Structural dynamic test method of partially similar model

Abstract

The invention relates to the technical field of structural engineering, in particular to a structural dynamic test method for a partially similar model, which comprises the following steps: S1, determining a geometric similarity ratio S1; s2, making a model; s3, installing a sensor; s4, model test and data processing: debugging a test system and loading equipment, and performing a vibration test after the test system and the loading equipment are stable; after the test is finished, original test data are processed, and the inherent frequency fm, the speed response vm, the acceleration response am and the displacement response dm of the model are obtained respectively; and S5, calculating corresponding data of the prototype structure according to a test result. The invention provides the similarity criterion suitable for the dynamic test of the partially similar structure model made of the same material as the prototype material, so that a designer can more accurately invert the dynamic index of the prototype structure according to the model test result, the redundancy of the structure design is reduced, the structure cost is reduced, and the design efficiency is improved. Therefore, an economical and safe engineering structure is designed.

Description

Technical Field

[0001] The invention relates to the technical field of structural engineering, and in particular to a structural dynamic test method for a partially similar model. Background Art

[0002] Structural model testing is an essential step before finalizing a new or important structural design. Ideally, a fully similar model should be used for structural model testing, meaning that all structural and physical parameters of the model should meet dynamic similarity criteria. This allows the model test results to be used to infer the dynamic characteristics of the structural prototype based on similarity criteria.

[0003] However, due to limitations in test conditions and available materials, fully similar models are difficult to obtain in current structural model testing. Structural dynamic tests cannot use models of the same size as the prototype structure, i.e., full-scale models. Therefore, only scaled models (i.e., models smaller than the prototype) can be used. Current structural dynamic tests have to be completed using partially similar models, which leads to similarity issues between the model and the prototype.

[0004] However, the partial similarity model structure tests currently used still use the similarity criterion of the full similarity model to invert the dynamic indicators of the prototype structure, which leads to the dynamic indicators of the structural prototype inverted from the model test results being too large. The smaller the geometric similarity ratio between the model and the prototype, the greater the deviation between the inverted prototype dynamic indicators and the true value, which will lead to the design of the prototype structure being too conservative, thereby increasing the cost of structural construction and causing waste. Summary of the Invention

[0005] In order to address the deficiencies in the prior art, the present invention provides a structural dynamic test method for a partially similar model. The fundamental difference between the present invention and the existing partially similar model dynamic test method is that the dynamic performance of the prototype structure can be accurately calculated based on the model test results.

[0006] The method of the present invention comprises the following steps:

[0007] S1. Determine the geometric similarity ratio S l ;

[0008] S2, making models;

[0009] S3, install the sensor;

[0010] S4. Model test and data processing: debug the test system and loading equipment, and conduct vibration test after they are stable. After the test, process the original test data to obtain the natural frequency f of the model. m , speed response v m , acceleration response a mand displacement response d m ;

[0011] S5. Calculate the corresponding data of the prototype structure based on the test results:

[0012] 1) Acceleration response a p

[0013]

[0014] Where: a p — acceleration response of the prototype structure;

[0015] a m — acceleration response of the model;

[0016] S l —Geometric similarity ratio between the prototype and the model;

[0017] 2) Natural frequency f p

[0018]

[0019] Where: f p — natural frequencies of the prototype structure;

[0020] f m — natural frequency of the model;

[0021] S l —Geometric similarity ratio between the prototype and the model;

[0022] 3) Speed response v p

[0023] v p =v m (13)

[0024] Where: v p — velocity response of the prototype structure;

[0025] v m — velocity response of the model;

[0026] 4) Displacement response d p

[0027] d p =d m S l (15)

[0028] Where: d p — displacement response of the prototype structure;

[0029] d m — displacement response of the model;

[0030] S l ——The geometric similarity ratio between the prototype and the model.

[0031] Furthermore, in step S1, the scale ratio of the model is determined according to the space of the laboratory, the load-bearing capacity of the test bench and the capacity of the power loading equipment, thereby calculating the geometric similarity ratio S between the prototype and the model. l .

[0032] Furthermore, in step S2, the model is made of the same material as the prototype structure, so that the elastic modulus similarity ratio S between the prototype and the model is E Similarity ratio S to material density ρ are all equal to 1.

[0033] Furthermore, in step S3, the specific operation of installing the sensor is: firmly installing the motion measurement sensor on the model structure, and connecting the output signal of the sensor to the test instrument.

