CN101000294A - Investigating method for impact loading spectrum of aircraft laminated structure and its investigating device - Google Patents

Abstract

The invention discloses a method for monitoring the impact load spectrum of aircraft laminated structures. Firstly, several piezoelectric sensitive elements are pasted or pre-embedded on the surface of the laminated structure as discrete piezoelectric plate units. When the structure is subjected to random impact, The dynamic response of each piezoelectric modal sensor caused by random impact is collected through the data acquisition and processing integrated board; the modal response coordinates of the structure are obtained through the calculation of the dynamic response of the above piezoelectric plate unit, and the unconditional and stable fine stepwise integration method is used to solve the structure The modal dynamic differential equation of the structure, and finally the time history of the impact load is obtained iteratively from the modal coordinates of the structure. The monitoring device for realizing the method includes a computer, a discrete piezoelectric sensor pasted or pre-embedded on the surface of the laminated structure and electrically connected to the charge amplifier, and the charge amplifier is connected to the computer through a data collector; the computer A data acquisition and processing integrated board is inserted in the expansion slot of the main board.

Description

Monitoring method and monitoring device for impact load spectrum of aircraft laminated structure

technical field

The invention relates to the technical field of aircraft structure damage monitoring, in particular to a method for monitoring the time history of impact loads on the surface of aircraft laminated structures. The invention also relates to a monitoring device implementing the method.

Background technique

With the application of laminated structures on engineering components such as aircraft wings, in order to ensure the safe operation of the structure, the problem of delamination damage caused by uncertain impact energy has attracted people's attention, because delamination damage occurs in the material The interior cannot be detected from the surface and has the potential for sudden and catastrophic failure. The impact damage mechanism of composite laminated structures is very complex, and the research in this area is still in the development stage. Experimental research shows that the dynamic response of composite laminated structures is significantly correlated with the damage of the structure when it is impacted, and there is also a certain correlation between the delamination damage area and the impact energy. Therefore, real-time identification of the time history of uncertain impact loads of laminated structures during service and calculation of the impact energy is one of the effective ways to evaluate the type and degree of structural damage. The crux of the problem is how to monitor in real time the impact load spectrum of the laminated structure when it is subjected to random impacts during service, and the device used will not affect the function of the laminated structure itself and the dynamic performance of the laminated structure itself.

The monitoring of impact load spectrum actually belongs to the problem of identification of structural dynamic load. The identification of dynamic load is to invert the dynamic load of the structure based on the dynamic characteristics of the known system and the measured dynamic response, which is a relatively difficult dynamic inverse problem. The general technique is to lay out acceleration sensors on the structure, and use the method based on multi-point acceleration vibration pickup to invert the dynamic load of the structure. However, since this method requires many measuring sensors, and the frequency response range of the acceleration sensor is narrow and has a certain mass and volume, it has a great influence on the dynamic characteristics of the structure itself. Obviously, this method is not suitable for Laminated structures on aircraft.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for the impact load spectrum of the laminated structure of the aircraft that can monitor in real time without affecting the function of the laminated structure itself and the dynamic performance of the laminated structure itself. In addition, another technical problem to be solved by the present invention is to provide a device for realizing the monitoring method.

In order to solve the above-mentioned technical problems, the monitoring method of the impact load spectrum of the laminated structure of the aircraft of the present invention is that at first a number of piezoelectric sensitive elements are pasted or pre-embedded on the surface of the laminated structure as discrete piezoelectric plate units to form a Piezoelectric laminated intelligent structure with the function of dynamic sensor; when the structure is subject to random impact, the dynamic response of each piezoelectric modal sensor caused by random impact is collected through the data acquisition and processing integrated board; through the dynamic response calculation of the above piezoelectric plate unit The modal response coordinates of the structure are obtained, and the unconditional and stable fine stepwise integration method is used to solve the modal dynamic differential equation of the structure. Finally, the time history of the impact load (shock load spectrum) is obtained iteratively from the modal coordinates of the structure.

The monitoring device of the present invention realizes the monitoring method of the impact load spectrum of the laminated structure of the aircraft, including a computer, and is characterized in that: the discrete piezoelectric sensor pasted or pre-embedded on the surface of the laminated structure is electrically connected to the charge amplifier, and the electric charge The amplifier is connected with the computer through the data collector; the expansion slot of the mainboard of the computer is inserted with a data collection and processing integrated board.

