JPH0523706B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a silicone rubber model used in vibration experiments to elucidate the dynamic characteristics of the ground, structures, equipment, etc. [Prior Art] Primarily in the fields of earthquake engineering and seismic engineering, vibration experiments are conducted using miniature models made of silicone rubber in order to elucidate the dynamic characteristics of the ground, structures, equipment, etc. In reduced model experiments, it is necessary to theoretically match the physical scale ratio, that is, the similarity ratio, between the reduced model and the real thing. There are various physical quantities necessary to match these similarity rates, but the most important physical quantity is the frequency f.
and a damping constant h. Of these two physical quantities,
The similarity rate η of the frequency f is theoretically given by the following equation (1). η＝f _p /f _n ∝(1/N)・(E _p /E _n ) ^1/2 ...(1) Here, f _p is the frequency of the actual object f _n is the frequency of the model 1/N is the frequency of the model The scale factor is l _n /l _p (where l _p is the length of the actual object and l _n is the length of the model) E _p is the dynamic Young's modulus of the actual object E _n is the dynamic Young's modulus of the model. Equation (1) above indicates that the smaller the model size l _n is, the higher the frequency f _n is for the model, and the smaller the model's dynamic Young's modulus (rigidity) E _n is, the lower the frequency f _n is for the model. It means that. On the other hand, since the attenuation constant h is originally a dimensionless quantity,
It is necessary to have the same characteristics between the real thing and the model. Therefore, when conducting an experiment based on the law of similarity, it is a prerequisite that the experiment be conducted in a frequency range in which the damping constant of the model does not significantly exceed the damping constant of the actual model. Furthermore, mainly in the fields of earthquake engineering and seismic engineering, the upper limit of the frequency f _p of the actual object to be examined varies depending on the actual object, but is approximately 5 to 20 Hz; The upper limit of the number f _n is generally set to about 60 Hz due to limitations in experimental methods such as measuring instruments and vibration devices. Therefore, taking these conditions into consideration, the lower limit of the frequency similarity factor η according to equation (1) should be approximately 1/12 even when viewed at its smallest value, although it varies depending on the actual object being considered. It is. By the way, the relationship between the dynamic Young's modulus E _d and the damping constant h of silicone rubber for a conventionally known vibration experimental model is as follows:
As shown in Figure 1, according to the test results at about 5 Hz, the dynamic Young's modulus E _d = 2 Kgf/cm ² is about 5%;
E _d =1Kgf/cm ² , which is about 10%, which is large.
Furthermore, as shown in FIG. 2, the damping constant h also had a property of becoming extremely large as the frequency f became high. When conventional silicone rubber with the above-mentioned physical properties is applied to a general model vibration experiment, the experiment is conducted in a frequency range in which the damping constant of the silicone rubber does not greatly exceed the damping constant of the actual product, so f _p In order to ensure an upper limit of 5 to 20 Hz for the similarity rate, or to ensure a lower limit of 1/12 for the similarity rate η, it is necessary to make the model larger according to equation (1), which is subject to cost and experimental method constraints. I was forced to do that. For example, in the case of an actual object such as alluvial ground where the rigidity is not very high and the damping constant is about 10% or less, in conventional experiments, the target frequency f _p of the actual object is limited to a low range. things are being done,
This does not necessarily result in an effective vibration experiment. In addition, when targeting a terrain that is several kilometers long, the scale factor 1/N in equation (1) inevitably becomes small (i.e., N
(inevitably becomes large), experiments based on the law of similarity are virtually impossible, and there are almost no conventional examples based on the law of similarity. [Problems to be Solved by the Invention] The purpose of the present invention is to eliminate the above-mentioned drawbacks of conventional silicone rubber for vibration experiment models, and to improve vibrations in which the damping constant of the silicone rubber does not greatly exceed the damping constant of the actual model. Even if the experiment is conducted over a range of numbers, it is possible to secure an upper limit of f _p of about 5 to 20 Hz, and the lower limit of the similarity rate η to 1/12 can be achieved without making the model so large that it is subject to cost and experimental method constraints. The purpose of the present invention is to provide a vibration experiment model that can be used securely. [Means for Solving the Problems] The vibration test model of the present invention that achieves the above object comprises alkenyl group-containing organopolysiloxane,