[0034] Furthermore, in step S5, the prototype structure acceleration response a p The specific steps are:

[0035] The elastic modulus and density of the model material must satisfy the following similarity criteria:

[0036]

[0037] Where: S E — Similarity ratio of elastic modulus between prototype and model;

[0038] E p , E m ——Elastic modulus of the prototype and model respectively;

[0039] S M —Mass similarity ratio between prototype and model;

[0040] S a — acceleration similarity ratio between the prototype and the model;

[0041] S l —Geometric similarity ratio between the prototype and the model;

[0042] S ρ —Material density similarity ratio between prototype and model;

[0043] The similarity ratio of elastic modulus between prototype and model is S E Similarity ratio S to material density ρ When both are equal to 1, we get:

[0044]

[0045] According to formula (9) and dimensional analysis, the acceleration response of the prototype structure is:

[0046]

[0047] Where: a p — acceleration response of the prototype structure;

[0048] a m — acceleration response of the model;

[0049] S l ——The geometric similarity ratio between the prototype and the model.

[0050] Furthermore, in step S5, the prototype structure natural frequency f p The specific steps are: From formula (9), we can get:

[0051] S t =S l (11)

[0052] Where: S t —Time similarity ratio between prototype and model;

[0053] S l —Geometric similarity ratio between the prototype and the model;

[0054] According to formula (11) and dimensional analysis, the natural frequency of the prototype structure is:

[0055]

[0056] Where: f p — natural frequencies of the prototype structure;

[0057] f m — natural frequency of the model;

[0058] S l ——The geometric similarity ratio between the prototype and the model.

[0059] Furthermore, in step S5, the prototype structure velocity response v p The specific steps are as follows: Based on formula (11) and dimensional analysis, the velocity response of the prototype structure can be calculated as:

[0060] v p =v m (13)

[0061] Where: v p — velocity response of the prototype structure;

[0062] v m ——The velocity response of the model.

[0063] Furthermore, in step S5, the prototype structure displacement response d p The specific steps are:

[0064] From dimensional analysis we can directly obtain:

[0065] S d =S l (14)

[0066] Where: S d ——Displacement similarity ratio between prototype and model;

[0067] S l —Geometric similarity ratio between the prototype and the model;

[0068] From formula (14), we can get:

[0069] d p =d m S l (15)

[0070] Where: d p — displacement response of the prototype structure;

[0071] d m — displacement response of the model;

[0072] S l ——The geometric similarity ratio between the prototype and the model.

[0073] The beneficial effects achieved by the embodiments of the present invention are:

[0074] The present invention proposes a similarity criterion for dynamic tests of partially similar structural models made of the same material as the prototype, and inversely derives the dynamic index of the prototype structure based on the test results of the model material, and proposes an acceleration similarity ratio S of the model made of the same material as the prototype. a The technical solution that is not equal to 1 reduces the redundancy of structural design and lowers structural costs, thereby designing an economical and safe engineering structure. DETAILED DESCRIPTION

[0075] The similarity between the structural model and its prototype includes geometric similarity, physical and dynamic index similarity. Since the size of the model is determined according to the size of the laboratory site and the load-bearing capacity of the test bench and the loading equipment, the geometric similarity ratio is the ratio of the prototype body size to the corresponding size of the model S. l is determined first, and the other similarity ratios are expressed as geometric similarity ratios.

[0076] The similarity criterion is based on dimensional analysis. Therefore, it is necessary to first select a non-geometric parameter including geometric dimensions as a reference parameter to derive the similarity ratio of all parameters included in the structural test. Since structural tests are usually carried out in a gravity field, the gravitational acceleration of the prototype and the model is the same, that is, the gravitational acceleration similarity ratio S of the prototype and the model is g is 1, and the dimension of acceleration is m / s 2 , is a non-geometric parameter (motion parameter) including geometric dimension (length unit m).

[0077]

[0078] Where: S g — Similarity ratio of gravitational acceleration between the prototype and the model;

[0079] g p , g m ——Gravitational acceleration of the prototype and model respectively;

[0080] l p , l m ——length dimensions of prototype and model respectively;

[0081] t p , t m — are the time dimensions of the prototype and model respectively;

[0082] S l —Geometric similarity ratio between the prototype and the model;

[0083] S t ——Time similarity ratio between prototype and model.

[0084] Then the time similarity ratio between the prototype and the model can be obtained from formula (1):

[0085]

[0086] Then, the dynamic characteristics and motion response parameter similarity ratio of the full similarity model can be directly obtained:

[0087]

[0088] S d =S l (4)

[0089]

[0090] Where: S f ——Frequency similarity ratio between prototype and model;

[0091] S d——Displacement similarity ratio between prototype and model;

[0092] S v ——Speed similarity ratio between prototype and model.

