CN105698975A - Suspension rod tension force measurement method in variable temperature environment based on frequency method - Google Patents

Abstract

The invention relates to the technical field of suspension rod tension force measurement, and specifically relates to a suspension rod tension force measurement method in a variable temperature environment based on a frequency method. The method is characterized in that the method comprises the steps: giving a movement equation (shown in the description) of suspension rod system no-damping free vibration during the introduction of an environment variable; solving the relation (shown in the description) among the n-order lateral vibration frequency fn, the environment temperature change (T-T0) and a suspension rod tension force F through the movement equation of suspension rod system no-damping free vibration, wherein T is the environment temperature, L is the length of a suspension rod, m<-> (shown in the description) is the mass per unit length of the suspension rod, A is the cross section area of the suspension rod, alpha is the coefficient of thermal expansion of the material of the suspension rod, T0 is the environment temperature after the stretch-draw adjustment of the suspension rod is completed, (T-T0) is the change of the environment temperature, and EI is the bending resistance rigidity of the suspension rod. The method introduces an environment temperature variable into the testing of the tension force of the suspension rod, is high in tension testing force of the suspension rod, and facilitates the actual engineering application.

Description

Based on suspension rod tension determining method under the varying temperature environment of frequency method

Technical field

Suspension rod tension detection technical field of the present invention, is specifically related to a kind of based on suspension rod tension determining method under the varying temperature environment of frequency method。

Background technology

Suspension rod is the Force transmission parts that half through or through arch bridge is important, and its force-bearing situation is closely related with the safe condition of arch bridge。In half through or through arch bridge health monitoring, it is possible to judged the health status of half through or through arch bridge by the change of suspension rod tension force, it is clear that the precision of judged result is closely related with suspension rod tension test precision。Following several method is mainly had at present: oil gauge numeratio, pressure transducer method, magnetic flux be mensuration and frequency method etc. for the health monitoring of the type suspension rod and the calculating of Suo Li, it is the most commonly used that the dynamic signal acquisition being wherein principle design with frequency method analyzes system, namely goes out this boom internal force by test suspension rod oscillation crosswise frequency indirect detection。

For improving suspension rod tension test precision, some scholars have studied the impact on suspension rod tension force such as suspension rod bending rigidity, suspension rod two ends boundary condition, vibroshock, suspension rod parameter。The Chinese patent that publication number is 102230833A discloses the suspension rod tension determining method based on frequency method, it includes step: determine suspension rod parameter, determine suspension rod boundary parameter, test suspension rod oscillation crosswise frequency, calculate suspension rod tension force, but do not consider the ambient temperature impact on the suspension rod natural frequency of vibration and tension force, and owing to structural material expands with heat and contract with cold characteristic in reality, for the suspension rod adjusting rope to complete, when the temperature is changed, suspension rod tension force can change, suspension rod oscillation crosswise frequency changes simultaneously, so can make the temperature of suspension rod, tension force and frequency produce reciprocal influence, if not considering the impact of ambient temperature when calculating suspension rod tension force, the degree of accuracy of the suspension rod tension force that measuring and calculation draws cannot be ensured, it is unfavorable for practical engineering application。

Therefore, a kind of suspension rod tension determining method considering suspension rod ambient temperature is needed badly。

Summary of the invention

It is an object of the invention to for above-mentioned Problems existing, it is provided that a kind of consider ambient temperature variable, can improve suspension rod tension test precision based on suspension rod tension determining method under the varying temperature environment of frequency method。

The present invention based on the technical scheme of suspension rod tension determining method under the varying temperature environment of frequency method is:

A kind of based on suspension rod tension determining method under the varying temperature environment of frequency method, including step:

Test suspension rod oscillation crosswise frequency f_n；

The equation of motion of suspension rod system undamped-free vibration during calculating introducing environmental variable:

$EI\frac{{\&part;}^{4}v(x,t)}{\&part;x^4}-\&lsqb;F-E\mathrm{\&alpha;}(T-T_0)A\&rsqb;\frac{{\&part;}^{2}v(x,t)}{\&part;x^2}+\stackrel{\&OverBar;}{m}\frac{{\&part;}^{2}v(x,t)}{\&part;t^2}=0;$