It is made of a silicone rubber obtained by curing an organopolykiloxane composition consisting of an organohydrodiene polysiloxane and a platinum-based catalyst, and the dynamic Young's modulus E _d of the silicone rubber with respect to vibrations in the frequency range f = 1 to 60 Hz is 0.1. Vibration characteristics in the range of ~5 Kgf/cm ² and the relationship between the dynamic Young's modulus (Kgf/cm ² ), frequency f (Hz), and damping constant h (%) such that h・√ _d ≦2.5 It is characterized by having the following. In the present invention, the applied silicone rubber is a silicone rubber obtained by curing an organopolysiloxane composition consisting of an alkenyl group-containing organopolysiloxane, an organohydrodiene polysiloxane, and a platinum catalyst. This silicone rubber cures quickly and uniformly at room temperature or by gentle heating, does not generate voids, and allows easy adjustment of Young's modulus and damping constant. In the above silicone rubber, the alkenyl group-containing organopolysiloxane is the main component of the silicone rubber, and due to the action of a platinum catalyst, the alkenyl group undergoes an addition reaction with the hydrosilyl group in the organohydrodiene polysiloxane, resulting in crosslinking and rubber elasticity. Express. This alkenyl group-containing organopolysiloxane must have at least two alkenyl groups, such as a vinyl group or an allyl group, in one molecule, and may have a linear or slightly branched chain structure. preferable.
From the viewpoint of rubber strength, alkenyl groups are preferably present at both ends of the molecular chain. This alkenyl group may exist in the side chain, but as the number of alkenyl groups in the side chain increases, the rubber elasticity increases accordingly, so it is preferable that it does not exist except when the viscosity and degree of polymerization are high. . The alkenyl group-containing organopolysiloxane may be either liquid or rubber-like at room temperature, but is preferably liquid from the viewpoint of moldability of a vibration test model. More specifically, the viscosity at 25° C. is 100 to 100,000 cp and the degree of polymerization is 128 to 1,890, more preferably the viscosity is 200 to 2,000 cp and the degree of polymerization is 230 to 540. Organic groups other than alkenyl groups are preferably alkyl groups, aryl groups, aralkyl groups, halogenated alkyl groups, etc. Among these, examples of alkyl groups include methyl, ethyl, and hexyl groups, and examples of aryl groups include phenyl groups. The halogenated alkyl group is exemplified by 3,3,3-trifluoropropyl group. Preferred typical examples of the alkenyl group-containing organopolysiloxane include dimethylpolysiloxane with dimethylvinylsiloxy groups at both ends, dimethylpolysiloxane with methylphenylvinylsiloxy groups at both ends, and dimethylsiloxane/methyl siloxane with dimethylvinylsiloxane groups at both ends. enylsiloxane copolymer, and dimethylsiloxane/methylvinylsiloxane copolymer endblocked with dimethylvinylsiloxy groups at both ends. These alkenyl group-containing organopolysiloxanes may be used in combination of two or more types, and a typical example is a combination of a linear or slightly branched chain type and a cyclic methylvinyl polysiloxane (degree of polymerization 4 to 5). be. The organohydrodiene polysiloxane applied to the present invention must contain at least two hydrosilyl groups in one molecule, and when the alkenyl group-containing organopolysiloxane has two alkenyl groups in one molecule, , it is necessary to contain at least three hydrosilyl groups in one molecule. The molecular structure of the organohydrodiene polysiloxane may be linear, branched, network, or cyclic, and is usually liquid at room temperature, with a degree of polymerization of 2 or more, preferably 3 or more. The organic group in this organohydrodiene polysiloxane is the same as the monovalent hydrocarbon group other than the alkenyl group in the alkenyl group-containing organopolysiloxane. Preferred typical examples of the above organohydrodiene polysiloxane include methylhydrogenpolysiloxane with trimethylsiloxy groups endblocked at both ends, dimethylsiloxane/methylhydrogensiloxane copolymer endblocked with trimethylsiloxy groups at both ends, methyltris(dimethylhydrodienesiloxane)silane, and methyl Examples include hydrodienecyclosiloxane tetramer, methylhydrogenpolysiloxane with dimethylphenylsiloxy groups endblocked at both ends, and dimethylpolysiloxane endblocked with dimethylhydrogensiloxy groups at both ends. In the above combination of alkenyl group-containing organopolysiloxane and organohydrodiene polysiloxane, it is preferable that the molar ratio of hydrosilyl group to alkenyl group is 0.5 to 0.75. If this molar ratio is less than 0.5, the silicone rubber will have low rigidity and high damping, and if it exceeds 0.75, the silicone rubber will have high rigidity and low damping, making it unsuitable for vibration experiment models. . However, organohydrodiene polysiloxane has two hydrosilyl groups in one molecule, such as diorganopolysiloxane with hydrosilyl groups blocked at both ends.
When there are only three alkenyl groups, the alkenyl group-containing organopolysiloxane needs to contain at least three alkenyl groups in one molecule. The organohydrodiene polysiloxane in this case is preferably one that is similar to the above-mentioned preferred alkenyl group-containing organopolysiloxane in terms of molecular structure, properties, viscosity, and degree of polymerization; Specific examples include those similar to the specific examples. In this case, the alkenyl group-containing organopolysiloxane is preferably one that is similar to the above-mentioned preferred organohydrodiene polysiloxane in terms of molecular structure, properties, and degree of polymerization. Specific examples include those similar to the examples. In this case, the organohydrodiene polysiloxane and the alkenyl group-containing organopolysiloxane are
The molar ratio of alkenyl group and hydrosilyl group is 0.5~
