CN103837400B - A kind of determine the method for Membrane deflection value under the circular membrane concentration power that periphery clamps - Google Patents

Abstract

The invention discloses and a kind of determine the method for Membrane deflection value under the circular membrane concentration power that periphery clamps: be a by radius, thickness is h, Young's modulus of elasticity is E, Poisson's ratio is the circular membrane of v, fix to clamp in its border, use a band with or without the flat cylinder that radius is b that rubs as loading axle, transverse load F is applied in the center of circular membrane, during loading, cylinder keeps on the same axis with circular membrane, and remember α=b/a, so based on this axial symmetry circular membrane problem standing balance analysis, utilize load measurement value F, then can accurately determine Membrane deflection value w (r) at a r.

Description

A kind of determine the method for Membrane deflection value under the circular membrane concentration power that periphery clamps

Technical field

The circular membrane Membrane deflection value under concentration power effect that the present invention relates to periphery clamping determines method.

Background technology

Membrane structure has a wide range of applications in fields such as machinery, electronics, biological engineering, the thinnest yet with thin film, thus Typically exhibit out bigger amount of deflection under load effect, i.e. belong to geometrical non-linearity problem on deformation, the essence of these nonlinear deformation problems Really Analytical Solution, the most difficult, is in most cases only capable of providing numerical result.

But, for design problems such as many such as diaphragm gauge instrument, it is necessary to Exacts based on these thin film problems It is designed, and numerical result is typically difficult to meet this requirement.

The present invention, for the actual demand of engineer applied problem, the accurate Analysis Solve problems of research circular membrane structure.

Summary of the invention

The circular membrane of periphery clamping loading structure under concentration power effect, can be used to develop various sensor, and at thin film The Mechanics Performance Testing of/basic unit system also has important application.The present invention, the loading for this circular membrane structure constructs, and gives Having gone out the determination method of Membrane deflection value, BROAD SUMMARY is as follows:

As it is shown in figure 1, by radius be a, thickness be h, Young's modulus of elasticity be E, Poisson's ratio be the circular membrane of v, at it Border fixes to clamp, and uses a band with or without the flat cylinder that radius is b that rubs as loading axle, at the center of circular membrane Place applies transverse load F, and during loading, cylinder keeps on the same axis with circular membrane, and remembers α=b/a, then base In the standing balance analysis of this axial symmetry circular membrane problem, it is readily obtained:

If 1.

(1+ν)(3-α²)=4,

Then the Membrane deflection value at some r is

$w\left(r\right)={\left(\frac{a^{2}F}{\mathrm{\πhE}}\right)}^{1/3}[{(3-{\mathrm{\α}}^2)}^{1/3}-{(3\frac{r^2}{a^2}-{\mathrm{\α}}^2)}^{1/3}]$

Wherein π is pi;

If 2.

(1+ν)(3-α²)<4

Then the Membrane deflection value at some r is

Wherein, π is pi,By formula

Determine, andWithValue (unit is radian) by formula

With

Determine；

If 3.

(1+ν)(3-α²)>4

Then the Membrane deflection value at some r is

Wherein, π is pi,By formula

Determine, andWithValue (unit is radian) by formula

With

Determine.

Accompanying drawing explanation

Fig. 1 is the circular membrane of periphery clamping loading organigram under concentration power effect, in FIG, 1-circular membrane, 2 -clamping device, 3-cylinder (loading axle), symbol therein is, a represents the radius of circular membrane, and b represents that cylinder (adds Carry axle) radius, r represents radial coordinate, and w (r) represents the lateral coordinates at some r, and F represents lateral external forces.

Detailed description of the invention

Below in conjunction with the accompanying drawings technical scheme is described in further detail:

As it is shown in figure 1, by radius be a, thickness be h, Young's modulus of elasticity be E, Poisson's ratio be the circular membrane of v, at it Border fixes to clamp, and the flat cylinder using radius to be b, as loading axle, applies a horizontal stroke in the center of circular membrane To load F, before loading cylindrical flat on smear Pulvis Talci, to reduce the friction between film/base, cylinder during loading Keep on the same axis with circular membrane, and remember α=b/a, then standing balance based on this axial symmetry circular membrane problem is divided Analysis, utilizes load measurement value F, Membrane deflection value w (r) at some r, can carry out calculating according to following three kinds of situations and determine:

If situation is 1.

(1+ν)(3-α²)=4,

Then the Membrane deflection value at some r is

$w\left(r\right)={\left(\frac{a^{2}F}{\mathrm{\&pi;hE}}\right)}^{1/3}[{(3-{\mathrm{\&alpha;}}^2)}^{1/3}-{(3\frac{r^2}{a^2}-{\mathrm{\&alpha;}}^2)}^{1/3}]$

Wherein π is pi;

If situation is 2.

(1+ν)(3-α²)<4

Then the Membrane deflection value at some r is

Wherein, π is pi,By formula

Determine, andWithValue (unit is radian) by formula

With

Determine；

If situation is 3.

(1+ν)(3-α²)>4

Then the Membrane deflection value at some r is

Wherein, π is pi,By formula

Determine, andWithValue (unit is radian) by formula

With

Determine.

All parameters all use the International System of Units.

Claims (1)

1. determine a method for Membrane deflection value under the circular membrane concentration power that periphery clamps, it is characterized in that: will be partly Footpath is a, thickness is h, Young's modulus of elasticity is E, Poisson's ratio is the circular membrane of v, at its border fixation clamp Tightly, use a band with or without the flat cylinder that radius is b that rubs as loading axle, at the center of circular membrane Place applies transverse load F, and during loading, cylinder keeps on the same axis with circular membrane, and remembers α=b/a, then standing balance analysis based on this axial symmetry circular membrane problem, utilizes load measurement value F, Membrane deflection value w (r) at some r, can carry out calculating according to following three kinds of situations and determine:

If situation is 1.

(1+ν)(3-α²)=4,

Then the Membrane deflection value at some r is

$w\left(r\right)={\left(\frac{a^{2}F}{\mathrm{\&pi;}hE}\right)}^{1/3}\&lsqb;{(3-{\mathrm{\&alpha;}}^2)}^{1/3}-{(3\frac{r^2}{a^2}-{\mathrm{\&alpha;}}^2)}^{1/3}\&rsqb;$

Wherein π is pi；

If situation is 2.

(1+ν)(3-α²) ＜ 4

Then the Membrane deflection value at some r is

Wherein, π is pi,By formula

Determine, andWithValue by formula

With

Determine；

If situation is 3.

(1+ν)(3-α²) ＞ 4

Then the Membrane deflection value at some r is

Wherein, π is pi,By formula

Determine, andWithValue by formula

With

Determine；

All parameters all use the International System of Units.