Morison equation-based approximate solution method for vibration mode damping coefficient of immersed beam

Abstract

The invention discloses an approximate solution method for a vibration mode damping coefficient of an immersed beam based on a Morison equation, and the method comprises the following steps: building a finite element model of a slender beam structure immersed in water, and calculating a hydrodynamic load acting on the beam structure; a transient impact load is applied to the beam structure, so that the beam structure does free attenuation motion in water, and then a free attenuation curve of the beam is extracted; according to a known free attenuation curve, the damping ratio of the structure is calculated, and finally the vibration mode damping coefficient of the structure is calculated according to the relational expression of the damping ratio and the vibration mode damping coefficient; and substituting the vibration mode damping coefficient into a vibration equation of the slender structure immersed in water, and solving to obtain the vibration mode and frequency of the structure. According to the method, the vibration mode damping magnitude order of the viscous damping effect of the liquid immersed in the slender structure can be approximately estimated. The method is high in calculation efficiency, and the theory is popular and easy to understand.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration calculation of structures in the ocean engineering field, and particularly relates to an approximate solution method for the mode damping coefficient of a submerged beam based on the Morison equation. Background Art

[0002] The marine environment is complex and changeable, and submerged slender structures are prone to vibration under the action of internal fluids. If the vibration frequency is close to the frequency of the external load, resonance may be triggered, resulting in structural damage. Therefore, studying the vibration frequency helps to predict and avoid resonance phenomena, thus ensuring the safety of engineering structures.

[0003] The main method for solving the natural frequency of a beam structure is to solve its vibration equation, and its vibration equation can be expressed as: Wherein, M is the element mass matrix, C is the damping coefficient matrix, and K is the element stiffness matrix. The key to solving this equation is the determination of the damping coefficient matrix. The vibration damping of a structure includes internal damping and external damping. The internal damping is determined by the material properties of the structure and is generally a constant, while the external damping is determined by the environment. In air, the external damping of structural vibration is much smaller than the internal damping, so it can be ignored. In fluid, the external damping effect of structural vibration is obvious. Relevant research shows that the natural frequency of a beam submerged in water differs by more than 20% from that in air. Therefore, how to determine the mode damping coefficient of a structure in fluid is the key to solving such problems.

[0004] Currently, there are mainly two methods for solving the mode damping coefficient of a beam in fluid. One is to conduct vibration tests in a water tank to collect vibration data and then obtain the damping coefficient, and the other is based on theoretical calculations, such as the fluid-structure coupling analytical method for solving the hydroelastic problem or the numerical method based on computational fluid dynamics (CFD) to determine the damping ratio of the liquid viscous effect, so as to obtain the damping coefficient. Although the mode damping coefficient solved by the above-mentioned schemes is more accurate, the time cost is high and the difficulty is great. When performing hydrodynamic calculations on large structures, the viscous effect in the fluid control equation is very weak, and the potential flow theory method is usually adopted, ignoring the viscous effect of the fluid. The approximate solution method for the mode damping coefficient of a submerged slender structure based on the Morison equation proposed in this patent can simplify the calculation process and is of great significance for promoting the vibration analysis of ocean engineering structures.

[0005] Therefore, it is urgent to design an approximate solution method for the mode damping coefficient of a submerged beam based on the Morison equation to solve the above-mentioned problems. Summary of the Invention

[0006] The object of the present invention is to provide an approximate solution method for the modal damping coefficient of a submerged beam based on the Morison equation, which has the advantages of calculating the hydrodynamic load on the structure based on the Morison equation, calculating the damping ratio by using the area enclosed by the free decay motion curve and the time axis, and then solving the modal damping coefficient of the vibration equation of the structure, and solves the problems mentioned in the background art.

[0007] To achieve the above object, the specific technical solution of an approximate solution method for the modal damping coefficient of a submerged beam based on the Morison equation of the present invention is as follows: An approximate solution method for the modal damping coefficient of a submerged beam based on the Morison equation includes the following steps: S1. Establish a finite element model of a slender beam structure submerged in water, and calculate the hydrodynamic load acting on the beam structure; S2. Apply a transient impact load on the beam structure to make it perform free decay motion in water, and then extract the free decay curve of the beam; S3. Calculate the damping ratio of the structure according to the known free decay curve, and finally calculate the modal damping coefficient of the structure from the relationship between the damping ratio and the modal damping coefficient; S4. Substitute the modal damping coefficient into the vibration equation of the slender structure submerged in water and solve it to obtain the mode and frequency of the structure.