Preferably, the ratio is 0.75. The platinum-based catalyst applied to the present invention is a catalyst necessary for crosslinking through the addition reaction of alkenyl group-containing organopolysiloxane and organohydrodiene polysiloxane, and representative preferred examples include chloroplatinic acid, potassium chloroplatinate, and chloroplatinic acid. complex salt of and sym-divinyltetramethyldisiloxane, complex salt of chloroplatinic acid and diketone, platinum chloride, fine platinum powder,
An example is platinum black. The platinum-based catalyst is suitably present in the organopolysiloxane composition in an amount of about 0.5 to 100 ppm by weight of platinum. In addition to the above three essential components, the silicone rubber of the present invention contains additives to suppress the addition reaction rate and facilitate handling at room temperature, such as alkyne alcohols, nitrogen-containing organic compounds, organic phosphorus compounds,
It may also contain reinforcing fillers (for example, made silica), pigments, and the like. The silicone rubber of the present invention can be obtained by mixing the above-mentioned three essential components and optional additives until uniform, and curing the mixture at room temperature or under heat. This silicone rubber has a dynamic Young's modulus (E _d ) in the range of 0.1 to 5 Kgf/cm ² for vibrations in the frequency range f = 1 to 60 Hz, and the frequency f (Hz) and damping constant h
(%), it is necessary to have a relationship of h·√ _d ≦2.5. This is based on the following reasons. If the dynamic Young's modulus is less than 0.1 Kgf/cm ² , the silicone ^rubber itself tends to be difficult to stand on its own, making it unsuitable as a silicone rubber for vibration experimental models. This is because the vibration frequency tends to be high, making it unsuitable for use as a vibration experimental model. Furthermore, h・√ _d is 2.5
This is because, if the value exceeds 100%, the damping constant of the silicone rubber becomes large, making it unsuitable for use as a vibration experimental model. Note that the dynamic Young's modulus and damping constant of the silicone rubber used in the present invention mean those measured according to the measuring method described in the Examples below. The silicone rubber of the present invention described above can be applied to a wide range of applications, including ground vibration test models and vibration test models for elucidating the dynamic characteristics of structures, equipment, and the like. Furthermore, it is possible to perform model experiments on real objects with small damping constants, low rigidity, or large scale objects, which were considered impossible to test using conventional silicone rubber models. [Example] Next, an example of the present invention will be described. In the examples described below, parts mean parts by weight, and viscosity is the value at 25°C. The degree of polymerization is
The average molecular weight in terms of polystyrene was obtained from the maximum peak of the gel permeation chromatography elution curve of a toluene solution of organopolysiloxane, and was determined by dividing it by the molecular weight of the siloxane unit in the organopolysiloxane. In addition, the dynamic Young's modulus and damping constant of silicone rubber were measured as follows. In other words, to measure the dynamic Young's modulus and damping constant, the bottom surface is 4 cm x 4 cm due to the silicone rubber to be measured.
Two or three rectangular specimens of 4 cm and 12 cm in height were cast, cured at 25°C or 70°C for 24 hours, and then cured at room temperature for 2 weeks. It was glued to a vibration table and an accelerometer was installed at the top. Then, shake the table at room temperature for 1
Steady vibration excitation or sweep excitation was applied from Hz to 60 Hz, the response of the sample was detected using an accelerometer on the top of the sample, a frequency response magnification curve was determined, and the dynamic Young's modulus and damping constant were determined from this curve. To explain with reference to Figure 3, s is a rounded sample (the example in the figure is 3
body), and a is a vibration table (ASE- manufactured by Akashi Seisakusho)
32S type), and b is an accelerometer (EGA-125 type manufactured by Entran Devices). The dynamic Young's modulus was determined by a simple average of the dynamic Young's modulus of two to three samples converted from the resonance frequency of the frequency response magnification curve. In addition, the damping constant is determined by the half power method (1/√
It was determined by a simple average of the attenuation constants of 2 to 3 samples calculated using the method 2). In the examples, "primary" refers to the value at the first resonant frequency, "secondary" refers to the value at the second resonant frequency, and "tertiary" refers to the value at the third resonant frequency. Example 1 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 330 cp, degree of polymerization 310) 100
1.65 parts, dimethylsiloxane/methylhydrodienesiloxane copolymer blocked at both ends with trimethylsiloxane groups (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl An amount of a disiloxane complex salt to give a platinum weight of 10 ppm based on the total composition and 0.02 part of a cyclic methylvinylsiloxane tetramer are mixed until homogeneous (the amount of the hydrosilyl group and vinyl group in the present organopolysiloxane composition is The molar ratio is 0.66:1), after degassing under reduced pressure, 4 cm x 4 cm x
The mixture was injected into a 12 cm block mold and kept at 25°C for 24 hours to harden to form a vibration experimental model. After curing this model at room temperature for two weeks, a vibration experiment was conducted to determine the frequency response magnification curve.
The dynamic Young's modulus E _d and damping constant h at each resonance frequency f were calculated, and the following results were obtained.