[0093] The fully similar model must meet the following similarity criteria for the elastic modulus and density of the model material:

[0094]

[0095] Where: S E — Similarity ratio of elastic modulus between prototype and model;

[0096] E p , E m ——Elastic modulus of the prototype and model respectively;

[0097] S M —Mass similarity ratio between prototype and model;

[0098] S a — acceleration similarity ratio between the prototype and the model;

[0099] S l —Geometric similarity ratio between the prototype and the model;

[0100] S ρ ——Material density similarity ratio between the prototype and the model.

[0101] If we follow the existing method, using the acceleration similarity ratio S a = 1 similarity criterion to deduce the dynamic performance of the prototype structure, then the acceleration similarity ratio S a =1, the elastic modulus and density of the model material can be obtained from formula (7) to satisfy the following relationship:

[0102] S E =S ρ S l (8)

[0103] Current structural tests usually use the same building materials as the prototype materials to make models. For example, brick-concrete structures use the same concrete and masonry materials as the prototype structure, that is, S E =1 and S ρ =1, and we can get the following equation (8):

[0104] S l =1 (8-1)

[0105] Unless the geometric similarity ratio S between the model and the prototype is l=1, i.e. full-scale model. Therefore, for the non-full-scale model made of the same material as the prototype structure, the similarity relationship of formula (8) is not satisfied. This type of structural model is called a partial similarity model. From formula (7), we can see that the acceleration similarity ratio S of the partial similarity model is a ≠1.

[0106] The dynamic performance of a structure includes natural frequency and dynamic response, so it can be determined based on one of the parameters. Since the current method is based on the equality of the gravitational acceleration of the prototype and the model, and thus the equality of the acceleration response of the prototype and the model, the similarity criterion between the prototype and the model is derived. However, this similarity criterion requires that the elastic modulus and material density similarity conditions of the prototype and the model must meet the requirements of formula (8). However, the model made of the same material as the prototype cannot meet the requirements of formula (8). From formula (7), it can be seen that the acceleration similarity ratio S of the model made of the same material as the prototype is a However, the currently used partial similarity model structure test still uses the similarity criterion of the full similarity model to invert the dynamic indicators of the prototype structure, which leads to the fact that the dynamic indicators of the structural prototype inverted by the model test results are too large, and the geometric similarity ratio S between the model and the prototype is too low. l The smaller it is, the greater the deviation between the inverted prototype dynamic indicators and the true values, which will lead to an overly conservative design of the prototype structure, thereby increasing the cost of structural construction and causing waste.

[0107] Therefore, the present invention proposes a structural dynamic test method of a partially similar model, comprising the following steps:

[0108] S1. Determine the geometric similarity ratio

[0109] The scale ratio of the model is determined according to the space of the laboratory, the load-bearing capacity of the test bench and the capacity of the power loading equipment, so as to calculate the geometric similarity ratio S between the prototype and the model. l .

[0110] S2. Make a model

[0111] The model is made of the same material as the prototype structure.

[0112] S3. Install the sensor

[0113] The motion measurement sensor is firmly mounted on the model structure and the output signal of the sensor is connected to the test instrument.

[0114] S4. Model test and data processing

[0115] Debug the test system and loading equipment, and conduct vibration tests after they are stable. After the test, process the original test data to obtain the natural frequency f of the model. m , speed response vm , acceleration response a m and displacement response d m .

[0116] S5. Calculate the corresponding data of the prototype structure based on the test results

[0117] 1) Acceleration response a p

[0118] For some similar models made of prototype materials, their elastic modulus similarity ratio S E Similarity ratio S to material density ρ are both equal to 1, then the acceleration similarity ratio between the prototype and the model can be obtained from formula (7):

[0119]

[0120] The acceleration response of the prototype structure is:

[0121]

[0122] Where: a p — acceleration response of the prototype structure;

[0123] a m — acceleration response of the model;

[0124] S l ——The geometric similarity ratio between the prototype and the model.

[0125] 2) Natural frequency f p

[0126] From formula (9), we can get:

[0127] S t =S l (11)

[0128] Where: S t —Time similarity ratio between prototype and model;

[0129] S l —Geometric similarity ratio between the prototype and the model;

[0130] Then the natural frequency of the prototype structure is:

[0131]

[0132] Where: f p — natural frequencies of the prototype structure;

[0133] f m — natural frequency of the model;

[0134] Sl ——The geometric similarity ratio between the prototype and the model.

[0135] 3) Speed response v p

[0136] The velocity response of the prototype structure can be calculated from formula (11):

[0137] v p =v m (13)

[0138] Where: v p — velocity response of the prototype structure;

[0139] v m ——The velocity response of the model.

[0140] 4) Displacement response d p

[0141] From dimensional analysis we get:

[0142] S d =S l (14)

[0143] Where: S d ——Displacement similarity ratio between prototype and model;

[0144] S l —Geometric similarity ratio between the prototype and the model;

[0145] The displacement response of the prototype structure can be obtained from formula (14):

[0146] d p =d m S l (15)

[0147] Where: d p — displacement response of the prototype structure;

[0148] d m — displacement response of the model;

[0149] S l ——The geometric similarity ratio between the prototype and the model.

