A Dynamic Equivalent Method for Substrate Constrained Damping Plate Composite Structures

Abstract

The present invention discloses a dynamic equivalent method for a substrate-constrained damping plate composite structure, including determination of the main parameters of the composite structure, a stiffness equivalent method for the composite structure, and a mass equivalent method for the composite structure, which comprises the following steps: Step 1: Define the geometric and material parameters of the substrate-constrained damping plate composite structure; Step 2: Determine the equivalent elastic modulus of the composite plate structure according to the stiffness equivalent principle; Step 3: Determine the equivalent density of the composite plate structure according to the mass equivalent principle; Step 4: Check the dynamic characteristics of the equivalent plate. Through stiffness equivalent and mass equivalent processing, the present invention can equivalent the substrate-constrained damping plate composite structure to a homogeneous plate to simplify the modeling calculation, and can maintain a certain calculation accuracy, making it more accurate for dynamic analysis.

Description

Technical Field

[0001] The present invention relates to damping and vibration reduction technology, and relates to a dynamic equivalent method for a substrate constrained damping plate composite structure, especially belonging to an equivalent method in the dynamic calculation of a composite structure with a constrained damping plate laid on a base plate. Background Art

[0002] Damping technology is one of the most commonly used vibration reduction and noise reduction technologies in engineering practice, mainly divided into free damping and constrained damping. Among them, constrained damping has better vibration reduction effect than free damping. In engineering design, laying a constrained damping layer on the plates of structures such as equipment bases and plate racks can improve the damping characteristics of the structure and increase the consumption of vibration energy. At present, in the calculation of the vibration reduction and noise reduction effect after laying constrained damping in engineering structures, usually only a simulation model of the actual structure is established. For the area where damping is laid, by modifying its loss factor to the equivalent loss factor of the substrate-damping plate composite structure, the loss factor characteristics after the structure is laid with damping are simulated.

[0003] The constrained damping plate consists of a damping layer and a constraint layer. The constraint layer has a certain bending stiffness and weight to increase the shear deformation of the constraint layer during the bending deformation of the substrate-constrained damping plate composite structure and improve the energy consumption ability. In order to improve the damping and vibration reduction effect, the thickness of the constrained damping plate is generally 1.5 to 2 times that of the substrate thickness. Therefore, only considering the damping characteristics of the constrained damping plate and ignoring its additional stiffness and mass effects on the substrate will cause errors in the magnitude of the structural vibration response. Theoretically speaking, when modeling and analyzing a structure with a constrained damping plate, models of the original structure, damping layer, and constraint layer can be established respectively, and the corresponding material properties can be assigned, and then dynamic calculation and analysis can be carried out.

[0004] Although the above method can ensure high calculation accuracy, it increases the calculation workload and has low efficiency. Especially for large and complex structures such as ship hull structures, when using the finite element method to model the original structure, damping layer, and constraint layer respectively, the calculation amount is huge. In order to ensure a certain calculation accuracy and high calculation efficiency, it is necessary to perform dynamic equivalent processing on the substrate-constrained damping composite plate structure. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a dynamic equivalent method for a substrate constrained damping plate composite structure, which can accurately simulate the stiffness, mass and other characteristics of the composite structure and has the characteristics of simple modeling.

[0006] To solve the above technical problem, a dynamic equivalent method for a substrate constrained damping plate composite structure of the present invention includes the following steps:

[0007] Step 1: Define the geometric and material parameters of the substrate-constrained damping plate composite structure;

[0008] Step 2: Determine the equivalent elastic modulus of the composite plate structure according to the principle of stiffness equivalence;

[0009] Step 3: Determine the equivalent density of the composite plate structure according to the principle of mass equivalence;

[0010] Step 4: Check the dynamic characteristics of the equivalent plate.

[0011] Furthermore, Step 1: Specify the geometric parameters and material parameters of the substrate-constrained damping plate composite structure: Determine the thickness of the substrate, the Young's elastic modulus, density, and Poisson's ratio of the substrate material, the thickness of the damping layer and the elastic modulus, density of the damping layer material, and the thickness of the constraint layer and the Young's elastic modulus, density, and Poisson's ratio of the constraint layer material;

[0012] Furthermore, Step 2: Conduct the stiffness equivalence of the substrate-constrained damping plate composite structure: Assume that the constrained damping plate is an additional structure of the substrate, its bending neutral plane is the neutral plane of the substrate, and the bending stiffness of the damping layer is very small relative to the substrate and the constraint layer. According to the principle that the bending stiffness of the composite structure plate is equal to the bending stiffness of the equivalent plate, keep the thickness of the equivalent plate consistent with the thickness of the substrate, and obtain the elastic modulus parameter E e , which can be approximately expressed as:

[0013]

[0014] In the formula, E1 and E2 are the Young's elastic moduli of the substrate and the constraint layer plate materials respectively, h1 and h2 are the thicknesses of the substrate and the constraint layer plate respectively, and H is the distance between the neutral planes of the substrate and the constraint layer plate.

[0015] Furthermore, Step 3: Conduct the mass equivalence of the substrate-constrained damping plate composite structure: According to the principle that the mass per unit area of the composite structure plate is equal to the mass per unit area of the equivalent plate, keep the thickness of the equivalent plate consistent with the thickness of the substrate, and obtain the density parameter ρ e , which can be approximately expressed as:

[0016]

[0017] In the formula, ρ1, ρ2, and ρ3 are the material densities of the substrate, the constraint layer plate, and the damping layer respectively, and h3 is the thickness of the damping layer.

[0018] Furthermore, Step 4: Check the dynamic characteristics of the equivalent plate: Establish the finite element models of the substrate-constrained damping plate and its equivalent plate respectively, conduct the low-frequency vibration mode analysis and vibration transmission characteristic analysis, and verify its effectiveness.

[0019] The method adopted by the present invention has the following advantages and beneficial effects: After the substrate-constrained damping plate is equivalent, its modeling and analysis are more convenient; compared with the traditional method that only considers the damping equivalent treatment, it is more accurate for dynamic analysis. Description of the Drawings

[0020] The present invention will be further described below in conjunction with the drawings and embodiments.

[0021] Figure 1 It is a flowchart of a dynamic equivalent method for a substrate-constrained damping plate composite structure.

[0022] Figure 2 It is a composite structure diagram of a substrate-constrained damping plate according to an embodiment of the present invention.

[0023] Figure 3 It is a finite element model diagram of a substrate-constrained damping plate and an equivalent plate finite element model according to an embodiment of the present invention.

[0024] Figure 4 It is a vibration mode diagram of a substrate-constrained damping plate composite structure and its equivalent plate according to an embodiment of the present invention. Detailed Embodiment

[0025] Figure 1 It is a flowchart of a dynamic equivalent method for a substrate-constrained damping plate composite structure of the present invention. In a specific embodiment, the substrate-constrained damping plate composite structure is as Figure 2 shown. For a certain hull side structure plate, the thickness h1 = 6 mm, the material is steel, and the Young's modulus of elasticity E1 = 2.06×10 11 Pa, and the density ρ1 = 7850 kg / m 3 . Under the excitation of equipment in the power cabin, the hull structure will undergo structural vibration and radiated noise. In order to control the structural vibration noise, a constrained damping layer is laid on the hull plate, where the thickness of the damping layer is h3 = 6 mm, the Young's modulus of elasticity E3 = 2.0×10 8 Pa, the density ρ3 = 1400 kg / m 3 , and the loss factor is 0.8; the constrained layer is made of aluminum, with a thickness of h2 = 6 mm, the Young's modulus of elasticity E2 = 7.2×10 10 Pa, and the density ρ2 = 2700 kg / m 3 . In the calculation of vibration noise, in order to simplify the modeling of the steel plate-damping layer-constrained layer composite structure, the dynamic equivalent method of the substrate-constrained damping plate composite structure of the present invention is used for equivalent simplification.

[0026] Step 1: Define the geometric and material parameters of the substrate-constrained damping plate composite structure;

[0027] For the hull steel plate-damping layer-constrained layer composite structure, the main parameters are determined as follows.