Since the present invention is based on the method of inverting the shock load spectrum based on the modal response of the piezoelectric structure, the modal response of the piezoelectric structure used is indirectly calculated from the piezoelectric response of the piezoelectric element itself according to the mode shape superposition and the principle of piezoelectric sensing As a result, the piezoelectric modal sensor is not additionally provided physically, so that the modal recognition theory is used without additional modal sensors, and the function and dynamic characteristics of the laminated structure itself will not be affected. At the same time, after calculating the modal response of the structure, in order to invert the structural impact load spectrum, the present invention adopts an unconditionally stable step-by-step integral method, which has simple algorithm, fast calculation speed, and no problems such as matrix ill-conditioning. And because the method adopts the analysis method of structural finite element piezoelectric mode, it is widely suitable for complex laminated structures with any irregular shape and boundary conditions.

In the monitoring device of the present invention, since the piezoelectric sensitive element is very thin, small in size and light in weight, it has very little influence on the function and dynamic performance of the laminated structure itself, and the piezoelectric sensitive element has low cost, high sensitivity, frequency The piezoelectric laminated intelligent structure with the function of piezoelectric modal sensor constituted by the present invention is used to monitor the impact load spectrum of the laminated structure without affecting the function of the laminated structure itself and the laminated structure The dynamic performance of itself and the dynamic response obtained by the piezoelectric modal sensor can conveniently reverse the impact load spectrum of the structure according to the method provided by the present invention.

Description of drawings

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

Fig. 1 is the schematic diagram of the monitoring device realizing the impact load spectrum monitoring method of aircraft laminated structure;

Fig. 2 is a schematic diagram of an embodiment of the method for monitoring the impact load spectrum of an aircraft laminate structure according to the present invention.

Detailed ways

Fig. 1 is a schematic diagram of a monitoring device for realizing the monitoring method of the impact load spectrum of an aircraft laminated structure. In Figure 1, 1 is the laminated structure of the aircraft, 2 is the discrete piezoelectric sensor (P1-P6), 3 is the computer, 4 is the data collector, 5 is the charge amplifier; k is the assumed position of the impact load. The discrete piezoelectric sensor 2 pasted or pre-embedded on the surface of the laminated structure 1 of the aircraft is electrically connected to the charge amplifier 5, and the charge amplifier 5 is connected to the computer 3 through the data collector 4; the discrete piezoelectric sensor 2 includes P1, P2, P3, P4, P5, and P6 are six piezoelectric sensing units (generally using PVDF film) pasted on the lower surface of the laminated structure of the aircraft. The electrode surfaces of each piezoelectric sensing unit are insulated from each other, so that when When an impact load acts on the laminated structure 1 of the aircraft, the piezoelectric responses received by each of the six piezoelectric sensing elements are transmitted to the data acquisition and processing integrator 4 through the charge amplifier 5 at the same time, and the structural response is obtained after data processing. Piezoelectric modal response to impact. Therefore, the six piezoelectric sensing elements are actually discrete piezoelectric sensors with the function of piezoelectric modal sensors.

As shown in FIG. 2 , it is a schematic diagram of an embodiment of the present invention on monitoring the impact load spectrum of an aircraft laminate structure. In Fig. 2, the laminated substrate 6 of the aircraft is 0.6m long, 0.6m wide, and 0.8mm thick, and is composed of four layers of graphite-epoxy composite materials, with four sides clamped. A layer of PVDF piezoelectric film 7 is pasted on the lower surface of the laminated substrate 6 of the aircraft, with a thickness of 0.1 mm. The entire PVDF piezoelectric film 7 is divided into 9 piezoelectric units, and each unit is a piezoelectric sensing unit chip. The impact test of the plate is carried out on the double-rail drop hammer test bench. For the convenience of verification, the impact waveform is a simple half-sine wave.

The purpose of the identification of the impact load spectrum is to express the impact load randomly acting on the surface of the intelligent structure of the piezoelectric laminate with the curve of the relationship between load and time. The method adopted in the present invention is as follows: according to the modal sensing principle of the piezoelectric smart structure, the piezoelectric smart board structure and the PVDF piezoelectric film are correspondingly divided into finite elements, that is, the laminated board in Fig. 2 is also divided into 9 units.