The equation of motion utilizing suspension rod system undamped-free vibration solves suspension rod vibration n-th order oscillation crosswise frequency f_nWith variation of ambient temperature (T-T₀) and the relational expression of suspension rod tension force F be: $F=4{\mathrm{mL}}^2{\left(\frac{f_n}{n}\right)}^2-EI{\left(\frac{n\mathrm{\&pi;}}{L}\right)}^2+EA\mathrm{\&alpha;}(T-T_0);$

Wherein, T is ambient temperature；

L is length of boom；

For length of boom quality；

A is suspension rod cross-sectional area；

α is suspension rod material thermal expansion coefficient；

T₀Ambient temperature when adjusting rope to complete for suspender tension；

(T-T₀) for variation of ambient temperature amount；

EI is suspension rod bending rigidity。

Further, the equation of motion of described suspension rod system undamped-free vibration adopts the separation of variable to solve。

Further, described suspension rod linear massFor the linear mass for the steel wire of suspension rod and sheath。

Further, the moment of inertia I in described suspension rod bending rigidity EI is the whole steel wires of the suspension rod the moment of inertia sums to the section row heart, and E is the elastic modelling quantity of steel wire。

Further, when derivation introduces the equation of motion of the suspension rod system undamped-free vibration of ambient temperature variable, the stress σ (T) and tension force F of the suspension rod caused during by variation of ambient temperature_N(T) it is:

σ (T)=E α (T-T₀)(1)

F_N(T)=F-σ (T) A (2)；

The equilibrium condition being obtained power by dAlembert principle is:

$F_s(x,t)-\&lsqb;F_s(x,t)+\frac{\&part;F_s(x,t)}{\&part;x}dx\&rsqb;+f_I(x,t)dx=0---\left(3\right);$

The equilibrium condition of the cross-section centroid square of suspension rod is:

$M(x,t)+F_s(x,t)dx-F_N\left(T\right)\frac{\&part;v(x,t)}{\&part;x}dx-\&lsqb;M(x,t)+\frac{\&part;M(x,t)}{\&part;x}dx\&rsqb;=0---\left(4\right);$

Moment of flexure and curvature relationship formula be: $M(x,t)=-EI\frac{{\&part;}^{2}v(x,t)}{\&part;x^2}---\left(5\right);$

During described consideration environment alternating temperature, the equation of motion of suspension rod system undamped-free vibration by bringing formula (3) into and utilizing formula (1) and formula (2) abbreviation and obtain by formula (4) and formula (5)。

Further, the equation of motion of described suspension rod system undamped-free vibration solves suspension rod vibration n-th order oscillation crosswise frequency and variation of ambient temperature (T-T₀) relational expression described inThen the critical temperature of temperature rise rear suspension bar thermal post-buckling is set to T_cr, thenAnd obtain suspension rod thermal post-buckling critical pressure when suspension rod initial tension is zero and be: $F_{cr}=EA\mathrm{\&alpha;}(T_{cr}-T_0)\&le;\frac{{\mathrm{\&pi;}}^{2}EI}{L^2}.$

The invention has the beneficial effects as follows: ambient temperature is incorporated in the calculating of suspension rod tension force as variable by the present invention, take into account the characteristic impact on suspension rod frequency of vibration of expanding with heat and contract with cold of the material that variations in temperature causes, extrapolate the equation of motion of suspension rod undamped-free vibration, solve an equation to obtain suspension rod tension force, the precision of the suspension rod tension force that this invention under equal conditions calculates is higher, environmental change in the actual suspension rod test of true simulation, result of calculation is accurate；Solve suspension rod undamped-free vibration equation and obtain suspension rod n rank frequency of vibration, thermal buckling critical temperature and the critical pressure excessively that calculate suspension rod can be calculated, so can in the application as the foundation avoiding suspension rod unstability。

Accompanying drawing explanation

Fig. 1 embodiment of the present invention provide based on suspension rod tension determining method under the varying temperature environment of frequency method；

The mechanical model that Fig. 2 suspension rod tension force provided by the invention calculates；

Fig. 3 is Practical Project example middle hanger numbering figure of the present invention。

Detailed description of the invention

The invention discloses a kind of based on suspension rod tension determining method under the varying temperature environment of frequency method, to improve the measuring accuracy of suspension rod tension force。