[0008] Further, in S1, a finite element model of a slender beam structure submerged in water is established by using the finite element method.

[0009] Further, in S1, the Morison equation is used to calculate the hydrodynamic load acting on the beam structure.

[0010] Further, the hydrodynamic load on the beam structure includes viscous effect and inertial effect Further, the physical parameters, geometric dimensions and boundary conditions of the finite element model of the slender beam structure submerged in water should be consistent with the actual structure.

[0011] Further, in S2, the maximum displacement amplitude of the beam caused by the applied impact load needs to be close to the motion amplitude of the actual structure.

[0012] Further, in S3, the damping ratio of the structure is obtained by calculating the area enclosed by the curve and the time axis, and finally the modal damping coefficient of the structure is calculated from the relationship between the damping ratio and the modal damping coefficient.

[0013] Further, calculate the area enclosed by the free decay curve and the time axis , and then through , calculate the modal damping ratio : ; Then, calculate the modal damping coefficient based on the relationship between the modal damping ratio and the modal damping coefficient: ; Furthermore, in S4, through the free decay results of multiple impact loads of different magnitudes, obtain the order of magnitude of the modal damping coefficient of the liquid viscous damping effect, and then substitute the modal damping coefficient into the vibration equation of the slender structure immersed in water.

[0014] Furthermore, this modal damping coefficient is used not only to calculate the beam mode shape and frequency immersed in water, but also to calculate the response of the beam in the analytical method.

[0015] The present invention has the following advantages: (1) Compared with the method of determining the modal damping coefficient of the viscous effect through the pool test, the calculation method of the modal damping coefficient of the liquid viscous effect proposed in this patent has less workload and saves time and effort; (2) Compared with the theoretical analytical method and the CFD numerical method, the approximate calculation method of the modal damping coefficient of the liquid viscous effect proposed in the present invention has a simple theory, a small amount of calculation, is easy to master, and greatly reduces the solution cost of the damping coefficient; (3) The calculation method of the modal damping coefficient of the liquid viscous effect proposed in the present invention is convenient for real-time load monitoring of marine structures because of its simple calculation, low requirement for computer performance, and short calculation time. Description of the Drawings

[0016] Figure 1 is a schematic diagram of a typical free decay curve; Figure 2 is a schematic diagram of the overall flow of the approximate solution method of the modal damping coefficient of the present invention; Detailed Embodiments

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts fall within the protection scope of the present invention.

[0018] Those skilled in the art can understand that although some of the embodiments herein include certain features included in other embodiments but not other features, the combination of the features of different embodiments means within the scope of the present invention and forms different embodiments. For example, in the claims, any one of the claimed embodiments can be used in any combination.

[0019] The following refers to the attached Figure 1 to the attached Figure 2 to describe an approximate solution method for the modal damping coefficient of a submerged beam based on the Morison equation of the present invention.

[0020] Currently, there are mainly two methods for solving the modal damping coefficient of a beam in a fluid. One is to conduct vibration tests in a water tank to collect vibration data and then obtain the damping coefficient. The other is based on theoretical calculations, such as the fluid-structure coupling analytical method for solving the hydroelastic problem or the numerical method based on computational fluid dynamics (CFD) to determine the damping ratio of the liquid viscous effect, so as to obtain the damping coefficient. Although the modal damping coefficient solved by the above solutions is more accurate, the time cost is relatively high and the difficulty is relatively large. When performing hydrodynamic calculations on large structures, the viscous effect in the fluid control equation is very weak, and the potential flow theory method is usually adopted, ignoring the viscous effect of the fluid.

[0021] Therefore, the approximate solution method for the modal damping coefficient of this submerged beam includes the following steps: S1. Establish a finite element model of a slender beam structure submerged in water, and calculate the hydrodynamic load acting on the beam structure; Preferably, a finite element model of a slender beam structure submerged in water is established by using the finite element method. In other embodiments of the present invention, other implementation manners may also be adopted, as long as a finite element model of a slender beam structure submerged in water can be established.

[0022] Preferably, the Morison equation is used to calculate the hydrodynamic load acting on the beam structure. In other embodiments of the present invention, other implementation manners may also be adopted, as long as the hydrodynamic load acting on the beam structure can be calculated.