After the piezoelectric smart board is divided by finite elements, its e-type linear positive piezoelectric equation can be expressed as

D＝eε+βE (1)

In the formula, D is the electric displacement array, e is the piezoelectric constant matrix, ε is the strain array, β is the dielectric constant matrix, and E is the electric field strength array. Strain Arrays for Arbitrary Points in a Piezoelectric Laminate

ε＝{ε _x ε _y γ _xy } ^T can be expressed as

ε=zψ; ψ=Bδ ^e (2)

In the formula, z is the coordinate of the point in the direction of deflection w, $\mathrm{\&psi;}=-{\left\{\begin{array}{ccc}\frac{{\&PartialD;}^{2}w}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="A20071001937100111.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}& \frac{{\&PartialD;}^{2}w}{{\&PartialD;\mathrm{the\; <figure-callout\; id="2"\; label="y"\; filenames="A20071001937100111.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}& 2\frac{{\&PartialD;}^{2}w}{\&PartialD;x\&PartialD;\mathrm{the\; y}}\end{array}\right\}}^T$ are the curvature and torsion vectors, B is the element deformation matrix, and δ ^e is the element node displacement array. When the piezoelectric laminate is used as a sensor, the electric field strength E=0, the electric displacement of the surface of the piezoelectric element in the polarization direction z can be obtained from formula (1)

D _z = e ₃₁ ε _x + e ₃₂ ε _y + e ₃₆ γ _xy (3)

Assuming that there are m piezoelectric sheets pasted on the surface of the structure, the electric quantity on the jth piezoelectric sheet can be obtained from the above formula

${\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}\underset{{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\mathrm{<span\; class="notranslate">\; B</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; D</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

表示对第j个压电片所覆盖的单元求和，

为压电片的平均z坐标。in

Indicates the summation of the cells covered by the jth piezoelectric film,

is the average z-coordinate of the piezoelectric sheet.

Let φ _ei be the e element of the i-th order mode in the structural modal matrix φ, x _i is the i-th order modal coordinate, expand the node displacement δ ^e according to the modal coordinate x and take m mode truncation, then have

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; ei</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Substituting the above formula into (4) and writing it in matrix form, the piezoelectric modal sensing equation can be obtained

Q＝AX (6)

Among them, Q={q ₁ , q ₂ ,...,q _m } ^T is the output charge column vector of the piezoelectric sheet, X={x ₁ , x ₂ ,...x _m } ^T is the modal coordinate column vector, $A_{\mathrm{the\; ji}}=\underset{j}{\overset{e}{\mathrm{\&Sigma;}}}\underset{A^e}{\&Integral;}{e}_{z}B{\mathrm{\&phi;}}_{\mathrm{ei}}{D}^e,(i,j=1,...,m).$

According to the above formula, as long as m piezoelectric sheets are arranged, the first m order modal responses of the structure can be measured, and m=9 in this embodiment. According to the m-order modal response, the following modal dynamic differential equations with n degrees of freedom can be solved:

$\mathrm{<span\; class="notranslate">\; m</span>}\stackrel{<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K\&delta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

分别为结构的节点位移、速度和加速度列阵。In the formula, M is the mass matrix, K is the stiffness matrix, and C is the damping matrix. δ,

are the nodal displacement, velocity and acceleration arrays of the structure, respectively.

If the first m order feature pairs (ω _m ² , {φ _m } of the system are obtained from the actual measurement, then the regularized mode matrix φ=[φ ₁ φ ₂ …φ _m ] is used as the transformation matrix, and the node displacement can be expressed as

δ＝φX (8)

Substituting the above formula into equation (7), the uncoupled modal differential equations can be obtained

$\stackrel{<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; E\&Omega;</span>}\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula,

E＝diag[ξ ₁ ξ ₂ …ξ _m ], Ω ² =diag[ω ₁ ² ω ₂ ² …ω _m ² ], ω _r , ξ _r are the natural frequency and damping ratio of the rth order mode respectively, and characteristic load array

{p(t)}＝ ^φT {F(t)}

(10)

Write formula (9) into a decomposition formula as

${\stackrel{<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$

(r=1,...,m) (11)

If the modal coordinate x _r (t) has been obtained by formula (9), then the characteristic load p _r (t) can be obtained by solving the differential equation (11), and then the load array can be obtained inversely by formula (10)

{F(t)}＝[φ ^T ] ^-1 {p(t)}

(12)

In order to obtain the exact solution of equation (11) modal differential equation, what the present invention adopts is following unconditionally stable fine step-by-step integral solution method: first equation (11) is reduced to first-order differential equation

$<span\; class="notranslate">\; \{</span>\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

in

$<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right\}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; r</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

The general solution of equation (13) within the integration step t∈τ′(t _j , t _j+1 ) is

{v(t)}＝[T(τ)]({v(t _j )}-{v _p (t _j )})+{v _p (t)} (16)

in, $\left[T\left(\mathrm{\&tau;}\right)\right]=e^{\left[h\right]\mathrm{\&tau;}},$ τ=tt _j , {v _p (t)} is the special solution of the equation.