【table】

【table】

[Table] When the above model is applied to a model vibration experiment for alluvial ground with a damping constant of about 10% or less, the upper limit of the frequency corresponding to the damping constant is about 76 Hz (Note: 21.75
(value extrapolated from 4.44% at Hz and 7.04% at 46.97Hz), the upper limit of the target frequency f _n of the vibration experimental model is 60
Hz. Frequency f _p of the actual object to be considered
If the upper limit of is 20Hz, the lower limit of the frequency similarity rate η is f _p /f _n =1/3. At this time, 1/N is determined by equation (2), which is a stricter version of equation (1).
seek. η=1/N・(E _p /E _n ) ^1/2・(ρ _n /ρ _p ) ^1/2 ...(2) Here, ρ _n is the unit volume weight of the model, and ρ _p is the unit of the actual product. Indicates volumetric weight. E _p =4500Kgf/cm ² , ρ _p =
1.6gf/cm ³ , E _n =1.25Kgf/cm ² , ρ _n =1.0gf/
cm ³ , η = 1/3, 1/N = 1/142. Conventionally, in model vibration experiments for alluvial ground,
E _n =2.0Kgf/cm ² , ρ _n =1.0gf/cm ³ , f _n =30Hz
(In other words, the damping constant of the model is in the range of about 10% or less), and if f _p = 20Hz, 1/N =
Since it is necessary to use a model with a large size of 1/56, there is an example where a model with a size of 1/N = 1/100 is used and f _p = 11Hz, but compared to this, the frequency to be considered is lower than that of the actual product.
Not only can you secure 20Hz as the upper limit of f _p ,
This is a model vibration experiment with a small scale and cost. Note that when the above model is applied to a model vibration experiment for an RC (reinforced concrete) structure with a damping constant of about 5%, the upper limit of the frequency corresponding to the damping constant f _n
is about 27Hz (Note: 4.44% at 21.75Hz, 46.97Hz
(value interpolated from 7.04%). If the upper limit of the frequency f _p of the actual object to be considered is 20 Hz, the lower limit of the frequency similarity ratio η is f _p /f _n =1/1.35. Calculating 1/N in the same manner as the above example, E _p = 210000Kgf/cm ² , ρ _p = 2.4gf/cm ³ , E _n =
From 1.25Kgf/cm ² , ρ _n =1.0gf/cm ³ , and η = 1/1.35, 1/N = 1/357. Conventionally, E _n = 200Kg for RC structures.
Model experiments are conducted at f/cm ² , ρ _n = 1.5 gf/cm ³ , f _p = 20 Hz, f _n = 40 Hz, and there are examples of using models with large dimensions of 1/N = 1/50. However, compared to this, it is possible to conduct model vibration experiments that are lighter in scale and cost. Example 2 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 330 cp, degree of polymerization 310) 100
part, 1.60 parts of dimethylsiloxane/methylhydrodienesiloxane copolymer blocked with trimethylsiloxane groups at both ends (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl A disiloxane complex salt in an amount of 10 ppm based on the platinum weight of the entire composition and 0.02 part of a cyclic methylvinylsiloxane tetramer are mixed until homogeneous (the amount of the hydrosilyl group and vinyl group in the present organopolysiloxane composition is The molar ratio is 0.64:1), after degassing under reduced pressure, 4 cm x 4 cm x
The mixture was injected into a 12 cm block mold and kept at 25°C for 24 hours to harden to form a vibration experimental model. After curing this model for two weeks at room temperature, a vibration experiment was conducted to obtain a frequency response magnification curve, and the dynamic Young's modulus E _d and damping constant h at each resonance frequency f were determined.
was calculated and obtained the following results.