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete description, it is clear that described embodiment is only a part of embodiment of the present invention, rather than whole embodiment。Based on the embodiment in the present invention, those of ordinary skill in the art are obtained every other embodiment under not making creative work premise, broadly fall into protection scope of the present invention。

Provided by the invention based on suspension rod tension determining method under the varying temperature environment of frequency method, including:

Step one: determine suspension rod parameter；

If homogenizing suspension rod length is L, cross-sectional area is A, and suspension rod linear mass isSuspension rod material thermal expansion coefficient is α, the practical situation according to suspension rod, it is determined that go out the corresponding above-mentioned parameter of suspension rod。Wherein, suspension rod linear mass m is the linear mass of the steel wire of suspension rod and sheath。Assuming that ambient temperature is T when suspender tension adjusts rope to complete₀, suspension rod tension force is F, and when ambient temperature is T, the suspension rod tension force variable that variations in temperature causes is F_N(T)。

Step 2: the oscillation crosswise frequency f of test suspension rod_n；

Step 3: calculate the oscillation crosswise frequency f of suspension rod_nAnd the relation between suspension rod tension force F and variation of ambient temperature；

Consider that under ambient temperature, the relation of suspension rod oscillation crosswise frequency and suspension rod tension force F is:

$F=4{\mathrm{mL}}^2{\left(\frac{f_n}{n}\right)}^2-EI{\left(\frac{n\mathrm{\&pi;}}{L}\right)}^2+EA\mathrm{\&alpha;}(T-T_0);$

Wherein,For suspension rod linear mass；L is length of boom；F_nN-th order oscillation crosswise frequency is vibrated for suspension rod；EI is suspension rod bending rigidity；E is suspension rod tensile modulus of elasticity；A is suspension rod cross-sectional area；α is suspension rod material thermal expansion coefficient；(T-T₀) for variation of ambient temperature amount。Wherein, the moment of inertia I in suspension rod bending rigidity EI is the whole steel wires of the suspension rod the moment of inertia sums to the section row heart。

The known suspension rod parameter of the present invention and variation of ambient temperature amount (T-T₀), calculate the equation of motion of suspension rod undamped-free vibration, solve the equation of motion and can obtain suspension rod vibration n-th order oscillation crosswise frequency f_nWith variation of ambient temperature (T-T₀) and the relational expression of suspension rod tension force F, bring suspension rod oscillation crosswise frequency f into_nSuspension rod tension force can be tried to achieve。Relational expression relatively accurately considers the tension change that variations in temperature causes, and truly simulates the environmental change in the test of actual suspension rod, and result of calculation is accurate。

1, the equation of motion of suspension rod system undamped-free vibration during calculating introducing environmental variable。

At the long L of Simple Boundary Conditions suspension rod, cross-sectional area A, suspension rod linear massWhen known with suspension rod material thermal expansion coefficient α, the stress σ (T) and tension force F of the suspension rod caused during variation of ambient temperature_N(T) it is represented by:

σ (T)=E α (T-T₀)(1)

F_N(T)=F-σ (T) A (2)

It is illustrated in figure 2 suspension rod mechanics model when ambient temperature is T,

According to dAlembert principle, at any instant of particle movement, active force, restraining forces and inertia force constitute balanced system of force, by the equilibrium condition of power, and equilibrium equation that can be capable:

$F_s(x,t)-\&lsqb;F_s(x,t)+\frac{\&part;F_s(x,t)}{\&part;x}dx\&rsqb;+f_I(x,t)dx=0---\left(3\right)$

In formula: $f_I(x,t)=\stackrel{\&OverBar;}{m}\frac{{\&part;}^{2}v(x,t)}{\&part;t^2}$

Abbreviation equilibrium equation (3) can obtain:

$\frac{\&part;F_s(x,t)}{\&part;x}=\stackrel{\&OverBar;}{m}\frac{{\&part;}^{2}v(x,t)}{\&part;t^2}---\left(4\right)$

Suspension rod cross-section centroid is sought square, the equilibrium condition of square can obtain the equilibrium equation of square:

