METHOD FOR IDENTIFYING THE DYNAMIC BEHAVIOUR OF A NON-RIGID OBJECT

Abstract

A method for identifying the dynamic behavior of a non-rigid object (10), the object being fixedly attached to a platform (12) that can be set in motion by an actuation device (14) is proposed. The method comprises actuation of the drive device (14) so ​​as to impart to the object a predefined periodic movement at a frequency, called the "cycle frequency". The periodic movement is a combination of at least two geometrically independent periodic elementary movements. The method comprises recording during actuation the variation of at least one quantity representative of a dynamic behavior, called the "dynamic quantity", and calculating for each of the cycle frequencies of the components called "elementary components", a Fourier transform of the variation of said at least one dynamic quantity for each elementary frequency.A dynamic behavior of the object is determined based on the variation of the elementary components. Abstract figure: Figure 2.

Description

Title of the invention: METHOD FOR IDENTIFYING THE DYNAMIC BEHAVIOR OF A NON-RIGID OBJECT Technical field

[0001] The present invention refers to methods and devices for determining at least one characteristic of the dynamic behavior of an object capable of having at least one resonance mode, such as for example an object having at least one flexible, elastic or liquid part. Prior art

[0002] When a rigid object is subjected to linear or angular accelerations, it opposes reaction forces which are fully represented by the inertial characteristics: mass, coordinates of the center of gravity, moments and products of inertia. But if an object is not totally rigid and has, for example, flexible parts or contains liquid, it exhibits a particular behavior with resonance modes which correspond to the maximum displacement of the non-rigid parts relative to the rest of the object.

[0003] Resonance is a physical phenomenon that occurs when the frequency of a periodic motion applied to a system is equal to the natural resonant frequency of the system. The natural resonant frequency of a system is the frequency at which the system vibrates most easily and accumulates the most energy when excited by the periodic motion. A resonance mode is characterized by a frequency called the resonance frequency, the parameters of the motion that generates the resonance and the amplitude of the response of the object. The amplitude of the response of the object can be characterized by different physical quantities associated with the resonance mode such as, for example, the forces that must be applied to the object or to a part of the object, constraints in certain parts, pressures on the walls of a tank, the relative displacement of certain parts.Every physical system has one or more natural resonant frequencies associated with its physical and geometric properties. An object is considered rigid if it does not exhibit any resonant frequencies under the conditions of its operational use. Resonance can have undesirable effects, for example, it can cause damage or structural failure, as in the case of liquid contained in a tank.

[0004] As a result, the reaction forces of an object having a non-rigid part can be very different from those of a rigid object and cannot be represented by the inertial characteristics mentioned above alone. If the non-rigid parts have a significant mass compared to that of the complete object, their behavior can significantly modify that of the complete object or the vehicle to which it belongs. Resonance modes can damage certain parts beyond a certain amplitude of the stress.

[0005] In the particular case of a partially filled tank subjected to movements, the liquid itself is animated by complex movements, combinations of free surface waves generated by the movements of the tank. These waves induce reaction forces on the walls of the tank. They can have an effect on the behavior of the mobile to which the tank is attached, for example any type of land, air or sea vehicle. This problem is also critical for liquid propellant tanks of space launchers. One can cite, for example, the loss of a Falcon 1 satellite launcher due to the uncontrolled sloshing of the propellant in a tank. They can also focus on a point on the walls, generating very high local pressures likely to damage these walls. The forces depend strongly on the filling rate of the tank, the type of movement applied to it and their frequency.Such liquid movements are generally referred to as "sloshing". Identifying the characteristics of sloshing in relation to the tank movements is therefore important. The main characteristics to identify are the resonance modes which induce the greatest forces on the tank and are likely to promote focalizations on certain points of the walls.

[0006] This identification is generally done by placing the object or a reduced-scale model on a platform which applies generic movements to it identified by other means as representative of the movements to which it may be subjected in its operational use. Force sensors placed on the platform, on the object to be measured or on certain parts thereof make it possible to identify the response to the stresses and to detect the resonance modes. In the case of a tank, there may be local pressure sensors making it possible to quantify the response of the liquid to the stresses. The generic movements may be, for example, oscillations in roll, pitch and yaw applied successively with different amplitudes and different frequencies. Descriptions of these methods applied to liquid tanks can be found in KR101721498B1, CN105806578A, KR101259146B1, WO2020225353A1.