【table】

【table】

[Table] When the above model is applied to a model vibration experiment for alluvial ground with a damping constant of about 10% or less, the upper limit of the frequency corresponding to the damping constant is about 42 Hz (Note: 16.26
(value extrapolated from 5.56% at Hz and 8.93% at 35.69Hz), the upper limit of the target frequency f _n of the vibration experimental model is 42
Hz. The upper limit of the actual frequency f _p to be considered is 20Hz.
Then, the lower limit of the frequency similarity rate η is f _p /f _n =
It becomes 1/2.1. When 1/N is determined using the same method as in Example 1, E _p =4500 Kgf/cm ² , ρ _p =1.6 gf/cm ³ , E _n =
From 0.68Kgf/cm ² , ρ _n =1.0gf/cm ³ , and η = 1/2.1, 1/N = 1/135. Compared to the conventional model vibration experiment for alluvial ground shown in Example 1, it is not only possible to secure 20 Hz as the upper limit of the actual vibration frequency f _p to be considered, but it is also possible to conduct a model vibration experiment with a smaller scale and cost. . Example 3 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 330 cp, degree of polymerization 310) 100
part, 1.75 parts of dimethylsiloxane/methylhydrogensiloxane copolymer blocked with trimethylsiloxane groups at both ends (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl A disiloxane complex salt in an amount of 10 ppm based on the platinum weight of the entire composition and 0.02 part of a cyclic methylvinylsiloxane tetramer are mixed until homogeneous (the amount of the hydrosilyl group and vinyl group in the present organopolysiloxane composition is The molar ratio is 0.70:1), after degassing under reduced pressure, 4 cm x 4 cm x
The mixture was injected into a 12 cm block mold and kept at 25°C for 24 hours to harden to form a vibration experimental model. After curing this model for two weeks at room temperature, a vibration experiment was conducted to obtain a frequency response magnification curve, and the dynamic Young's modulus E _d and damping constant h at each resonance frequency f were determined.
was calculated and obtained the following results.

【table】

[Table] When the above model is applied to a model vibration experiment for terrain spanning several kilometers, targeting rock with a damping constant of about 5% or less, the upper limit of the frequency corresponding to the damping constant is approximately
33Hz (Note: 2.32% at 5.32Hz, 4.13 at 23.94Hz
%), the upper limit of the target frequency f _n of the vibration experimental model is 33 Hz. If the upper limit of the frequency f _p of the actual object to be considered is 5 Hz, the lower limit of the frequency similarity η is f _p /f _n =1/6.6. When 1/N is determined by the same method as in Example 1, E _p =270000 Kgf/cm ² , ρ _p =2.2 gf/cm ³ , E _n =
Since 1.52Kgf/cm ² , ρ _n =1.0gf/cm ³ , and η = 1/6.6, 1/N = 1/1875, so it is possible to conduct model vibration experiments on topography over several kilometers. In the case of conventional model vibration experiments targeting rock mass,
The damping constant is approximately 5% or less up to high frequencies.
E _n =72 Kgf/cm ² , ρ _n =1.5 gf/cm ³ Silicone rubber is sometimes used, but f _n = 60 Hz, f _p =
If it is 5 Hz, then 1/N=1/607, so the dimensions of a terrain model spanning several kilometers would be large, making experiments based on the law of similarity virtually impossible. Example 4 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 620 cp, degree of polymerization 378) 100
1.49 parts, dimethylsiloxane/methylhydrodienesiloxane copolymer blocked at both ends with trimethylsiloxy groups (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl A disiloxane complex salt in an amount of 10 ppm based on the platinum weight of the entire composition and 0.02 part of a cyclic methylvinylsiloxane tetramer are mixed until homogeneous (the amount of the hydrosilyl group and vinyl group in the present organopolysiloxane composition is The molar ratio is
The ratio is 0.70:1. ), after vacuum degassing, 4cm x 4cm x 12
The mixture was injected into a cm block mold and kept at 25°C for 24 hours to harden and form a vibration experimental model.
After curing this model for two weeks at room temperature, we performed a vibration experiment to obtain a frequency response magnification curve, and calculated the dynamic Young's modulus E _d and damping constant h at each resonance frequency f, and obtained the following results. .