$M(x,t)+F_s(x,t)dx-F_N\left(T\right)\frac{\&part;v(x,t)}{\&part;x}dx-\&lsqb;M(x,t)+\frac{\&part;M(x,t)}{\&part;x}dx\&rsqb;=0---\left(5\right)$

Equilibrium equation (5) abbreviation of square obtains:

$F_s(x,t)=F_N\left(T\right)\frac{\&part;v(x,t)}{\&part;x}+\frac{\&part;M(x,t)}{\&part;x}---\left(6\right)$

According to moment of flexure and curvature relationship formula:

$M(x,t)=-EI\frac{{\&part;}^{2}v(x,t)}{\&part;x^2}---\left(7\right)$

Formula (6), (7) are substituted into formula (4), can consider that during environment alternating temperature, the equation of motion of suspension rod system undamped-free vibration is:

$EI\frac{{\&part;}^{4}v(x,t)}{\&part;x^4}-\frac{\&part;}{\&part;x}\&lsqb;F_N\left(T\right)\frac{\&part;v(x,t)}{\&part;x}\&rsqb;+\stackrel{\&OverBar;}{m}\frac{{\&part;}^{2}v(x,t)}{\&part;t^2}=0---\left(8\right)$

By the equation of motion (8) of formula (1), (2) substitution suspension rod system undamped-free vibration:

$EI\frac{{\&part;}^{4}v(x,t)}{\&part;x^4}-\&lsqb;F-E\mathrm{\&alpha;}(T-T_0)A\&rsqb;\frac{{\&part;}^{2}v(x,t)}{\&part;x^2}+\stackrel{\&OverBar;}{m}\frac{{\&part;}^{2}v(x,t)}{\&part;t^2}=0---\left(9\right)$

2, the solving of the equation of motion of suspension rod system undamped-free vibration。

The separation of variable is adopted to solve the differential equation of undamped-free vibration, if the form of the solution of equation (9) is: v (x, t)=φ (x) Y (t)

The form of the solution of equation (9) is substituted into formula (9), has

$\frac{{\mathrm{\&phi;}}^{iv}\left(x\right)}{\mathrm{\&phi;}\left(x\right)}-\frac{F-EA\mathrm{\&alpha;}(T-T_0)}{EI}\frac{{\mathrm{\&phi;}}^{\&prime;\&prime;}\left(x\right)}{\mathrm{\&phi;}\left(x\right)}+\frac{\stackrel{\&OverBar;}{m}}{EI}\frac{\stackrel{\&CenterDot;\&CenterDot;}{Y}\left(t\right)}{Y\left(t\right)}=0---\left(10\right)$

Wherein, ${\mathrm{\&phi;}}^{iv}\left(x\right)=\frac{{\&part;}^4\mathrm{\&phi;}}{\&part;x^4},{\mathrm{\&phi;}}^{\&prime;\&prime;}\left(x\right)=\frac{{\&part;}^2\mathrm{\&phi;}}{\&part;x^2},\stackrel{\&CenterDot;\&CenterDot;}{Y}\left(t\right)=\frac{{\&part;}^{2}Y}{\&part;t^2};$

To equation (10) two ends variables separation, have:

$\frac{{\mathrm{\&phi;}}^{iv}\left(x\right)}{\mathrm{\&phi;}\left(x\right)}-\frac{F-EA\mathrm{\&alpha;}(T-T_0)}{EI}\frac{{\mathrm{\&phi;}}^{\&prime;\&prime;}\left(x\right)}{\mathrm{\&phi;}\left(x\right)}=-\frac{\stackrel{\&OverBar;}{m}}{EI}\frac{\stackrel{\&CenterDot;\&CenterDot;}{Y}\left(t\right)}{Y\left(t\right)}---\left(11\right)$

Order $a^4=\frac{{\mathrm{\&omega;}}^{2}m}{EI},g^2=\frac{F-EA\mathrm{\&alpha;}(T-T_0)}{EI},\mathrm{\&delta;}=\sqrt{\sqrt{a^4+\frac{g^4}{4}}-\frac{g^2}{2}},\mathrm{\&epsiv;}=\sqrt{\sqrt{a^4+\frac{g^4}{4}}+\frac{g^2}{2}}$

In formula, ω is suspension rod oscillation crosswise circular frequency；EI is suspension rod bending rigidity。