[0150] The present invention establishes a dynamic test method for partially similar models and proposes similarity criteria applicable to partially similar structural models made of the same material as the prototype material, so that designers can more accurately invert the dynamic indicators of the prototype structure based on the model test results, reduce the redundancy of structural design, lower structural costs, and thus design economical and safe engineering structures.

[0151] The above-described embodiments of the present invention do not limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A structural dynamic test method for a partially similar model, characterized in that: The following steps are involved: S1. Determine the geometric similarity ratio S l ; S2, making models; S3, install the sensor; S4. Model test and data processing: debug the test system and loading equipment, and conduct vibration test after they are stable. After the test, process the original test data to obtain the natural frequency f of the model. m , speed response v m , acceleration response a m and displacement response d m ; S5. Calculate the corresponding data of the prototype structure based on the test results: 1) Acceleration response a p Where: a p — acceleration response of the prototype structure; a m — acceleration response of the model; S l —Geometric similarity ratio between the prototype and the model; 2) Natural frequency f p Where: f p — natural frequencies of the prototype structure; f m — natural frequency of the model; S l —Geometric similarity ratio between the prototype and the model; 3) Speed response v p v p =v m (13) Where: v p — velocity response of the prototype structure; v m — the velocity response of the model; 4) Displacement response d p d p =d m S l (15) Where: d p — displacement response of the prototype structure; d m — displacement response of the model; S l ——The geometric similarity ratio between the prototype and the model.

2. The structural dynamic test method of a partially similar model according to claim 1, characterized in that: In step S1, the scale ratio of the model is determined according to the space of the laboratory, the load-bearing capacity of the test bench and the capacity of the power loading equipment, so as to calculate the geometric similarity ratio S between the prototype and the model. l .

3. The structural dynamic test method of a partially similar model according to claim 1, characterized in that: In step S2, the model is made of the same material as the prototype structure, so that the elastic modulus similarity ratio S between the prototype and the model is E Similarity ratio S to material density ρ Both are equal to 1.

4. The structural dynamic test method of a partially similar model according to claim 1, characterized in that: In step S3 , the specific operation of installing the sensor is: firmly installing the motion measurement sensor on the model structure, and connecting the output signal of the sensor to the test instrument.

5. The structural dynamic test method of a partially similar model according to claim 3, characterized in that: In step S5, the prototype structure acceleration response a p The specific steps are: The elastic modulus and density of the model material must satisfy the following similarity criteria: Where: S E — Similarity ratio of elastic modulus between prototype and model; E p , E m ——Elastic modulus of the prototype and model respectively; S M —Mass similarity ratio between prototype and model; S a — acceleration similarity ratio between the prototype and the model; S l —Geometric similarity ratio between the prototype and the model; S ρ —Material density similarity ratio between prototype and model; The similarity ratio of elastic modulus between prototype and model is S E Similarity ratio S to material density ρ When both are equal to 1, we get: According to formula (9) and dimensional analysis, the acceleration response of the prototype structure is: Where: a p — acceleration response of the prototype structure; a m — acceleration response of the model; S l ——The geometric similarity ratio between the prototype and the model.

6. The structural dynamic test method of a partially similar model according to claim 5, characterized in that: In step S5, the prototype structure natural frequency f p The specific steps are: From formula (9), we can get: S t =S l (11) Where: S t —Time similarity ratio between prototype and model; S l —Geometric similarity ratio between the prototype and the model; According to formula (11) and dimensional analysis, the natural frequency of the prototype structure is: Where: f p — natural frequencies of the prototype structure; f m — natural frequency of the model; S l ——The geometric similarity ratio between the prototype and the model.

7. The structural dynamic test method of a partially similar model according to claim 6, characterized in that: In step S5, the prototype structure velocity response v p The specific steps are: The velocity response of the prototype structure can be calculated from formula (11) and dimensional analysis as follows: v p =v m (13) Where: v p — velocity response of the prototype structure; v m ——The velocity response of the model.

8. The structural dynamic test method of a partially similar model according to claim 1, characterized in that: In step S5, the prototype structure displacement response d p The specific steps are: From dimensional analysis we can get: S d =S l (14) Where: S d ——Displacement similarity ratio between prototype and model; S l —Geometric similarity ratio between the prototype and the model; From formula (14), we can get: d p =d m S l (15) Where: d p — displacement response of the prototype structure; d m — displacement response of the model; S l ——The geometric similarity ratio between the prototype and the model.

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