【table】

[Table] When the above model is applied to a model vibration experiment for alluvial ground with a damping constant of about 10% or less, the upper limit of the frequency corresponding to the damping constant is about 61 Hz (Note: 5.35 Hz)
(value extrapolated from 3.17% at 24.3Hz and 5.5% at 24.3Hz),
The upper limit of the target frequency f _n of the vibration experiment model is 60 Hz. If the upper limit of the frequency f _p of the actual object to be considered is 20Hz, the lower limit of the frequency similarity η is f _p /f _n = 1/3
becomes. When 1/N is determined using the same method as in Example 1, E _p =4500 Kgf/cm ² , ρ _p =1.6 gf/cm ³ , E _n =
1.56Kgf/cm ² , ρ _n =1.0gf/cm ³ , η = 1/3 from 1/3
N=1/127. Compared to the conventional model vibration experiment for alluvial ground shown in Example 1, it is not only possible to secure 20 Hz as the upper limit of the actual vibration frequency f _p to be considered, but it is also possible to conduct a model vibration experiment with a smaller scale and cost. . Example 5 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 330 cp, degree of polymerization 310) 100
1.46 parts, dimethylsiloxane/methylhydrodienesiloxane copolymer blocked at both ends with trimethylsiloxane groups (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl Mix the disiloxane complex salt in an amount equal to 10 ppm based on the platinum weight of the entire composition until homogeneous (the molar ratio of hydrosilyl groups and vinyl groups in this organopolysiloxane composition is
The ratio is 0.60:1. ), after vacuum degassing, 4cm x 4cm x 12
The mixture was injected into a cm block mold and kept at 25°C for 24 hours to harden and form a vibration experimental model.
After curing this model for two weeks at room temperature, we performed a vibration experiment to obtain a frequency response magnification curve, and calculated the dynamic Young's modulus E _d and damping constant h at each resonance frequency f, and obtained the following results. .

【table】

【table】

[Table] When the above model is applied to a model vibration experiment for alluvial ground with a damping constant of about 10% or less, the upper limit of the frequency corresponding to the damping constant is about 66 Hz (Note: 25.3 Hz)
(extrapolated value from 5.05% at 44.6Hz and 7.7% at 44.6Hz),
The upper limit of the target frequency f _n of the vibration experiment model is 60 Hz. If the upper limit of the frequency f _p of the actual object to be considered is 20Hz, the lower limit of the frequency similarity η is f _p /f _n = 1/3
becomes. When 1/N is determined using the same method as in Example 1, E _p =4500 Kgf/cm ² , ρ _p =1.6 gf/cm ³ , E _n =
1.12Kgf/cm ² , ρ _n = 1.0gf/cm ³ , η = 1/3 from 1/3
N=1/150. Compared to the conventional model vibration experiment for alluvial ground shown in Example 1, it is not only possible to secure 20 Hz as the upper limit of the actual vibration frequency f _p to be considered, but it is also possible to conduct a model vibration experiment with a smaller scale and cost. . Example 6 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 330 cp, degree of polymerization 310) 100
1.46 parts, dimethylsiloxane/methylhydrodienesiloxane copolymer blocked at both ends with trimethylsiloxane groups (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl A disiloxane complex salt in an amount of 10 ppm based on the platinum weight of the entire composition and 0.005 part of methylbutynol were mixed until homogeneous (the molar ratio of hydrosilyl groups to vinyl groups in this organopolysiloxane composition was 0.60). After defoaming under reduced pressure, the mixture was poured into a block mold of 4 cm x 4 cm x 12 cm, and cured by keeping at 25°C for 24 hours to form a model for vibration experiments. After curing this model for two weeks at room temperature, we performed a vibration experiment to obtain a frequency response magnification curve, and calculated the dynamic Young's modulus E _d and damping constant h at each resonance frequency f, and obtained the following results. .