[0023] Specifically, the hydrodynamic load on the beam structure includes viscous effect and inertial effect.

[0024] Specifically, the physical parameters, geometric dimensions, and boundary conditions for establishing the finite element model of the slender beam structure submerged in water should be consistent with the actual structure.

[0025] S2. Apply a transient impact load on the beam structure to make it perform free decay motion in water, and then extract the free decay curve of the beam; Specifically, the maximum displacement amplitude of the beam caused by the applied impact load needs to be close to the motion amplitude of the actual structure.

[0026] S3. Calculate the damping ratio of the structure according to the known free decay curve, and finally calculate the modal damping coefficient of the structure from the relationship between the damping ratio and the modal damping coefficient; Further, by calculating the area enclosed by the curve and the time axis, the damping ratio of the structure is obtained, and finally, the modal damping coefficient of the structure is calculated from the relationship between the damping ratio and the modal damping coefficient. Specifically, calculate the area enclosed by the free decay curve and the time axis , and then through , calculate the modal damping ratio : ; Then calculate the modal damping coefficient from the relationship between the modal damping ratio and the modal damping coefficient: ; S4. Substitute the modal damping coefficient into the vibration equation of the slender structure immersed in water and solve it to obtain the mode shape and frequency of the structure.

[0027] Further, through the free decay results of multiple impact loads of different magnitudes, the order of magnitude of the modal damping coefficient of the liquid viscous damping effect is obtained, and then the modal damping coefficient is substituted into the vibration equation of the slender structure immersed in water.

[0028] Further, this modal damping coefficient is used not only to calculate the beam mode shape and frequency of the structure immersed in water, but also to calculate the response of the beam in the analytical method.

[0029] By implementing the above steps, the order of magnitude of the modal damping of the liquid viscous damping effect of the immersed slender structure can be approximately estimated. This method has high calculation efficiency and simple theory, so this patent has important guiding significance for solving the vibration equation of ocean engineering structures.

[0030] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, and are not intended to limit the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for approximating the damping coefficient of the submerged beam based on the Morison equation, characterized in that: The following steps are involved: S1. Establish a finite element model of a slender beam structure immersed in water and calculate the hydrodynamic load acting on the beam structure; S2. Apply a transient impact load to the beam structure, make it do free decay motion in water, and then extract the free decay curve of the beam; S3. Calculate the damping ratio of the structure according to the known free decay curve, and finally calculate the modal damping coefficient of the structure according to the relationship between the damping ratio and the modal damping coefficient; S4. Substitute the modal damping coefficient into the vibration equation of the slender structure immersed in water and solve it to obtain the modal shape and frequency of the structure.

2. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 1 is characterized in that: In S1, a finite element model of a slender beam structure immersed in water is established using the finite element method.

3. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 2, characterized in that: In S1, the Morison equation is used to calculate the hydrodynamic loads acting on the beam structure.

4. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 1 is characterized in that: The hydrodynamic loads on the beam structure include viscous effects and inertial effects.

5. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 4, characterized in that: The physical parameters, geometric dimensions and boundary conditions of the finite element model of a slender beam structure immersed in water should be consistent with the actual structure.

6. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 1, characterized in that: In S2, the maximum displacement amplitude of the beam caused by the applied impact load needs to be close to the motion amplitude of the actual structure.

7. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 1, characterized in that: In S3, the area enclosed by the curve and the time axis is calculated to obtain the damping ratio of the structure, and finally the modal damping coefficient of the structure is calculated from the relationship between the damping ratio and the modal damping coefficient.

8. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 7, characterized in that: Calculate the area enclosed by the free decay curve and the time axis , and then by , calculate the modal damping ratio : ； Then the modal damping coefficient is calculated based on the relationship between the modal damping ratio and the modal damping coefficient: 。 9. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 1, characterized in that: In S4, the magnitude of the modal damping coefficient of the liquid viscous damping effect is obtained through the free decay results of multiple impact loads of different sizes, and then the modal damping coefficient is introduced into the vibration equation of the slender structure immersed in water.

10. The method for approximating the damping coefficient of the submerged beam vibration mode according to claim 1, characterized in that: This modal damping factor is used both in computing the mode shapes and frequencies of the beam immersed in water and in computing the response of the beam analytically.

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