Subdivide the integration step τ' into s=2 ^N equal parts (take 20 for the general structure N), then Δt=τ'/s=2 ^-N τ', in the time period of Δt, we have

[T(τ)]＝[e ^[H]Δt ] ^s

≈[I+HΔt+(HΔt) ² /2! +(HΔt) ³ /3! +(HΔt) ⁴ /4! ^]

≡[I+T _a0 ] ^s

(17)

Construct iterative

[T _ai ]＝2[T _ai-1 ]+[T _ai-1 ][T _ai-1 ]

(i=1, 2,..., N) (18)

then there is

$<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ]</span>}^{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ]</span>}^{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; ]</span>}^{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

Assuming that the load changes linearly within the integration step (t _j , t _j+1 ); {k ₀ }, {k ₁ } are time-invariant vectors, then

$\begin{array}{cc}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>& <span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; \}</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

For {r(t)}={k ₀ }+{k ₁ }×(tt _j ) (21)

The particular solution of equation (13) is

{v _p (t)}＝([H] ^-1 +[I]×t)(-[H] ^-1 {k ₁ })-[H] ^-1 ({k ₀ }-{k ₁ }× t _j )

＝-[H] ^-1 ({k ₀ }+[H] ^-1 {k ₁ })+[H] ^-1 {k ₁ }(t _j -t) (22)

Substituting the above formula into formula (16) and sorting out

{v(t _j+1 )}＝[T(τ)]({v(t _j )}+[H] ^-1 ({k ₀ }+[H] ^-1 {k ₁ }))-

[H] ^-1 ({k ₀ }+[H] ^-1 {k ₁ }+{k ₁ }×τ)

=[T(τ)]{v(t _j )}+[C(τ)]{k ₀ }+[D(τ)]{k ₁ } (23)

where [C(τ)]=[T(τ)][H] ^-1 -[H] ^-1

[D(τ)]＝[T(τ)IH] ^-1 [H] ^-1 -[H] ^-1 [H] ^-1 -[H] ^-1 τ (24)

Using formula (14, 15) and formula (23) can be written as

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\end{array}\right\}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\\ {\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\end{array}\right\}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\end{array}\right\}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 25</span>}<span\; class="notranslate">\; )</span>$

Its decomposition formula is

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\stackrel{<span\; class="notranslate">\; .</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}\frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}$

According to the above formula, the impact load spectrum p _r (t) can be iteratively calculated from the modal coordinate x _r (t).

Compared with the applied half-sine waveform, the result calculated in this embodiment according to the above method is in good agreement with the waveform, which shows that the method of the present invention is used to monitor the impact load spectrum with high accuracy.

Claims (2)

1, a kind of monitoring method of aircraft laminated structure impact load spectrum is, it is characterized in that: at first some piezoelectric sensitive elements are pasted or pre-embedded on laminated structure surface as discrete piezoelectric plate unit, constitute the The piezoelectric laminated intelligent structure with the function of dynamic sensor; when the structure is subject to random impact, the dynamic response of each piezoelectric modal sensor caused by random impact is collected through the data acquisition and processing integrated board; through the dynamic response calculation of the above piezoelectric plate unit The modal response coordinates of the structure are obtained, and the modal dynamic differential equation of the structure is solved by using the unconditional and stable fine stepwise integration method, and finally the time history of the impact load is iteratively obtained from the modal coordinates of the structure. 2. A monitoring device for realizing the monitoring method of the impact load spectrum of the laminated structure of the aircraft according to claim 1, comprising a computer, characterized in that: a discrete piezoelectric sensor and a charge amplifier pasted or pre-embedded on the surface of the laminated structure are electrically connected to each other, and the charge amplifier is connected to the computer through the data collector; the expansion slot of the computer motherboard is inserted with a data collection and processing integrated board.

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