【table】

【table】

[Table] When the above model is applied to a model vibration experiment for alluvial ground with a damping constant of about 10% or less, the upper limit of the frequency corresponding to the damping constant is about 94 Hz (Note: 21.3 Hz)
(value extrapolated from 4.85% at 47.1Hz and 6.69% at 47.1Hz),
The upper limit of the target frequency f _n of the vibration experiment model is 60 Hz. If the upper limit of the frequency f _p of the actual object to be considered is 20Hz, the lower limit of the frequency similarity η is f _p /f _n = 1/3
becomes. When 1/N is determined using the same method as in Example 1, E _p =4500 Kgf/cm ² , ρ _p =1.6 gf/cm ³ , E _n =
1.25Kgf/cm ² , ρ _n = 1.0gf/cm ³ , η = 1/3 from 1/3
N=1/142. Compared to the conventional model vibration experiment for alluvial ground shown in Example 1, not only can 20 Hz be secured as the upper limit of the actual vibration frequency f _p to be considered, but the scale and cost of the model vibration experiment is small. In addition, when the above model is applied to a model vibration experiment for terrain spanning several kilometers, targeting rock with a damping constant of about 5% or less, the upper limit of the frequency corresponding to the damping constant is about 23 Hz (Note 21.3 Hz). 4.85% at 47.1Hz
(a value interpolated from 6.69%), so the upper limit of the target frequency f _n of the vibration experimental model is 23 Hz. If the upper limit of the frequency f _p of the actual object to be considered is 5 Hz, the lower limit of the frequency similarity η is f _p /f _n =1/4.6. When 1/N is determined by the same method as in Example 1, E _p =270000 Kgf/cm ² , ρ _p =2.2 gf/cm ³ , E _n =
Since 1.25Kgf/cm ² , ρ _n =1.0gf/cm ³ , and η = 1/4.6, 1/N = 1/1441, making it possible to conduct model vibration experiments on topography over several kilometers. Example 7 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 1600 cp, degree of polymerization 500)
100 parts, 1.38 parts of dimethylsiloxane/methylhydrogensiloxane copolymer (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), both ends blocked with trimethylsiloxy groups, chloroplatinic acid and sym-divinyltetra A complex salt of methyldisiloxane in an amount of 10 ppm based on the platinum weight of the entire composition and 0.02 part of cyclic methylvinylsiloxane tetramer are mixed until homogeneous (hydrosilyl group and vinyl group in the present organopolysiloxane composition). The molar ratio of
The mixture was injected into a 12 cm x 12 cm block mold and kept at 70°C for 24 hours to harden to form a vibration experiment model. After curing this model for two weeks at room temperature, a vibration experiment was conducted to obtain a frequency response magnification curve, and the dynamic Young's modulus E _d and damping constant h at each resonance frequency f were determined.
was calculated and obtained the following results.

【table】

[Table] When the above model is applied to a model vibration experiment for alluvial ground with a damping constant of about 10% or less, the upper limit of the frequency corresponding to the damping constant is about 95 Hz (Note: 7.44 Hz)
(value extrapolated from 3.71% at 33.51Hz and 5.58% at 33.51Hz), the upper limit of the target frequency f _n of the vibration experimental model is 60
Hz. The upper limit of the actual frequency f _p to be considered is 20Hz.
Then, the lower limit of the frequency similarity rate η is f _p /f _n =
It becomes 1/3. When 1/N is determined using the same method as in Example 1, E _p =4500 Kgf/cm ² , ρ _p =1.6 gf/cm ³ , E _n =
3.02Kgf/cm ² , ρ _n = 1.0gf/cm ³ , η = 1/3 to 1/
N=1/92. Compared to the conventional model vibration experiment for alluvial ground shown in Example 1, not only can 20 Hz be secured as the upper limit of the actual vibration frequency f _p to be considered, but the scale and cost of the model vibration experiment is small. In addition, when the above model is applied to a model vibration experiment for terrain spanning several kilometers, targeting rock with a damping constant of about 5% or less, the upper limit of the frequency corresponding to the damping constant is about 25 Hz (Note 7.44 Hz). 3.71% at 33.51Hz
(a value interpolated from 5.58%), so the upper limit of the target frequency f _n of the vibration experimental model is 28 Hz. If the upper limit of the frequency f _p of the actual object to be considered is 5 Hz, the lower limit of the frequency similarity ratio η is f _p /f _n =1/5. When 1/N is determined by the same method as in Example 1, E _p =270000 Kgf/cm ² , ρ _p =2.2 gf/cm ³ , E _n =
3.02Kgf/cm ² , ρ _n = 1.0gf/cm ³ , η = 1/5 from 1/5
Since N=1/1008, it is possible to conduct model vibration experiments over several kilometers of terrain. Comparative Example 1 Dimethylpolysiloxane with dimethylvinylsiloxy groups blocked at both ends (viscosity 6000 cp, degree of polymerization 770) 100
0.71 parts, dimethylsiloxane/methylhydrodienesiloxane copolymer with trimethylsiloxy groups blocked at both ends (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), chloroplatinic acid and sym-divinyltetramethyl An amount of a disiloxane complex salt of 10 ppm based on the platinum weight of the entire composition and 0.02 part of a cyclic methylvinylsiloxane tetramer are mixed until homogeneous (the molar amount of hydrosilyl groups and vinyl groups in the present organopolysiloxane composition). The ratio is
The ratio is 0.70:1. ), after vacuum degassing, 4cm x 4cm x 12
The mixture was injected into a cm block mold and kept at 25°C for 24 hours to harden and form a vibration experimental model.
After curing this model for two weeks at room temperature, we performed a vibration experiment to obtain a frequency response magnification curve, and calculated the dynamic Young's modulus E _d and damping constant h at each resonance frequency f, and obtained the following results. .