Then formula (11) can be changed into:

$\stackrel{\&CenterDot;\&CenterDot;}{Y}\left(t\right)+{\mathrm{\&omega;}}^{2}Y\left(t\right)=0---\left(12\right)$

${\mathrm{\&phi;}}^{iv}\left(x\right)-\frac{F-EA\mathrm{\&alpha;}(T-T_0)}{EI}{\mathrm{\&phi;}}^{\&prime;\&prime;}\left(x\right)-a^4\mathrm{\&phi;}\left(x\right)=0---\left(13\right)$

Shape function φ (x) can be expressed as:

φ (x)=D₁cos(δx)+D₂sin(δx)+D₃cosh(εx)+D₄sinh(εx)(14)

In formula: D₁,D₂,D₃,D₄For undetermined coefficient, can be determined by suspension rod boundary condition。

For the suspension rod that length is bigger, two ends can be reduced to rotational restraint, then the boundary condition of suspension rod vibration equation is: φ (0)=0, φ " (0)=0, φ (L)=0, φ " (L)=0 (15)

Formula (15) is substituted into formula (14), has

${\mathrm{\&omega;}}_n^2=\frac{{\left(n\mathrm{\&pi;}\right)}^4}{L^4}\frac{EI}{m}+\frac{F-A\mathrm{\&alpha;}(T-T_0)}{EI}\frac{{\left(n\mathrm{\&pi;}\right)}^2}{L^2}\frac{EI}{\stackrel{\&OverBar;}{m}}---\left(16\right)$

Note suspension rod vibration n-th order oscillation crosswise frequency is f_n, andThen formula (16) can abbreviation be:

$f_n=\frac{n}{2L}\sqrt{\frac{{\left(n\mathrm{\&pi;}\right)}^{2}EI}{L^2\stackrel{\&OverBar;}{m}}+\frac{F-EA\mathrm{\&alpha;}(T-T_0)}{\stackrel{\&OverBar;}{m}}}---\left(17\right)$

When known suspension rod tension force and variation of ambient temperature, formula (17) suspension rod frequency of vibration can be obtained。

When known suspension rod oscillation crosswise frequency and variation of ambient temperature, by formula (17) can the expression formula of suspension rod tension force be:

$F=4{\mathrm{mL}}^2{\left(\frac{f_n}{n}\right)}^2-EI{\left(\frac{n\mathrm{\&pi;}}{L}\right)}^2+EA\mathrm{\&alpha;}(T-T_0)---\left(18\right)$

Formula (18) is suspension rod tension force and oscillation crosswise frequency relation formula when considering variation of ambient temperature, hang-rod rigidity。

Under different conditions, formula (18) can be reduced to following form:

(1) when being left out bending rigidity and variation of ambient temperature, i.e. EI=0, T-T₀=0 relation that can obtain suspension rod tension force and oscillation crosswise frequency is:

$F=4\stackrel{\&OverBar;}{m}{L}^2{\left(\frac{f_n}{n}\right)}^2$

(2) when being left out bending rigidity, it is considered to during variation of ambient temperature, namely obtain during EI=0:

$F=4\stackrel{\&OverBar;}{m}{L}^2{\left(\frac{f_n}{n}\right)}^2+EA\mathrm{\&alpha;}(T-T_0)$

(3) when considering bending rigidity, when being left out variation of ambient temperature, i.e. T-T₀Obtain when=0:

$F=4\stackrel{\&OverBar;}{m}{L}^2{\left(\frac{f_n}{n}\right)}^2-EI{\left(\frac{n\mathrm{\&pi;}}{L}\right)}^2---\left(19\right)$

Wherein, formula (18) is and considers that temperature environment becomes the computing formula of suspension rod tension force under lower condition；Formula (19) is be left out ambient temperature environment to become the computing formula of suspension rod tension force under lower condition；

3, suspension rod crosses the calculating of thermal buckling critical pressure。

When temperature is stepped up, boom internal force is progressively become pressure from tension force, temperature condition when now can also be obtained suspension rod thermal post-buckling by formula (17)。By

$\frac{{\left(n\mathrm{\&pi;}\right)}^{2}EI}{L^2\stackrel{\&OverBar;}{m}}+\frac{F-EA\mathrm{\&alpha;}(T-T_0)}{\stackrel{\&OverBar;}{m}}\&GreaterEqual;0$ Can obtain:

$T_{cr}\&le;T_0+\frac{1}{EA\mathrm{\&alpha;}}\&lsqb;\frac{{\mathrm{\&pi;}}^{2}EI}{L^2}+F\&rsqb;$

Wherein, T_crFor temperature rise rear suspension bar thermal post-buckling critical temperature；

So, when suspension rod initial tension is 0, if F_crCritical pressure, then F during for suspension rod thermal post-buckling_crIt is represented by:

$F_{cr}=EA\mathrm{\&alpha;}(T_{cr}-T_0)\&le;\frac{{\mathrm{\&pi;}}^{2}EI}{L^2}---\left(20\right)$

Formula (20) is pin-ended compression rod critical pressure at failed stability Euler's formula。

Analysis according to above example, can be calculated the tension force obtaining considering the suspension rod of ambient temperature environmental effect by formula (18)。

3. in the above embodiment of the present invention, the technology of tension detection realizes the comparison of application example and actual tension test number。

Test data is taken as south water to north Xichuan Duan Xiying Through Concrete-filled Steel Tubular Arch Bridge data, this bridge crane bar relevant parameter is: bridge major arch rib adopts uiform section dumb-bell shape concrete filled steel tube, arch is second-degree parabola, calculates across footpath 90m, and calculating ratio of rise to span is 1/5。Bridge floor width 7.7m。Uiform section dumb-bell shape main arch rib outer profile size is 0.82m × 2.2m, and chord member steel pipe is φ 820mm × 16mm, irrigates C50 slightly expanded concrete in the upper and lower string steel pipe of arch rib；Arranging one Rigid Tie Beam of Long between per pass arch rib arch springing, binder adopts C50 inherent stress concrete box-beam, and cross section is the single box single chamber box section of wide 1.5m, high 2.0m；Full-bridge sets 30 pairs of suspension rods altogether, and suspension rod adopts the zinc-plated high-strength parallel steel wire flexible suspension rod of PES7-73, and normal intensity is 1670MPa。Suspension rod cross-sectional area is 2.809 × 10^-3m², elasticity modulus of materials 195GPa, the moment of inertia 6.26 × 10^-7m⁴, thermal coefficient of expansion is 1.0 × 10^-5/℃。

Main suspension rod Tension design value is as shown in table 1, according to construction monitoring data, when ground temperature is 27 DEG C when Arch Bridge Construction closure suspender tension adjusts rope to complete。

Suspension rod vibration-testing have employed DH5906 no trace force tester。Collection vibration signal is tested by being built-in with the DH5906A wireless vibration acquisition module of highly sensitive acceleration transducer, it is wirelessly transmitted to ZigBee receiver module, and input computer by USB line, DHDAS_5906 dynamic signal acquisition analyze systematic analysis and obtain suspension rod time-domain diagram and spectrogram。According to suspension rod time-domain diagram and spectrogram, it is respectively adopted formula (18) and calculates suspension rod tension force and as shown in table 1 with actual measurement tension force comparative result with formula (19)。

Table 1 south water to north Xichuan section CFST Arch Bridge suspension rod measured data and tension force value of calculation

As can be seen from Table 1, formula (18) is adopted to calculate suspension rod tension force maximum error less than 3.07% when considering ambient temperature effect for long suspension rod tension test 5, and adopt formula (19) to calculate maximum error when being left out ambient temperature effect and reach 10.17%, can be seen that when surveying suspension rod tension force, formula (18) considers the impact of ambient temperature, hence it is evident that improve measuring accuracy。Being left out when temperature affects and adopt formula (19), result of calculation is generally bigger than normal than actual value。Ambient temperature effect up-to-date style (19) is left out for 1, No. 2 suspension rods and calculates error respectively to 29.71%, 32.04%, and consider that ambient temperature effect up-to-date style (18) calculates error respectively 18.21%, 22.45%。Two suspension rod errors are all relatively big, are 3.84m mainly due to No. 1 length of boom, belong to short steeve；And No. 2 length of booms are 7.37m, belong to middle hanger。According to literature research achievement, in, short steeve two ends boundary condition can be reduced to consolidation, be unsatisfactory for formula boundary condition, thus calculate error and increase, but relative error about 10% can be reduced when the formula of employing (18) considers ambient temperature effect。

