CN106777504B - Vehicle mode vehicle body torsion mode recognition methods - Google Patents
Vehicle mode vehicle body torsion mode recognition methods Download PDFInfo
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Abstract
The invention discloses a kind of vehicle mode vehicle body torsion mode recognition methods, comprising the following steps: (a), whole vehicle model piecemeal;(b), torsion mode identification constraint;(c), vehicle body integrally reverses frame identification, including vehicle body integrally reverses 18 recognition methods and vehicle body integrally reverses 12 point frame recognition methods, and optionally one of vehicle body that carries out integrally reverses frame identification;(d), body tail reverses 15 points of identifications;(e), vehicle foreside reverses 8 points of identifications;(f), vehicle vehicle body torsion slice identification.Vehicle mode under body is reversed and carries out modal idenlification, it is implementable strong, it can effectively avoid that the erroneous judgement of vehicle mode occurs.
Description
Technical field
The present invention relates to the simulation analysis technical fields of vehicle Car body model, and in particular to a kind of vehicle mode vehicle body torsion
Modal identification method.
Background technique
It is an important job that torsion mode is defined during NVH performance simulation, but due to reorganizing and outfit vehicle body, vehicle
Structure it is complex, further include multiple systems such as interior trim, exterior trim, electric appliance, chassis, braking other than vehicle body, and each
System interacts, intercouples, and often encounters difficulties or identify mistake on defining torsion mode order.
Summary of the invention
The present invention improves in view of the above technical problems, it is desirable to provide a kind of vehicle mode vehicle body torsion mode identification side
Method avoids that the erroneous judgement of vehicle mode occurs.
For this purpose, the technical scheme adopted by the invention is as follows: a kind of vehicle mode vehicle body torsion mode recognition methods, including with
Lower step:
(a), whole vehicle model piecemeal:
First vehicle lumped mass point and shutter member are removed, vehicle is divided into tire, tank bracket, vehicle body A column, automobile body B
Column, body C pillar, body rear end, wherein vehicle body A column, center body pillar, the main identification that body C pillar is torsion mode under vehicle mode
Response point, tire are constraint translation and rotational freedom;
(b), torsion mode identification constraint:
The position of torsion mode identification obligatory point under vehicle mode, by right front turret, left front gun turret, it is right after gun turret, left back
Gun turret, frame assembly composition, specific constraint and combination are as shown in Table 1;
(c), vehicle body integrally reverses frame identification, and vehicle body introduced below integrally reverses 18 recognition methods and vehicle body is integrally turned round
Turn 12 point frame recognition methods, optionally one of vehicle body that carries out integrally reverses frame identification;
Vehicle body integrally reverses 18 recognition methods: vehicle body left and right side is each provided with 9 response points, including by vehicle body A column three
3 response points, 3 response points of center body pillar trisection, 3 response points of body C pillar trisection of equal part, together constitute
Vehicle body integrally reverses 18 response points;Each front-wheel obligatory point of vehicle body left and right side, rear-wheel obligatory point constitute 4 constraints of vehicle body
Point, right front turret, left front gun turret, it is right after the 4 excitation points of gun turret, left back gun turret as vehicle body, by 9 response points in left side
Response curve and average calculating operation obtain resultant curve one, and the response curve of 9 response points on right side and average calculating operation are closed
At curve two, resultant curve one subtracts resultant curve two and obtains resultant curve three, and resultant curve one plus resultant curve two are synthesized
Curve four finally does average calculating operation to resultant curve three, resultant curve four and obtains resultant curve five, and resultant curve one rings for left side
Point set is answered, resultant curve two is right side response point set, and resultant curve five is and average and difference is averagely gathered, and compares synthesis song
Line one, resultant curve two, resultant curve five are vehicle body entirety torsional frequency in peak of curve overlapping region;
Vehicle body integrally reverses 12 point frame recognition methods: 5 response points is each provided with along vehicle body left and right side, before ceiling
It is provided with 1 response point in the middle part of crossbeam, 1 response point is provided in the middle part of back doorframe, collectively forms what vehicle body integrally reversed
12 response points, each front-wheel obligatory point of vehicle body left and right side, rear-wheel obligatory point constitute 4 obligatory points of vehicle body, right front turret, a left side
The 4 excitation points of gun turret, left back gun turret as vehicle body behind front turret, the right side;By the response curve of 5, left side response point and average fortune
Calculation obtains resultant curve one, and the response curve of 5, right side response point and average calculating operation are obtained resultant curve two, will be before and after ceiling
The response curve of 6 response points and average calculating operation obtain resultant curve three, and resultant curve one is subtracted resultant curve two and is synthesized
Resultant curve one plus resultant curve two are obtained resultant curve five by curve four, by resultant curve four, resultant curve five and average fortune
Calculation obtains resultant curve six, and comparison resultant curve four, five peak value overlapping region of resultant curve are whole torsional frequency.
(d), body tail reverses 15 points of identifications:
As shown in figure 5, in back door, circumferentially 15 response points of setting, 15 response points are in clockwise point around back door
Cloth, wherein response point 5, response point 6, response point 7 are located at right above back door, and response point 13, response point 14, response point 15 are located at
Immediately below back door, left back gun turret and it is right after gun turret be 2 excitation points, by the response curve of response point 5,6,7 and response point 13,
14,15 response curve and average calculating operation obtain resultant curve one, and the response of response point 1,2,3,4,8,9,10,11,12 is bent
Line and average calculating operation obtain resultant curve two, compare resultant curve one and two crest frequency overlapping region of resultant curve as after vehicle body
Portion's torsional frequency;
(e), vehicle foreside reverses 8 points of identifications:
In tank bracket, 8 response points are set up and down, 8 response points are distributed around tank bracket in counterclockwise,
Middle response point 4 is located at water tank lower beam middle position, and response point 8 is located at water tank upper beam middle position, left front gun turret and it is right before
Gun turret is 2 excitation points, and the response curve of response point 1,2,3 and the response curve of response point 5,6,7 and average calculating operation are obtained
The response curve of response point 4,8 and average calculating operation are obtained resultant curve two, compare resultant curve one and synthesis by resultant curve one
Two crest frequency overlapping region of curve is vehicle foreside torsional frequency;
(f), vehicle vehicle body torsion slice identification:
Three parts region before, during and after vehicle body is divided into, vehicle foreside cutting line are response point slice 1, and body tail is cut
Secant is response point slice 2, draws response point curve displacement figure, and according to front, rear portion and the integrally recognition methods reversed
The crest frequency for obtaining coincidence, response point relative shift and unique vibration shape cloud atlas in the case where comparing each crest frequency determine office
Portion and whole torsion mode, judgment principle is that peak value is closer to, and the relative displacement of Response to selection position is larger and vibration mode is
The first-order modal of the lateral changing of the relative positions.
Preferably, the vehicle body integrally reverses in 12 point frame recognition methods, if resultant curve three, five peak of resultant curve
Value frequency has multiple and is difficult to judge, then needs to compare calculating with the relative deformation of ceiling frame, the diagonal line at ceiling
Position carries out the foundation of virtual displacement unit, and the cornerwise displacement relative quantity of ceiling for comparing multiple crest frequencies is judged, selects
With the big peak value of deflection torsional frequency as a whole.
Preferably, the body tail reverses in 15 recognition methods, if resultant curve one, resultant curve two occur it is more
A coincidence crest frequency then carries out crest frequency investigation by imaginary line method, vehicle body back door displacement curve is connected into upper small
Big, symmetrical closed A-B-C-D is displaced bending vibation mode picture down, and connects diagonal line and form two curves of L1 and L2, more having
When a crest frequency occurs, displacement deformation amount difference and A-B-C-D the displacement bending vibation mode picture of reduced parameter L1 and L2 are checked,
If it is torsional frequency that A-B-C-D, which is displaced when bending vibation mode picture is the lateral changing of the relative positions and L1, L2 relative displacement deflection maximum,.
Preferably, the vehicle foreside reverses in 8 recognition methods, if resultant curve one, resultant curve two occur it is more
A coincidence crest frequency then carries out crest frequency investigation by imaginary line method, tank bracket displacement curve is connected rectangular
A-B-C-D is displaced bending vibation mode picture, and connects diagonal line and form two curves of L1 and L2, when there is multiple crest frequencies to occur, comparison
Displacement deformation amount difference and A-B-C-D the displacement bending vibation mode picture of parameter L1 and L2 are checked, if A-B-C-D is displaced bending vibation mode picture
It is torsional frequency when for the lateral changing of the relative positions and L1, L2 relative displacement deflection maximum.