【table】

[Table] Since the above model has a large damping constant, it cannot be applied to model vibration experiments for real objects such as alluvial ground or rock where the damping constant is less than about 10%. Comparative Example 2 Dimethylpolysiloxane with dimethylvinylsiloxane groups blocked at both ends (viscosity 3300 cp, degree of polymerization 635)
100 parts, dimethylsiloxane/methylhydrogensiloxane copolymer blocked at both ends with trimethylsiloxane groups (viscosity 5 cp, degree of polymerization of dimethylsiloxane units 3, degree of polymerization of methylhydrogensiloxane units 5), 0.85 parts, chloroplatinic acid and sym-divinyltetra A complex salt of methyldisiloxane in an amount of 10 ppm based on the platinum weight of the entire composition and 0.02 part of methylvinylsiloxane tetramer are mixed until homogeneous. The molar ratio is 0.70:1), after degassing under reduced pressure, 4 cm x 4 cm x
The mixture was injected into a 12 cm block mold and kept at 25°C for 24 hours to harden to form a vibration experimental model. After curing this model for two weeks at room temperature, a vibration experiment was conducted to obtain a frequency response magnification curve, and the dynamic Young's modulus E _d and damping constant h at each resonance frequency f were determined.
was calculated and obtained the following results.

【table】

〔Effect of the invention〕

The vibration experiment model of the present invention is made of a silicone rubber obtained by curing an organopolysiloxane composition consisting of an alkenyl group-containing organopolysiloxane, an organohydrodiene polysiloxane, and a platinum catalyst, and the silicone rubber has a vibration frequency f = dynamic Young's modulus for vibrations in the range of 1 to 60 Hz
E _d is 0.1 to 5 Kgf/cm ² , and the dynamic Young's modulus (Kgf/cm ² ), frequency f (Hz), and damping constant h
(%), so the _damping constant is 10.
It is possible to perform vibration experiments at high frequencies up to about 60Hz based on the law of similarity for real objects with a frequency of about 30% or less. For example, for an actual object such as alluvial ground that does not have very high rigidity and has a damping constant of about 10% or less, the target frequency f _p of the actual object cannot be limited to a low range, and moreover, the scale factor is 100%. Experiments based on the law of similarity are possible with a small model of about 1.
Furthermore, for terrain that is several kilometers long, the similarity rate η
The lower limit of 1/12 can be secured, and experiments based on the law of similarity can be conducted using a small model with a scale of about 1/1000th. In addition, the conventional dynamic Young's modulus is 5
It can be applied to reinforced concrete structures, steel frame structures, equipment, etc. where the damping constant is around 2 to 5%, where silicone rubber smaller than Kgf/cm ² cannot be applied due to its large damping constant. becomes.

[Brief explanation of drawings]

Figure 1 is a graph showing the relationship between dynamic Young's modulus and damping constant between the silicone rubber used in the vibration experiment model of the present invention and that of a conventional model, and Figure 2 is a graph showing the relationship between damping constant and vibration frequency. This is the graph shown. FIG. 3 is an explanatory diagram showing a method for measuring the dynamic Young's modulus and damping constant of silicone rubber.

Claims (1)

[Claims] 1. Alkenyl group-containing organopolysiloxane,
It is made of a silicone rubber obtained by curing an organopolysiloxane composition consisting of an organohydrodiene polysiloxane and a platinum-based catalyst, and the dynamic Young's modulus E _d of the silicone rubber is 0.1 to 0.1 to vibrations in a frequency range of f = 1 to 60 Hz. 5Kgf/cm ² , and the relationship between the dynamic Young's modulus (Kgf/cm ² ), frequency f (Hz), and damping constant h (%) is h・√ _d ≦2.5. A model for vibration experiments.