Result above shows the suspension rod tension test bigger for length, when considering ambient temperature effect, adopts formula (18) to calculate precision during suspension rod tension force higher, closer to actual value。And formula is Explicit Form, it is simple to the practical application of engineering。Also precision about 10% can be improved when ambient temperature effect is considered for middle short steeve。

In sum, the present invention, according to dynamic equilibrium condition, hangs tension force and oscillation crosswise frequency relation formula when giving consideration ambient temperature effect, hang-rod rigidity, and result of calculation shows, for Seasonal Temperature Difference larger area, during suspension rod tension test, ambient temperature effect be can not ignore。The present invention has accurately accounted for the tension change that variations in temperature causes, the environmental change in the actual suspension rod test of true simulation, can significantly improve the measuring accuracy of suspension rod。

Described above to the disclosed embodiments, makes professional and technical personnel in the field be capable of or uses the present invention。The multiple amendment of these embodiments be will be apparent to one skilled in the art, and generic principles defined herein can without departing from the spirit or scope of the present invention, realize in other embodiments。Therefore, the present invention is not intended to be limited to the embodiments shown herein, and is to fit to the widest scope consistent with principles disclosed herein and features of novelty。

Claims (6)

1. one kind based on suspension rod tension determining method under the varying temperature environment of frequency method, it is characterised in that include step:

1) test suspension rod oscillation crosswise frequency f_n；

2) equation of motion of suspension rod system undamped-free vibration during foundation introducing environmental variable:

3) equation of motion utilizing suspension rod system undamped-free vibration solves suspension rod vibration n-th order oscillation crosswise frequency f_nWith variation of ambient temperature (T-T₀) and the relational expression of suspension rod tension force F be:

Wherein, T is ambient temperature；

L is length of boom；

For length of boom quality；

A is suspension rod cross-sectional area；

α is suspension rod material thermal expansion coefficient；

T₀Ambient temperature when adjusting rope to complete for suspender tension；

(T-T₀) for variation of ambient temperature amount；

EI is suspension rod bending rigidity。

2. according to claim 1 based on suspension rod tension determining method under the varying temperature environment of frequency method, it is characterised in that: the equation of motion of described suspension rod system undamped-free vibration adopts the separation of variable to solve。

3. according to claim 1 based on suspension rod tension determining method under the varying temperature environment of frequency method, it is characterised in that: described suspension rod linear mass m is the linear mass of the steel wire of suspension rod and sheath。

4. according to claim 1 based on suspension rod tension determining method under the varying temperature environment of frequency method, it is characterised in that: the moment of inertia I in described suspension rod bending rigidity EI is the whole steel wires of the suspension rod the moment of inertia sums to the section row heart, and E is the elastic modelling quantity of steel wire。

5. according to claim 1 based on suspension rod tension determining method under the varying temperature environment of frequency method, it is characterized in that: when derivation introduces the equation of motion of the suspension rod system undamped-free vibration of ambient temperature variable, the stress σ (T) and tension force F of the suspension rod caused during by variation of ambient temperature_N(T) it is:

σ (T)=E α (T-T₀)(1)

F_N(T)=F-σ (T) A (2)；

The equilibrium condition being obtained inner power by dAlembert principle is:

The equilibrium condition of the cross-section centroid square of suspension rod is:

Moment of flexure and curvature relationship formula be:

During described consideration environment alternating temperature, the equation of motion of suspension rod system undamped-free vibration by bringing formula (3) into and utilizing formula (1) and formula (2) abbreviation and obtain by formula (4) and formula (5)。

6. according to claim 1 based on suspension rod tension determining method under the varying temperature environment of frequency method, it is characterised in that: the equation of motion of described suspension rod system undamped-free vibration solves suspension rod vibration n-th order oscillation crosswise frequency and variation of ambient temperature (T-T₀) relational expression described inThen the critical temperature of temperature rise rear suspension bar thermal post-buckling is set to T_cr, thenAnd obtain suspension rod thermal post-buckling critical pressure when suspension rod initial tension is zero and be: