I, J, K ....
Step S5, set up the coupled vibrations governing equation of total model, all transfer matrixes are integrated together, finally can obtain the overall transformation relation d=Sa+s of coupling plate structure, d={d
id
hd
jd
k}
t, a={a
ia
ha
ja
k}
trepresent the unknown wave amplitude vectors leaving ripple and arrival ripple all in coupling plate structure respectively.S=diag < S
is
hs
js
k> is the exact transfer matrix method of coupling plate structure.S is the wave source vector because the existence of external excitation produces.
Step S6, the phase relation that plate arrives ripple and leaves between ripple can be determined based on deformation compatibility condition, for plate IH,
for local phase matrix.Definition substitution matrix
Arrival ripple then in plate IH in Two coordinate system and the phase relation left between ripple are
By integrating the phasing matrix between all plates, the phase relation that can obtain the whole plate structure that is of coupled connections is a
n=P
lnud
n, P
lnfor the overall phasing matrix of coupling plate structure, U is the integral replacement matrix of coupling plate structure.
Step S7, simultaneous step S5 and step S6, can obtain the wave amplitude coefficient in each local dual coordinates system, and then can obtain into the finite size plate structure vibratory response of arbitrarily angled connection.
In a specific embodiment of the present invention, concrete grammar step of the present invention is as follows:
Step 1: the structural parameters and the excitation parameters that obtain connecting board structure, described structural parameters comprise length L
x1=0.76m, L
x2=0.76m, width L
y=0.6m, thickness h=10mm.Each plate material parameter value is consistent: Young modulus E=2.0 × 10
11pa, Poisson ratio μ=0.3, density p=7800kg/m
3, damping loss factor is η=0.01.The position of exciting force under global coordinate system is (0.38m, 0.3m, 0m), and amplitude is unit power.Design parameter represents size as shown in Figure 2.
Step 2: according to raw data input, carry out dividing multiple minor structure in the junction of plate, every block minor structure just can use border letter I, J, K ... be numbered and represent.Each minor structure is set up dual coordinates system, ensures that the y of dual coordinates system is to unanimously, x is to relatively, and z is to meeting the right-hand rule.On this basis, the displacement state vector sum internal force status vector expression under corresponding coordinate system is provided, namely
Wherein
it is the motion vector under the n-th joint mode.
For phasing matrix, Y
n=diag{sink
yy cosk
yy sink
yy sink
yy cosk
yy} is mode in the y-direction, a
n={ a
1na
2na
3na
4na
5n}
tand d
n={ d
1nd
2nd
3nd
4nd
5n}
tfor arriving ripple and the wave amplitude coefficient vector leaving ripple.A
n δ, D
n δfor corresponding to the displacement coefficient matrix arriving ripple and leave ripple.F
n={ M
xxnm
xynv
xnn
xnn
xyn}
tfor corresponding to force vector in the n-th joint mode.A
nf, D
nffor arriving ripple and the Force coefficient matrix leaving ripple.
Step 3: consider that an external excitation acts on H border, as shown in Figure 1, it can be expressed as the form D=f of Dirac function
0δ (x-x
0) δ (y-y
0), by carrying out orthogonalization integration in the y-direction, external excitation can be expressed as the form of the summation of series
f
0n=2f
0sink
yy
0/ L
y.
Step 4: consider that plate IH and plate HJ exists the effect of external excitation, introduce deformation compatibility condition and dynamic balance condition in local coordinate system; In the junction of plate HJ and plate JK, demand fulfillment continuous modification compatibility conditions and dynamic balance condition can set up the transformational relation of corresponding vibration ripple in corresponding junction, i.e. d
sIGN=S
sIGNa
sIGN, SIGN=I, J, K ...
Step 5: be integrated together by all scattering matrixes, finally can obtain the overall scattering transformational relation d=Sa+s of coupling plate structure, wherein, and d={d
id
hd
jd
k}
t, a={a
ia
ha
ja
k}
tall unknown wave amplitude vectors leaving ripple and arrive ripple in display plate structure respectively.S=diag < S
is
hs
js
k> is the overall transformation matrix of coupling plate structure.S is the wave source vector because the existence of external excitation produces.Motion vector in every block minor structure and interior force vector all can represent in this two covers local coordinate system.
Step 6: for plate IH, can determine phase relation plate arriving ripple and leaves between ripple, namely based on deformation compatibility condition
wherein
for local phase matrix.Definition substitution matrix
Arrival ripple in plate IH in Two coordinate system and the phase relation left between ripple, namely
By integrating the phasing matrix between all plates, the phase relation a of the whole plate structure that is of coupled connections can be obtained
n=P
lnud
n, wherein P
lnfor the overall phasing matrix of coupling plate structure, U is the integral replacement matrix of coupling plate structure.
Step 6: by the overall governing equation d of the plate structure that can be of coupled connections after step 5 and step 6 simultaneous
n=(I-SP
lnu)
-1s, a
n=P
lnud
n.The d obtained will be solved
nand a
nbe updated in the displacement state vector sum internal force status vector expression in step 2, the state vector of the plate structure that can obtain being of coupled connections.
Fig. 3 and Fig. 4 is this method acquired results and the comparing of business finite element software ABAQUS result, and excitation frequency scope is 0Hz ~ 500Hz, frequency step 1Hz.Remove the mode of oscillation number N=40 meeting analysis frequency.2 longitudinal opposite side of plate are simple boundary, I and K border is free boundary.As can be seen from Fig. 3 and Fig. 4, no matter both result of calculations are that shearing or displacement all coincide good, and error is no more than 0.6%.Solve the dynamic response of coupling plate structure by MRRM method and finite element result coincide very well, computational accuracy can be guaranteed.
Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all these improve and convert the protection domain that all should belong to claims of the present invention.
Claims (6)
1. become a quantitative calculation method for the finite size plate structure vibratory response of arbitrarily angled connection, it is characterized in that, comprise the following steps:
Step 1: with junction and power excitation place for border, is divided into multiple minor structure by becoming the finite size plate structure of arbitrarily angled connection;
Step 2: the structural parameters and the excitation parameters that obtain connecting board structure, described structural parameters comprise physical dimension and the material characteristic parameter of multiple minor structure; Excitation parameters comprises amplitude and the distributing position of exciting force;
Step 3: according to the structural parameters obtained and external excitation parameter, builds displacement and the Wave Solutions form of internal force under the dual coordinates system of local of minor structure;
Step 4: according to Wave Solutions form and the minor structure condition of continuity in power excitation place, boundary and junction, set up the coupled vibrations governing equation of whole plate structure model;
Step 5: solve the vibratory response of finite size plate structure and poower flow that obtain into arbitrarily angled connection according to coupled vibrations governing equation.
2. method according to claim 1, is characterized in that, described Wave Solutions form comprise minor structure its local dual coordinates system in displacement state vector expression and internal force status vector expression.
3. method according to claim 1, is characterized in that, step 4 specifically comprises the following steps:
According to the condition of continuity of minor structure in power excitation place, boundary and junction, set up the vibration wave transitive relation of multiple junction;
Set up the coupled vibrations governing equation of total model, the transfer matrix of all vibration wave transitive relations is integrated together, obtain the overall transformation relation of coupling plate structure
, wherein
d with
a represent the unknown wave amplitude vectors leaving ripple and arrival ripple all in coupling plate structure respectively,
s for the exact transfer matrix method of coupling plate structure,
for the wave source vector produced due to the existence of external excitation.
4. become a quantitative computing system for the finite size plate structure vibratory response of arbitrarily angled connection, it is characterized in that, comprising:
Minor structure divides module, for junction and power excitation place for border, be divided into multiple minor structure by becoming the finite size plate structure of arbitrarily angled connection;
Parameter acquisition module, for obtaining structural parameters and the excitation parameters of connecting board structure, described structural parameters comprise physical dimension and the material characteristic parameter of multiple minor structure; Excitation parameters comprises amplitude and the distributing position of exciting force;
Wave Solutions form builds module, for according to the structural parameters obtained and external excitation parameter, builds displacement and the Wave Solutions form of internal force under the dual coordinates system of local of minor structure;
Coupled vibrations governing equation sets up module, for according to Wave Solutions form and the minor structure condition of continuity in power excitation place, boundary and junction, sets up the coupled vibrations governing equation of whole plate structure model;
Computing module, for solving the vibratory response of finite size plate structure and poower flow that obtain into arbitrarily angled connection according to coupled vibrations governing equation.
5. system according to claim 4, is characterized in that, described Wave Solutions form comprise minor structure its local dual coordinates system in displacement state vector expression and internal force status vector expression.
6. system according to claim 1, is characterized in that, described coupled vibrations governing equation is set up module and specifically comprised:
Vibration wave transitive relation sets up module, for according to the condition of continuity of minor structure in power excitation place, boundary and junction, sets up the vibration wave transitive relation of multiple junction;
Establishing equation module, for being integrated together by the transfer matrix of all vibration wave transitive relations, obtains the overall transformation relation of coupling plate structure
, wherein
d with
a represent the unknown wave amplitude vectors leaving ripple and arrival ripple all in coupling plate structure respectively,
s for the exact transfer matrix method of coupling plate structure,
for the wave source vector produced due to the existence of external excitation.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109598087A (en) * | 2018-12-20 | 2019-04-09 | 武汉海王科技有限公司 | A kind of calculation method and system of finite size structural vibration response |
| CN112699433A (en) * | 2020-11-16 | 2021-04-23 | 西南交通大学 | Method for classifying nuclear reactor fuel assembly seismic analysis mold building structure types |
| CN112836269A (en) * | 2020-11-16 | 2021-05-25 | 西南交通大学 | Method for splicing nuclear reactor fuel assembly anti-seismic analysis modeling substructure types |
| CN114969632A (en) * | 2022-05-10 | 2022-08-30 | 上海索辰信息科技股份有限公司 | Method for obtaining coupling loss factor of orthotropic plate |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109598087A (en) * | 2018-12-20 | 2019-04-09 | 武汉海王科技有限公司 | A kind of calculation method and system of finite size structural vibration response |
| CN112699433A (en) * | 2020-11-16 | 2021-04-23 | 西南交通大学 | Method for classifying nuclear reactor fuel assembly seismic analysis mold building structure types |
| CN112836269A (en) * | 2020-11-16 | 2021-05-25 | 西南交通大学 | Method for splicing nuclear reactor fuel assembly anti-seismic analysis modeling substructure types |
| CN114969632A (en) * | 2022-05-10 | 2022-08-30 | 上海索辰信息科技股份有限公司 | Method for obtaining coupling loss factor of orthotropic plate |
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Inventor after: Wang Xianzhong Inventor after: Chen Zhe Inventor after: Chen Di Inventor after: Jiang Chenban Inventor after: Xu Ruiyang Inventor after: Gu Xin Inventor after: Wu Weiguo Inventor before: Wang Xianzhong Inventor before: Wu Weiguo Inventor before: Zhou Yong Inventor before: Ma Li Inventor before: Xu Ruiyang Inventor before: Qi Qiongfang |
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