[0007] The "Sloshel" project is a joint industrial project between several companies and whose aim is to collect data from large-scale sloshing experiments. The main disadvantage of the calculation method used in the "Sloshel" project is that it requires a large number of tests to explore the different combinations of movements and frequencies. For a tank, it is also necessary to look for the resonance modes for different filling rates. The identification the movements to be applied is a preliminary phase which can be costly in terms of time and resources.

[0008] Furthermore, an inertial balance device is known as disclosed in FR1858787 making it possible to apply to an object a predefined periodic movement composed of the superposition of elementary movements at harmonic frequencies of the frequency of the complete cycle. This device aims to measure the inertial characteristics of a rigid object but the method described in FR1858787 does not make it possible to determine the characteristics of an object having a flexible or liquid part. Summary

[0009] The present disclosure improves the situation.

[0010] A method is proposed for identifying the dynamic behavior of a non-rigid object, the object being fixedly attached to a platform that can be set in motion by an actuating device, the method comprising: actuating the drive device so as to impart to the object a predefined periodic movement at a frequency, called the “cycle frequency”, the periodic movement being a combination of at least two geometrically independent periodic elementary movements, said at least two elementary movements each having a frequency, called the “elementary frequency”, an integer multiple of the cycle frequency, at most two of said at least two elementary movements being of the same elementary frequency, if the periodic movement comprises two elementary movements of the same elementary frequency then they are of different phase, preferably in phase quadrature,the actuation being carried out during at least one period of the periodic movement; recording during the actuation the variation of at least one quantity representative of a dynamic behavior, called "dynamic quantity", collected by at least one sensor arranged on the platform and / or the object; repeating the actuation of the drive device and the recording of the variation of said at least one dynamic quantity at various cycle frequencies each time during at least one period of the periodic movement, the various cycle frequencies being in a predefined frequency range; calculating, by a calculation unit, for each of the cycle frequencies of the predefined frequency range the components of a Fourier transform of the variation of said at least one dynamic quantity for each elementary frequency, the components, called "elementary components",including an elementary intensity component and an elementary phase component; and determining, based on the variation of the elementary components, a dynamic behavior of the object.

[0011] The features set out in the following paragraphs may, optionally, be implemented, independently of one another or in combination with one another:

[0012] - said at least two elementary movements have two elementary frequencies different, preferably with ratios 2 and 3 or 3 and 4 relative to the cycle frequency, or said at least two elementary movements have three different elementary frequencies, preferably with ratios 4, 5 and 6 relative to the cycle frequency.

[0013] - determining the dynamic behavior of the object includes noting that the variation of the elementary components is not a linear function of the square of the cycle frequency.

[0014] - said at least one quantity representative of dynamic behavior is representative of a resonance condition of the object, and this quantity is called "resonance quantity", and determining the dynamic behavior of the object comprises identifying at least one resonance frequency for each of said at least two elementary movements from the variations according to the elementary frequencies of the elementary components of each of said at least two elementary movements.

[0015] - identifying at least one resonant frequency for each of said at least two elementary movements, includes identifying an extremum of the elementary intensity component for each of said at least two elementary movements.

[0016] - the method further comprises determining an amplitude of said at least a resonance quantity for said at least one resonance frequency, this determination being made from the variations of said at least one resonance quantity according to the elementary frequencies of the elementary components for each of said at least two elementary movements.

[0017] - the amplitude of said at least one resonance quantity is the amplitude of the extremum of the elementary intensity component of said at least one resonance quantity at said at least one identified resonance frequency.

[0018] - the method further comprises the identification for each of said frequencies identified resonance of a resonance mode of said at least one resonance quantity, the resonance mode being further characterized by an amplitude of the elementary intensity component at said resonance frequency considered, and a direction associated with the elementary movement for said resonance frequency considered.

[0019] - if one of said resonant frequencies identified for each of said at least two elementary movements is identical for several elementary movements, then the resonance mode is characterized by the combination of these elementary movements.

[0020] - the object is a reservoir containing a liquid, and the determination of the behavior dynamic including a step of measuring the dynamic quantities with the tank empty, and deducing, by subtraction of the elementary components, only the effects of the liquid.

