CN103837400A - Method for determining thin film deflection value of periphery-clamped circular thin film under concentrated force - Google Patents

Abstract

The invention discloses a method for determining a thin film deflection value of a periphery-clamped circular thin film under concentrated force. The method comprises the following steps: fixing and clamping the circular thin film with the radius of a, the thickness of h, the Young elastic modulus of E and the Poisson ratio of v on the peripheral ring; applying a transverse load F to the center of the circular thin film, wherein a cylinder with a friction-free flat bottom and the radius of b is used as a loading shaft; in the loading process, keeping the cylinder and the circular thin film on the same axis and marking alpha=b/a; carrying out static force balance analysis based on an axial symmetry circular thin film problem; and accurately determining a thin film deflection value w(r) at a point r by using the load measuring value F.

Description

The method of Membrane deflection value under the circular membrane concentrated force that a kind of definite periphery clamps

Technical field

The present invention relates to the Membrane deflection value of circular membrane under concentrated force effect that periphery clamps and determine method.

Background technology

Membrane structure has a wide range of applications in fields such as machinery, electronics, bioengineering, but because film is very thin, thereby under load, conventionally present larger amount of deflection, belong to geometrical non-linearity problem on deformation, the accurate Analysis of these nonlinear deformation problems solves, conventionally very difficult, in most cases only can provide numerical result.

But,, must design by the Exact based on these film problems, and numerical result is difficult to meet this requirement conventionally design problems such as diaphragm gauge instrument for many.

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

Summary of the invention

The loading structure of the circular membrane that periphery clamps under concentrated force effect, can be used for developing various sensors, and in the Mechanics Performance Testing of film/basic unit system, also have important application.The present invention, for the loading structure of this circular membrane structure, has provided definite method of Membrane deflection value, and main summary of the invention is as follows:

As shown in Figure 1, be that a, thickness are that h, Young's modulus of elasticity are the circular membrane that E, Poisson ratio are v by radius, fix to clamp in its border, to adopt a band to have or not the flat radius of friction be b right cylinder is as loading axle, apply a transverse load F in the center of circular membrane, when loading, right cylinder and circular membrane remain on same axis, and remember α=b/a, statical equilibrium analysis based on this rotational symmetry circular membrane problem so, easily obtains:

If 1.

(1+ν)(3-α ²)=4,

The Membrane deflection value of putting r place is

$w\left(r\right)={\left(\frac{a^{2}F}{\mathrm{\&pi;hE}}\right)}^{1/3}[{(3-{\mathrm{\&alpha;}}^2)}^{1/3}-{(3\frac{{\mathrm{<figure-callout\; id="2a"\; label="r"\; filenames="HDA0000481282210000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{a^2}-{\mathrm{\&alpha;}}^2)}^{1/3}]$

Wherein π is circular constant;

If 2.

(1+ν)(3-α ²)<4

The Membrane deflection value of putting r place is

Wherein, π is circular constant, by formula

Determine, and

with

value (unit is radian) by formula

With

Determine;

If 3.

(1+ν)(3-α ²)>4

The Membrane deflection value of putting r place is

Wherein, π is circular constant,

by formula

Determine, and

with

value (unit is radian) by formula

With

Determine.

Brief description of the drawings

Fig. 1 is the loading organigram of circular membrane under concentrated force effect that periphery clamps, in Fig. 1,1-circular membrane, 2-clamp device, 3-right cylinder (loading axle), symbol is wherein, a represents the radius of circular membrane, and b represents the radius of right cylinder (loading axle), and r represents radial coordinate, w (r) represents the lateral coordinates at some r place, and F represents lateral external forces.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

As shown in Figure 1, be a by radius, thickness is h, Young's modulus of elasticity is E, Poisson ratio is the circular membrane of v, fix to clamp in its border, adopt flat right cylinder that a radius is b as loading axle, apply a transverse load F in the center of circular membrane, before loading, smear talcum powder cylindrical on flat, to reduce the friction between film/base, when loading, right cylinder and circular membrane remain on same axis, and remember α=b/a, statical equilibrium analysis based on this rotational symmetry circular membrane problem so, utilize load measurement value F, the Membrane deflection value w (r) at some r place, can carry out calculative determination according to following three kinds of situations:

If situation 1.

(1+ν)(3-α ²)=4,

The Membrane deflection value of putting r place is

$w\left(r\right)={\left(\frac{a^{2}F}{\mathrm{\&pi;hE}}\right)}^{1/3}[{(3-{\mathrm{\&alpha;}}^2)}^{1/3}-{(3\frac{{\mathrm{<figure-callout\; id="2a"\; label="r"\; filenames="HDA0000481282210000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{a^2}-{\mathrm{\&alpha;}}^2)}^{1/3}]$

Wherein π is circular constant;

If situation 2.

(1+ν)(3-α ²)<4

The Membrane deflection value of putting r place is

Wherein, π is circular constant,

by formula

Determine, and

with

value (unit is radian) by formula

With

Determine;

If situation 3.

(1+ν)(3-α ²)>4

The Membrane deflection value of putting r place is

Wherein, π is circular constant, by formula

Determine, and with

value (unit is radian) by formula

With

Determine.

All parameters all adopt International System of Units.

Claims (1)

1. the method for Membrane deflection value under the circular membrane concentrated force of a definite periphery clamping, it is characterized in that: be a by radius, thickness is h, Young's modulus of elasticity is E, Poisson ratio is the circular membrane of v, fix to clamp in its border, to adopt a band to have or not the flat radius of friction be b right cylinder is as loading axle, apply a transverse load F in the center of circular membrane, when loading, right cylinder and circular membrane remain on same axis, and remember α=b/a, statical equilibrium analysis based on this rotational symmetry circular membrane problem so, utilize load measurement value F, the Membrane deflection value w (r) at some r place, can carry out calculative determination according to following three kinds of situations:

If situation 1.

(1+ν)(3-α ²)=4,

The Membrane deflection value of putting r place 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 circular constant;

If situation 2.

(1+ν)(3-α ²)<4

The Membrane deflection value of putting r place is

Wherein, π is circular constant,

by formula

Determine, and

with

value by formula

With

Determine;

If situation 3.

(1+ν)(3-α ²)>4

The Membrane deflection value of putting r place is

wherein, π is circular constant,

by formula

Determine, and

with

value by formula

With

Determine.

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