Beneficial effects of the present invention: first carrying out block model for vehicle, and determines and identify the way of restraint under torsion mode, then
Recognition methods, body tail torsion recognition methods, vehicle foreside torsion recognition methods and vehicle vehicle body are integrally reversed in conjunction with vehicle body
Torsion slice method of identification, reverses vehicle mode under body and carries out modal idenlification, implementable strong, can effectively avoid that vehicle mould occurs
State erroneous judgement.
Detailed description of the invention
Fig. 1 is whole vehicle model segmented areas figure.
Fig. 2 is that torsion mode identifies constrained figure.
Fig. 3 is that vehicle body integrally reverses 18 recognition methods obligatory points and response point distributing position.
Fig. 4 is that vehicle body integrally reverses 12 point frame recognition methods response point distributing positions.
Fig. 5 is back door response point distribution map.
Fig. 6 is back door imaginary line method.
Fig. 7 is water tank response point distribution map.
Fig. 8 is water tank imaginary line method.
Fig. 9 is vehicle vehicle body torsion slice identification region layout drawing.
Figure 10 is that response point is sliced 1. profile diagram.
Figure 11 is that response point is sliced 2. profile diagram.
Specific embodiment
By way of example and in conjunction with the accompanying drawings, the invention will be further described:
A kind of vehicle mode vehicle body torsion mode recognition methods, comprising the following steps:
(a), whole vehicle model piecemeal:
As shown in Figure 1, first vehicle lumped mass point and shutter member are removed, by vehicle be divided into tire 1., tank bracket 2.,
Vehicle body A column 3., center body pillar 4., body C pillar 5., body rear end 6., wherein vehicle body A column 3., center body pillar 4., body C pillar be 5.
1. the main identification response point of torsion mode under vehicle mode, tire are constraint translation and rotational freedom.
(b), torsion mode identification constraint:
As shown in Fig. 2, under vehicle mode torsion mode identification obligatory point position, by right front turret 1., left front gun turret 2.,
Behind the right side gun turret 3., left back gun turret 4., frame assembly 5. form, specific constraint and combination are as shown in Table 1.
Vehicle foreside reverse vehicle frame right front turret 1., left front gun turret 2. locate application reverse energization, while about tires
1-6 freedom degree;Body tail torsion behind the right side of vehicle frame gun turret 3., left back gun turret 4. locate application reverse energization, while constraining wheel
Tire 1-6 freedom degree;Vehicle body integrally reverse right front turret 1., left front gun turret 2. locate to apply reverse energization, behind the right side gun turret 3., it is left
Afterwards 4. gun turret is located to apply reverse energization, while about tires 1-6 freedom degree.
(c), vehicle body integrally reverses frame identification, and vehicle body introduced below integrally reverses 18 recognition methods and vehicle body is integrally turned round
Turn 12 point frame recognition methods, optionally one of vehicle body that carries out integrally reverses frame identification.
Vehicle body integrally reverses 18 recognition methods: as shown in figure 3, vehicle body left and right side is each provided with 9 response points, including
2., 3., 4. by 3 response points of vehicle body A column trisection, 3 response points of center body pillar trisection 5., 6., 7., body C pillar three
8., 9., 10. 3 response points of equal part, together constitute vehicle body and integrally reverse 18 response points;Each front-wheel of vehicle body left and right side is about
Beam spot 1., rear-wheel obligatory point4 obligatory points of vehicle body are constituted, gun turret, left back gun turret are made behind right front turret, left front gun turret, the right side
For 4 excitation points of vehicle body, the response curve of 9 response points in left side and average calculating operation are obtained into resultant curve one, by right side
9 response points response curve and average calculating operation obtain resultant curve two, resultant curve one subtracts resultant curve two and is synthesized
Curve three, resultant curve one plus resultant curve two obtain resultant curve four, are finally averaged to resultant curve three, resultant curve four
Operation obtains resultant curve five, and resultant curve one is that left side responds point set, and resultant curve two is that right side responds point set, synthesis
Curve five is and average and difference is averagely gathered, and compares resultant curve one, resultant curve two, resultant curve five, in peak of curve weight
Closing region is vehicle body entirety torsional frequency.
Vehicle body integrally reverses 12 point frame recognition methods: as shown in figure 4, being each provided with 5 responses along vehicle body left and right side
Point is provided with 1 response point in the middle part of ceiling front beam, and 1 response point is provided in the middle part of back doorframe, collectively forms vehicle body
12 response points integrally reversed, each front-wheel obligatory point of vehicle body left and right side, rear-wheel obligatory point constitute 4 obligatory points of vehicle body,
The 4 excitation points of gun turret, left back gun turret as vehicle body behind right front turret, left front gun turret, the right side;By the response of 5 response points in left side
Curve and average calculating operation obtain resultant curve one, and the response curve of 5, right side response point and average calculating operation are obtained resultant curve
Two, the response curve of ceiling front and back 6 response point and average calculating operation are obtained into resultant curve three, it is bent that resultant curve one is subtracted synthesis
Line two obtains resultant curve four, and resultant curve one plus resultant curve two are obtained resultant curve five, and resultant curve four, synthesis is bent
Line five and average calculating operation obtain resultant curve six, and comparison resultant curve four, five peak value overlapping region of resultant curve are whole torsion
Frequency.
Vehicle body integrally reverses in 12 point frame recognition methods, if resultant curve three, five crest frequency of resultant curve have it is more
It is a and be difficult to judge, then it needs to compare calculating with the relative deformation of ceiling frame, diagonal positions carry out empty at ceiling
Quasi- displacement unit is established, and the cornerwise displacement relative quantity of ceiling for comparing multiple crest frequencies is judged, selects deflection big
Peak value torsional frequency as a whole.
(d), body tail reverses 15 points of identifications:
As shown in figure 5, in back door, circumferentially 15 response points of setting, 15 response points are in clockwise point around back door
Cloth, it is preferable that the circular back door of 15 response points is close to be equidistantly uniformly distributed.Wherein response point 5., response point 6., response point 7.
Right above back door, response pointResponse pointResponse pointImmediately below back door.After left back gun turret and the right side
Gun turret is 2 excitation points, response curve 5., 6., 7. and response point by response pointResponse curve and
Average calculating operation obtains resultant curve one, by response point 1., 2., 3., 4., 8., 9., 10.,Response curve and average
Operation obtains resultant curve two, compares resultant curve one and two crest frequency overlapping region of resultant curve is body tail torsion frequency
Rate.
Body tail reverses in 15 recognition methods, if multiple coincidence peak values occur in resultant curve one, resultant curve two
Frequency then carries out crest frequency investigation by imaginary line method.Specific method is: as shown in fig. 6, vehicle body back door is displaced bent
Line connects into up-small and down-big, symmetrical closed A-B-C-D displacement bending vibation mode picture, i.e. A-B-C-D is displaced bending vibation mode picture and vehicle body
Back door profile is corresponding, and connects diagonal line and form two curves of L1 and L2.When there is multiple crest frequencies to occur, reduced parameter
Displacement deformation amount difference and A-B-C-D the displacement bending vibation mode picture of L1 and L2 is checked, if A-B-C-D displacement bending vibation mode picture is cross
To being torsional frequency when the changing of the relative positions and L1, L2 relative displacement deflection maximum, remaining is checked as non-twisted frequency.
(e), vehicle foreside reverses 8 points of identifications:
As shown in fig. 7,8 response points are arranged up and down in tank bracket, 8 response points are in the inverse time around tank bracket
Needle distribution, it is preferable that the circular tank bracket of 8 response points is close to be equidistantly uniformly distributed.Wherein 4. response point is located under water tank horizontal
8. beam middle position, response point are located at water tank upper beam middle position, left front gun turret and right front turret are 2 excitation points, will be rung
Response curve 1., 2., 3. and response point response curve 5., 6., 7. should be put and average calculating operation obtains resultant curve one, will be rung
The response curve and average calculating operation that should be put 4., 8. obtain resultant curve two, compare resultant curve one and resultant curve two peak values frequency
Rate overlapping region is vehicle foreside torsional frequency.
Vehicle foreside reverse 8 recognition methods in, as shown in figure 8, if resultant curve one, resultant curve two occur it is multiple
It is overlapped crest frequency and then carries out crest frequency investigation by imaginary line method, tank bracket displacement curve is connected to rectangular A-
B-C-D is displaced bending vibation mode picture, i.e. it is corresponding with tank bracket profile that A-B-C-D is displaced bending vibation mode picture, and connects diagonal line and form L1 and L2
Two curves.When there is multiple crest frequencies to occur, the displacement deformation amount difference and A-B-C-D of reduced parameter L1 and L2 are displaced
Bending vibation mode picture is checked, if A-B-C-D displacement bending vibation mode picture is torsion when being the lateral changing of the relative positions and L1, L2 relative displacement deflection maximum
Turn frequency, remaining is checked as non-twisted frequency.
(f), vehicle vehicle body torsion slice identification:
As shown in figure 9, three parts region before, during and after vehicle body is divided into, vehicle foreside cutting line is response point slice
1. body tail cutting line be response point be sliced 2., draw response point curve displacement figure (such as Fig. 9, Figure 10), and according to front,
Rear portion and the recognition methods integrally reversed obtain the crest frequency of coincidence, and the response point in the case where comparing each crest frequency is opposite
Displacement and unique vibration shape cloud atlas determine part and whole torsion mode, and judgment principle is that peak value is closer to then Response to selection position
Set that relative displacement is larger and vibration mode is the first-order modal of the lateral changing of the relative positions.
Claims (4)
1. a kind of vehicle mode vehicle body torsion mode recognition methods, which comprises the following steps:
(a), whole vehicle model piecemeal:
First vehicle lumped mass point and shutter member are removed, vehicle is divided into tire, tank bracket, vehicle body A column, center body pillar, vehicle
Body C column, body rear end, wherein vehicle body A column, center body pillar, the main identification response that body C pillar is torsion mode under vehicle mode
Point, tire are constraint translation and rotational freedom;
(b), torsion mode identification constraint:
Torsion mode identifies that corresponding energisation mode and the way of restraint are divided into three kinds:
(1), vehicle foreside reverses:
The exciting force of left front gun turret application -1N, the exciting force of right front turret application+1N, tire constrain 6 freedom degrees;
(2), body tail reverses:
The exciting force of left back gun turret application+1N, it is right after gun turret application -1N exciting force, tire constrains 6 freedom degrees;
(3), vehicle body integrally reverses:
The exciting force of left front gun turret application -1N, the exciting force of right front turret application+1N, the exciting force of left back gun turret application+1N,
The exciting force of gun turret application -1N behind the right side, tire constrain 6 freedom degrees;
(c), vehicle body integrally reverses frame identification, and vehicle body introduced below integrally reverses 18 recognition methods and vehicle body integrally reverses 12
Point frame recognition methods, optionally one of vehicle body that carries out integrally reverse frame identification;
Vehicle body integrally reverses 18 recognition methods: vehicle body left and right side is each provided with 9 response points, including by vehicle body A column trisection
3 response points, 3 response points of center body pillar trisection, 3 response points of body C pillar trisection, together constitute vehicle body
18 response points of whole torsion;Each front-wheel obligatory point of vehicle body left and right side, rear-wheel obligatory point constitute 4 obligatory points of vehicle body, right
The 4 excitation points of gun turret, left back gun turret as vehicle body behind front turret, left front gun turret, the right side, by the response of 9 response points in left side
Curve and average calculating operation obtain resultant curve one, and it is bent that the response curve of 9 response points on right side and average calculating operation are obtained synthesis
Line two, resultant curve one subtract resultant curve two and obtain resultant curve three, and resultant curve one plus resultant curve two obtain resultant curve
Four, average calculating operation finally is done to resultant curve three, resultant curve four and obtains resultant curve five, resultant curve one is left side response point
Set, resultant curve two are that right side responds point set, and resultant curve five is and averagely with the average set of difference, compares resultant curve
One, resultant curve two, resultant curve five are vehicle body entirety torsional frequency in peak of curve overlapping region;
Vehicle body integrally reverses 12 point frame recognition methods: 5 response points is each provided with along vehicle body left and right side, in ceiling front beam
Middle part is provided with 1 response point, and 1 response point is provided in the middle part of back doorframe, collectively forms 12 that vehicle body integrally reverses
Response point, each front-wheel obligatory point of vehicle body left and right side, rear-wheel obligatory point constitute 4 obligatory points of vehicle body, right front turret, left front big gun
The 4 excitation points of gun turret, left back gun turret as vehicle body behind tower, the right side;The response curve of 5, left side response point and average calculating operation are obtained
To resultant curve one, the response curve of 5, right side response point and average calculating operation are obtained into resultant curve two, by 6 before and after ceiling
The response curve of response point and average calculating operation obtain resultant curve three, and resultant curve one is subtracted resultant curve two and obtains resultant curve
Four, resultant curve one plus resultant curve two are obtained into resultant curve five, resultant curve four, resultant curve five and average calculating operation are obtained
To resultant curve six, resultant curve four is compared, five peak value overlapping region of resultant curve is whole torsional frequency;
(d), body tail reverses 15 points of identifications:
In circumferential 15 response points of setting of back door, 15 response points around back door in distribution clockwise, wherein response point 5,
Response point 6, response point 7 are located at right above back door, and response point 13, response point 14, response point 15 are located at immediately below back door, left
Gun turret and gun turret behind the right side are 2 excitation points afterwards, by the response curve of the response curve of response point 5,6,7 and response point 13,14,15
Resultant curve one is obtained with average calculating operation, the response curve of response point 1,2,3,4,8,9,10,11,12 and average calculating operation are obtained
Resultant curve two, compares resultant curve one and two crest frequency overlapping region of resultant curve is body tail torsional frequency;
(e), vehicle foreside reverses 8 points of identifications:
8 response points are set up and down in tank bracket, 8 response points are distributed around tank bracket in counterclockwise, wherein ringing
4 should be put and be located at water tank lower beam middle position, response point 8 is located at water tank upper beam middle position, left front gun turret and right front turret
For 2 excitation points, the response curve of response point 1,2,3 and the response curve of response point 5,6,7 and average calculating operation are synthesized
The response curve of response point 4,8 and average calculating operation are obtained resultant curve two, compare resultant curve one and resultant curve by curve one
Two crest frequency overlapping regions are vehicle foreside torsional frequency;
(f), vehicle vehicle body torsion slice identification:
Three parts region before, during and after vehicle body is divided into, vehicle foreside cutting line are response point slice 1, body tail cutting line
For response point slice 2, draw response point curve displacement figure, and according to front, rear portion and integrally the recognition methods reversed obtain
The crest frequency of coincidence, response point relative shift and unique vibration shape cloud atlas in the case where comparing each crest frequency determine part and
Whole torsion mode, judgment principle are that peak value is big close to then Response to selection position relative displacement and vibration mode is the lateral changing of the relative positions
First-order modal.
2. vehicle mode vehicle body torsion mode recognition methods described in accordance with the claim 1, it is characterised in that: the vehicle body is whole
It reverses in 12 point frame recognition methods, if resultant curve three, five crest frequency of resultant curve have multiple and be difficult to judge, needs
Calculating is compared with the relative deformation of ceiling frame, diagonal positions carry out the foundation of virtual displacement unit at ceiling, right
Displacement relative quantity more cornerwise than the ceiling of multiple crest frequencies is judged that the peak value for selecting deflection big reverses as a whole
Frequency.
3. vehicle mode vehicle body torsion mode recognition methods described in accordance with the claim 1, it is characterised in that: the body tail
It reverses in 15 recognition methods, by virtual song if multiple coincidence crest frequencies occur in resultant curve one, resultant curve two
Collimation method carries out crest frequency investigation, and vehicle body back door displacement curve is connected into up-small and down-big, symmetrical closed A-B-
C-D is displaced bending vibation mode picture, and connects diagonal line and form two curves of L1 and L2, when there is multiple crest frequencies to occur, reduced parameter
Displacement deformation amount difference and A-B-C-D the displacement bending vibation mode picture of L1 and L2 is checked, if A-B-C-D displacement bending vibation mode picture is cross
To when the changing of the relative positions and L1, L2 relative displacement deflection maximum be torsional frequency.
4. vehicle mode vehicle body torsion mode recognition methods described in accordance with the claim 1, it is characterised in that: the vehicle foreside
It reverses in 8 recognition methods, by imaginary line if multiple coincidence crest frequencies occur in resultant curve one, resultant curve two
Method carries out crest frequency investigation, and tank bracket displacement curve is connected rectangular A-B-C-D and is displaced bending vibation mode picture, and is connected diagonal
Line forms two curves of L1 and L2, when there is multiple crest frequencies to occur, the displacement deformation amount difference of reduced parameter L1 and L2 with
And A-B-C-D displacement bending vibation mode picture is checked, if A-B-C-D displacement bending vibation mode picture is the lateral changing of the relative positions and L1, L2 relative displacement become
It is torsional frequency when shape amount maximum.
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