CN113218615A - Equivalent method of distributed aerodynamic force and limited excitation point excitation load - Google Patents

Equivalent method of distributed aerodynamic force and limited excitation point excitation load Download PDF

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CN113218615A
CN113218615A CN202110620988.1A CN202110620988A CN113218615A CN 113218615 A CN113218615 A CN 113218615A CN 202110620988 A CN202110620988 A CN 202110620988A CN 113218615 A CN113218615 A CN 113218615A
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excitation
aerodynamic
aerodynamic force
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曹登庆
李基鹏
邵崇晖
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Harbin Qinglin Jiecheng Technology Co ltd
Harbin Institute of Technology
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • G01M9/06—Measuring arrangements specially adapted for aerodynamic testing
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

An equivalent method of distributed aerodynamic force and limited excitation point excitation load belongs to the field of aircraft ground aerodynamic tests, and specifically relates to an aerodynamic force equivalent technology in the aerodynamic test. The invention aims to solve the problem that the pneumatic action of the distributed aerodynamic force on the structure is equivalently simulated by a limited excitation point in the structure pneumatic flutter test. In the process of the structure pneumatic flutter test, the aerodynamic force is integrated along the surface of the structure, the excitation load of the equivalent finite excitation point is made to work equally to the structure by the aerodynamic force based on the energy equivalence principle, and then the equivalent excitation load of each excitation point is obtained by solving.