[0021] - said at least one sensor comprises a plurality of force sensors and / or accelerometers arranged on parts of the object likely to resonate and / or pressure sensors arranged on rigid parts of the object and / or strain gauges arranged on flexible parts of the object.

[0022] - said at least one resonance quantity collected by said at least one sensor is recorded at a rate greater than at least 4 times higher than the elementary frequencies and preferably greater than 10 times.

[0023] - in which the repetition of the actuation is done by cycle frequencies increasing in the predefined frequency range.

[0024] Advantages

[0025] An advantage of this method is that it is not necessary to successively apply different elementary movements at different frequencies to identify the resonance modes. The periodic movement applied to the object makes it possible to solicit all the elementary movements in a single frequency ramp. The consequence is a saving of time for taking measurements.

[0026] Another advantage of the method is that it allows the use of a movement means whose movement is completely predefined, possibly including mechanical connections, such as that described in FR1752729. Such a means will allow reproducibility of movements and simplicity of use.

[0027] The method presented uses, by combining elementary movements, all the axes of movement of the solid. Therefore, it is not necessary to first identify the possible movements of the solid in its operational context.

[0028] By making it possible to systematically identify all the resonance modes and their frequency, the method makes it possible to find combinations of modes of different frequencies but whose temporal combination of the extremes is potentially more damaging. Brief description of the drawings

[0029] Other characteristics, details and advantages will appear on reading the detailed description below, and on analyzing the attached drawings, in which: Fig.l

[0030] [Fig. 1] shows a flowchart of a method for identifying the dynamic behavior of a non-rigid object according to one embodiment. Fig. 2

[0031] [Fig.2] shows a training device according to one embodiment, the device being used for the implementation of the method of [Fig. 1]. Fig. 3

[0032] [Fig.3] shows an example of a displacement curve of an object set in motion according to the method of [Fig.l]. Fig. 4

[0033] [Fig.4] shows an example of measurements captured by a sensor relating to displacement of a non-rigid part of an object set in motion according to the method of [Fig.l]. Fig. 5

[0034] [Fig.5] shows an example of variations of elementary components as a function of the cycle frequency of the movement imposed on the object according to the method of [Fig.l]. Fig. 6

[0035] [Fig.6] shows an example of variations of elementary components as a function of elementary frequencies of the movement imposed on the object according to the process of [Fig.l]. Description of the embodiments

[0036] Reference is now made to [Fig.l], which illustrates a method 50. The method 50 described herein relates to the experimental identification of the dynamic behavior of an object 10 (shown in [Fig.2]), in particular its resonance modes, in a predefined frequency range, without prior knowledge of the movements which may excite them.

[0037] The method 50 is applied to a non-rigid object, that is to say one capable of exhibiting resonant behavior. For example, the object 10 is partly or entirely flexible, elastic or has an articulation. The object 10 may, according to one embodiment, be a rigid reservoir containing a liquid.

[0038] To identify the dynamic behavior of the object 10, the method 50 uses a platform 12 animated by a predefined periodic movement thanks to a drive device 14. According to one embodiment, the drive device 14 is a hexapod turret. An example of a hexapod turret (also called a Stewart platform) is notably described in FR1752729.

[0039] According to one example, and as illustrated in [Fig. 2], an example of a hexapod turret 110 includes a base 112, a plate 114 for receiving the object 10, and six supports 116 connecting the base 112 to the plate 114. The supports 116 are, in this embodiment, connecting rods. The connecting rods 116 have their upper ends 117 connected to the plate 114 and their lower ends 118 connected to the base 112. The lower ends 118 of at least three connecting rods 116, called controlled supports, are set in motion in order to set the plate 114 in motion. The supports are controlled by a central unit UC. In another embodiment, the supports can be mechanically connected to each other by gear wheels.

[0040] The drive device 14 makes it possible in particular to impart to the object 10 a predefined periodic movement at a frequency, called the “cycle frequency”. The periodic movement makes it possible in one cycle to move the object 10 in several directions. Thus, the periodic movement is a combination of two or more elementary movements. The elementary movements are periodic and geometrically independent (in other words if and only if the vectors describing the movements are independent, we also speak of “algebraically independent”, that is to say that none is a linear combination of the others). Each elementary movement has a frequency, called the “elementary frequency”, which is an integer multiple of the cycle frequency (i.e. harmonic). The periodic movement can comprise up to 6 elementary movements representing the 3 rotational movements and the 3 translational movements of any displacement of an object.