[0028] Geometric parameters: h1 = 6 mm, h2 = 6 mm, h3 = 6 mm, H = 12 mm

[0029] Material parameters: E1 = 2.06×10 11 Pa, E2 = 7.2×10 10 Pa, E3 = 2.0×10 8 Pa

[0030] ρ1 = 7850 kg / m 3 and ρ2 = 2700 kg / m 3 and ρ3 = 1400 kg / m 3

[0031] Step 2: Perform stiffness equivalence of the substrate-constrained damping plate composite structure

[0032] Equivalent the thickness of the composite structure to h1, substitute the parameters in Step 1 into Equation (1), and calculate the equivalent elastic modulus E e = 5.66×10 11 Pa

[0033]

[0034] Step 3: Perform mass equivalence of the substrate-constrained damping plate composite structure

[0035] Equivalent the thickness of the composite structure to h1, substitute the parameters in Step 1 into Equation (2), and calculate the equivalent density ρ e = 11950 kg / m 3

[0036]

[0037] Step 4: Check the dynamic characteristics of the equivalent plate

[0038] Considering that the structural vibration noise is mainly the bending vibration of the plate, select a 1m×0.5m plate grid, and use the finite element method to model the steel plate-damping layer-constraint layer composite structure and its equivalent plate structure respectively, as shown in Figure 3 . In the modeling of the composite structure, the substrate and the constraint layer both adopt shell elements, and the damping layer adopts solid elements; the equivalent plate model adopts shell elements. The vibration natural frequencies and vibration modes obtained by the two models are shown in Figure 4 .

[0039] This specification specifically describes this embodiment to better explain the principle and practical application of the present invention, so that those skilled in the art can make good use of the present invention​

Claims

1. A dynamic equivalent method for a substrate constrained damping plate composite structure, characterized in that, It includes the following steps: Step 1: Define the geometric and material parameters of the substrate-constrained damping plate composite structure; Step 2: Determine the equivalent elastic modulus of the composite plate structure according to the stiffness equivalence principle; The stiffness of the constrained damping layer is equivalently added to the substrate, and the equivalent plate thickness is the same as the substrate thickness; Assume that the constrained damping plate is an additional structure of the base plate, its bending neutral plane is the neutral plane of the base plate, and the bending stiffness of the damping layer is very small relative to the base plate and the constraint layer. According to the principle that the bending stiffness of the composite structural plate is equal to the bending stiffness of the equivalent plate, keeping the thickness of the equivalent plate consistent with the thickness of the base plate, the elastic modulus parameter E of the equivalent plate is obtained e , which can be approximately expressed as: In the formula, E1 and E2 are the Young's elastic moduli of the materials of the substrate and the constrained layer plate respectively, h1 and h2 are the thicknesses of the substrate and the constrained layer plate respectively, and H is the neutral plane distance between the substrate and the constrained layer plate; Assume that the constrained damping plate is an additional structure of the substrate, its bending neutral plane is the neutral plane of the substrate, and the bending stiffness of the damping layer is very small relative to the substrate and the constraint layer. According to the principle that the bending stiffness of the composite structural plate is equal to the bending stiffness of the equivalent plate, keeping the thickness of the equivalent plate consistent with the thickness of the substrate, the elastic modulus parameter E of the equivalent plate is obtained e , which can be approximately expressed as: In the formula, E1 and E2 are the Young's elastic moduli of the materials of the substrate and the constrained layer plate respectively, h1 and h2 are the thicknesses of the substrate and the constrained layer plate respectively, and H is the neutral plane distance between the substrate and the constrained layer plate Step 3: Determine the equivalent density of the composite plate structure according to the mass equivalence principle; According to the principle that the mass per unit area of the composite structural board is equal to that of the equivalent board, while keeping the thickness of the equivalent board consistent with the thickness of the base board, the density parameter ρ of the equivalent board is obtained e , which can be approximately expressed as: In the formula, ρ1, ρ2, and ρ3 are the material densities of the substrate, the constrained layer plate, and the damping layer respectively, and h3 is the thickness of the damping layer; Step 4: Check the dynamic characteristics of the equivalent plate.

2. The dynamic equivalent method for a substrate constrained damping plate composite structure according to claim 1, characterized in that, In Step 1, determine the thickness, Young's elastic modulus, density, and Poisson's ratio of the substrate, the thickness and material elastic modulus, density of the damping layer, and the thickness and Young's elastic modulus, density, and Poisson's ratio of the constrained layer.

3. The dynamic equivalent method for a substrate constrained damping plate composite structure according to claim 1, characterized in that, In Step 4, establish the finite element models of the substrate-constrained damping plate and its equivalent plate respectively, carry out low-frequency vibration mode analysis and vibration transmission characteristic analysis, and verify its effectiveness.

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