Description

Equivalent method of distributed aerodynamic force and limited excitation point excitation load
Technical Field
The invention belongs to the field of aircraft ground pneumatic tests, and particularly relates to a structural pneumatic test method, in particular to a pneumatic equivalent technology in a pneumatic test.
Background
Aerodynamic flutter is a aerodynamic phenomenon that seriously threatens the stability and safety of an aircraft. The existing test research method is mainly a wind tunnel method, but the wind tunnel has the outstanding problems of complex structure, high test cost, high experiment technical difficulty and the like, so that the finding of a simple and efficient aircraft fluid-solid coupling ground wind tunnel test method has important practical significance.
The existing ground wind tunnel experiment method mainly tests the vibration displacement and the speed of the aircraft structure through an eddy current sensor, a laser displacement sensor and the like, obtains the aerodynamic force value of a measuring point based on empirical formulas such as a piston theory and the like, and applies corresponding aerodynamic force to the structure by using a vibration exciter so as to analyze the vibration response and the aerodynamic stability of the aircraft structure. Some of the existing test methods are based on finite element methods, and have low calculation speed and no real-time property; there are some methods based on equivalence, but the equivalence process lacks a strict theoretical basis.
The aerodynamic load borne by the aircraft structure belongs to distributed load, and the ground test is difficult to completely and truly simulate. The distributed load can be reduced to a plurality of concentrated loads according to an equivalent algorithm and then applied to the structure by the actuators. The equivalent algorithm needs to synthesize the test results of a plurality of sensors and calculate the result of the equivalent aerodynamic force in real time, so that high requirements on the accuracy and the real-time performance of the algorithm are provided, and the method is a key and difficult point for realizing the ground aerodynamic test of the aircraft.
Disclosure of Invention
The invention aims to solve the problem that the pneumatic action of distributed aerodynamic force on a structure is simulated equivalently by a limited excitation point in a structural pneumatic flutter test, provides an equivalent method of the distributed aerodynamic force and the excitation load of the limited excitation point, and realizes a simple, efficient and accurate structural pneumatic flutter ground test.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an equivalent method of distributed aerodynamic force and limited excitation point excitation load comprises the following steps:
arranging m piezoelectric actuators on the upper surface of the wallboard to apply excitation to simulate aerodynamic force, wherein the laying positions of the m piezoelectric actuators are aj(xj,yj) The force applied is fjWherein j is 1 … m;
n piezoelectric sensors are arranged on the upper surface or the lower surface of the wall plate for measuring displacement and speed, and the laying positions of the n piezoelectric sensors are sk(xk,yk) Measuring the displacement wkAnd velocity wkWherein k is 1 … n;
for a four-sided simply supported plate, the lateral displacement at any point on the plate at time t is expressed as:
Figure BDA0003099867580000021
wherein i is a modal order, l is a truncated modal order, and q is a linear orderi(t) is the modal coordinates at time t,
Figure BDA0003099867580000022
to satisfy the lattice function of the boundary condition of the wall plate, as shown in fig. 3, a and b are the geometric dimensions of the flat plate, i.e., the length and width;
displacement w measured by a piezoelectric sensorkAnd velocity
Figure BDA0003099867580000023
Expressed as:
Figure BDA0003099867580000024
wherein M is a matrix formed by first-order modal vectors of the structure, and each-order modal vector comprises the modal of n measuring points; the expression of M is as follows:
Figure BDA0003099867580000025
obtaining q by the above formulaiAnd
Figure BDA0003099867580000026
with respect to wk，
Figure BDA0003099867580000027
Calculating and solving the displacement and the speed of any point on the wall plate;
work P of aerodynamic force in unit time of whole wall plateΔPIs equal to the work done by m piezoelectric actuators per unit time of excitation
Figure BDA0003099867580000028
Namely:
Figure BDA0003099867580000029
wherein:
Figure BDA00030998675800000210
Figure BDA0003099867580000031
wherein, Δ p is the acting force of the airflow at each point on the surface of the wall plate, and can be obtained by the aeroelasticity theory; delta is a dirac function, and when the independent variable is not 0, the function value is constantly zero;
the formula (5) and the formula (6) may be taken into the formula (4):
Figure BDA0003099867580000032
namely:
Figure BDA0003099867580000033
wherein:
Figure BDA0003099867580000034
solving the m piezoelectric actuators according to the formulas (1) to (7) to obtain the force f required to be applied to the m piezoelectric actuatorsj，ΔpiWork, K, done for aerodynamic forcesijDenotes a symbol introduced for simplifying the expression of the formula (7), and has no particular physical meaning, v∞Infinite incoming flow velocity and gamma is the adiabatic coefficient. To represent
Further, regarding the matrix M, it is necessary to intercept the modes that are equal to the number of stations and are uncorrelated, so as to ensure that M is an invertible square matrix, i.e. n ═ l.
Compared with the prior art, the invention has the beneficial effects that: the equivalent method provided by the invention based on the energy equivalent principle has the outstanding advantages of simple calculation process, high processing efficiency and the like. In the process of the structure pneumatic flutter test, the aerodynamic force is integrated along the surface of the structure, the excitation load of the equivalent finite excitation point is made to work equally to the structure by the aerodynamic force based on the energy equivalence principle, and then the equivalent excitation load of each excitation point is obtained by solving.
Drawings
FIG. 1 is a hardware composition diagram of a wall flutter test in an embodiment;
FIG. 2 is a schematic view of the wall panel boundary installation of the embodiment;
FIG. 3 is a schematic diagram of the sensor laying position in the embodiment;
FIG. 4 shows dynamic pressure λ 580 < λcrA time history chart of transverse vibration of the time wall plate;
FIG. 5 shows dynamic pressure λ 620 > λcrTime history chart of transverse vibration of the time wall plate.
Detailed Description
The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. It is obvious that the described embodiments are only a part of the embodiments of the invention, not all embodiments, and all other embodiments obtained by those skilled in the art without any inventive work are within the scope of the present invention.
Example 1:
pneumatic flutter ground equivalent experiment of plate structure
The plate-shaped structure is very common, and the aerodynamic characteristics of the plate-shaped structure relate to the safe operation of engineering structures such as wings and blades. In this embodiment, a plate structure flutter experiment is taken as an example, a composition diagram of experimental hardware is shown in fig. 1, and a structure installation is shown in fig. 2. The aerodynamic loads are equivalent to the excitation loads of 8 excitation points as shown in fig. 3, according to the method described in the patent content. The specific parameters of the plate structure are as follows, the geometric parameters are 0.8m 0.6m 0.002m in length and width, and the density is 2689kg/m3The modulus of elasticity was 68.3 GPa.
In the embodiment, a rectangular plate structure is taken as an example, exciting force is applied at 8 exciting points, the test result and the numerical calculation result show that the pneumatic instability critical speed of the plate is 717.5m/s and has better consistency, and the calculation result is efficient, accurate and reliable.
As shown in fig. 4 and 5, it can be seen that when the dynamic pressure is taken 580, the structure is in a stable state, and the structural vibration caused by external excitation is gradually attenuated and approaches to zero; when dynamic pressure is taken 620, the structure is in a flutter destabilization state, and external disturbance causes the structure to enter a self-excited vibration state of periodic motion. Therefore, the method can well simulate the aerodynamic flutter phenomenon of the aircraft structure through ground tests, and also proves the feasibility, reliability and convenience of the equivalent method of distributed aerodynamic force and limited excitation point excitation load.

Claims (2)

1. An equivalent method of distributed aerodynamic force and limited excitation point excitation load is characterized in that: the method comprises the following steps:
arranging m piezoelectric actuators on the upper surface of the wallboard to apply excitation to simulate aerodynamic force, wherein the laying positions of the m piezoelectric actuators are aj(xj,yj) The force applied is fjWherein j is 1 … m;
n piezoelectric sensors are arranged on the upper surface or the lower surface of the wall plate for measuring displacement and speed, and the laying positions of the n piezoelectric sensors are sk(xk,yk) Measuring the displacement wkAnd velocity
Figure FDA0003099867570000019
Wherein k is 1 … n;
for a four-sided simply supported plate, the lateral displacement at any point on the plate at time t is expressed as:
Figure FDA0003099867570000011
wherein i is a modal order, l is a truncated modal order, and q is a linear orderi(t) is the modal coordinates at time t,
Figure FDA0003099867570000012
in order to satisfy the matrix function of the boundary condition of the wall plate, a and b are the geometric dimensions of the flat plate, namely the length and the width;
displacement w measured by a piezoelectric sensorkAnd velocity
Figure FDA0003099867570000013
Expressed as:
Figure FDA0003099867570000014
wherein M is a matrix formed by first-order modal vectors of the structure, and each-order modal vector comprises the modal of n measuring points; the expression of M is as follows:
Figure FDA0003099867570000015
obtaining q by the above formulaiAnd
Figure FDA0003099867570000016
with respect to wk，
Figure FDA0003099867570000017
Calculating and solving the displacement and the speed of any point on the wall plate;
work P of aerodynamic force in unit time of whole wall plateΔPIs equal to the work done by m piezoelectric actuators per unit time of excitation
Figure FDA0003099867570000018
Namely:
Figure FDA0003099867570000021
wherein:
Figure FDA0003099867570000022
Figure FDA0003099867570000023
wherein, Δ p is the acting force of the airflow at each point on the surface of the wall plate, and can be obtained by the aeroelasticity theory; delta is a dirac function, and when the independent variable is not 0, the function value is constantly zero;
the formula (5) and the formula (6) may be taken into the formula (4):
Figure FDA0003099867570000024
namely:
Figure FDA0003099867570000025
wherein:
Figure FDA0003099867570000026
solving the m piezoelectric actuators according to the formulas (1) to (7) to obtain the force f required to be applied to the m piezoelectric actuatorsj，ΔpiWork, K, done for aerodynamic forcesijDenotes a symbol introduced for simplifying the expression of the formula (7), and has no particular physical meaning, v∞Infinite incoming flow velocity and gamma is the adiabatic coefficient.
2. The equivalent method of distributed aerodynamic and finite excitation point excitation loads according to claim 1, characterized in that: regarding the matrix M, it is necessary to intercept the modes that are equal to the number of stations and are uncorrelated to ensure that M is an invertible square matrix, i.e. n ═ l.
CN202110620988.1A 2021-06-03 2021-06-03 Equivalent method of distributed aerodynamic force and limited excitation point excitation load Pending CN113218615A (en)

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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102866637A (en) * 2012-10-07 2013-01-09 西北工业大学 Quadratic order-reduction based method for simulating unsteady aerodynamic force of aerofoil with operation surface
CN104133933A (en) * 2014-05-29 2014-11-05 温州职业技术学院 Pneumatic elastic mechanical characteristic analytical method of hypersonic speed aircraft in thermal environment
CN109889094A (en) * 2019-03-12 2019-06-14 哈尔滨工业大学 A kind of double oscillator piezoelectric harvesters of tunable aerofoil profile flutter Exciting-simulator system
CN109933876A (en) * 2019-03-03 2019-06-25 西北工业大学 A kind of unsteady aerodynamic force order reducing method based on broad sense aerodynamic force
CN111324991A (en) * 2019-12-10 2020-06-23 中国飞机强度研究所 Reconstruction method of aerodynamic model in ground flutter test

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102866637A (en) * 2012-10-07 2013-01-09 西北工业大学 Quadratic order-reduction based method for simulating unsteady aerodynamic force of aerofoil with operation surface
CN104133933A (en) * 2014-05-29 2014-11-05 温州职业技术学院 Pneumatic elastic mechanical characteristic analytical method of hypersonic speed aircraft in thermal environment
CN109933876A (en) * 2019-03-03 2019-06-25 西北工业大学 A kind of unsteady aerodynamic force order reducing method based on broad sense aerodynamic force
CN109889094A (en) * 2019-03-12 2019-06-14 哈尔滨工业大学 A kind of double oscillator piezoelectric harvesters of tunable aerofoil profile flutter Exciting-simulator system
CN111324991A (en) * 2019-12-10 2020-06-23 中国飞机强度研究所 Reconstruction method of aerodynamic model in ground flutter test

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
邵崇晖: ""超声速流中壁板颤振的抑制和地面试验研究"", 《中国优秀博士学位论文全文数据库工程科技Ⅱ辑》 *

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