[0041] Each elementary movement is characterized by an amplitude vector which includes 6 components (Tx, Ty, Tz, Rx, Ry, Rz) where Tx, Ty, Tz are translations in the reference coordinate system, and Rx, Ry, Rz are rotations of roll, pitch and yaw relative to an axis passing through the origin of the reference system, the elementary frequency, and a possible phase shift relative to an origin of the cycle (chosen arbitrarily). An example of periodic movement is illustrated in [Fig.3]. It is composed of two elementary rotational movements: pitch and roll.

[0042] At most two of the elementary movements of the periodic movement have the same elementary frequency. If two elementary movements have the same frequency, their phases are then chosen to be different from each other, preferably in quadrature (90° phase shift). This is the case, for example, if one of the movements is sine and the other is cosine. In the case where there are only two different frequencies of the elementary movements, they can preferably be chosen in the ratios 2 and 3 or 3 and 4 with respect to the cycle frequency. In the case where there are 3 different frequencies of the elementary movements, they can preferably be chosen in the ratios 4, 5 and 6 with respect to the cycle frequency.

[0043] For a periodic movement at the cycle frequency f, we can give an example of such a combination of 6 elementary movements as follows: a rolling movement defined by Rx . sin (4.f.2.ir.t), a pitching movement defined by Ry . cos (4.f.2.ir.t), a yaw movement defined by Rz . sin (6.f.2.ir.t), a translational movement along X defined by Tx . sin (5.f.2.ir.t), a translational movement along Y defined by Ty . cos (5.f.2.ir.t), and a translational movement along Z defined by Tz . cos (6.f.2.ir.t).

[0044] The periodic motion is applied to the object 10 at several cycle frequencies to cover a frequency range of interest. This frequency range can be defined based on the knowledge of the frequency region in which the resonance is likely to be found or the operational operating domain of the object 10.

[0045] At each cycle frequency, the periodic movement is carried out in full, and can be repeated as many times as necessary to highlight the possible resonance modes at this frequency. The different cycle frequencies used as well as the frequency step between two cycle frequencies is preferably adapted to the dynamic behavior that one wishes to highlight. Thus, according to one embodiment, the frequency step between two cycle frequencies is at a frequency width of the resonance modes that one expects to find. One can initially place about ten frequencies between the high frequency and the low frequency of the predefined frequency range. One can then tighten the frequency step around the identified resonance frequencies.When performing periodic movements at different cycle frequencies, these can be performed in an orderly manner, for example by increasing cycle frequency from a lower limit of the predefined frequency range.

[0046] The actuation of the drive device 14 making it possible to impart the periodic movement to the object 10 takes place at the same time as a recording of data collected from one or more sensors C. The sensors C make it possible to collect the variation of at least one quantity representative of the dynamic behavior of the object, called a “dynamic quantity”, such as for example a resonance condition, called a “resonance quantity”. The resonance quantity is a measurement which makes it possible to measure, directly or indirectly, a relative displacement inside the object (e.g. force, displacement, acceleration, pressure, etc.).

[0047] The sensor(s) C are arranged on the platform 12 and / or the object 10. The type of sensor(s) C and the quantities that they measure are chosen by the user according to the characteristics of the parts susceptible to dynamic behavior (e.g. resonance) (i.e. the non-rigid parts) that he wishes to identify. The sensor(s) C may be, for example, force sensors making it possible to measure at each instant the forces undergone by the object 10 or a part of the object 10, accelerometers on parts of the object 10 susceptible to resonance, pressure sensors or force gauges at certain points of interest (e.g. the walls of a tank, if the object is a tank filled at least partially with liquid). The measurements of the sensors C are recorded at various times during each of the periodic movements. According to one embodiment, the collection of data from the sensors C is carried out at a frequency greater than at least 4 times the highest of the elementary frequencies (among the elementary frequencies of the elementary movements making up the periodic movement) and preferably greater than 10 times.

[0048] When the drive device 14 is a hexapod turret, it may be advantageous to equip at least 3 of the 6, or even each, support(s) 116 with a force sensor. Indeed, there then exists a one-to-one relationship between the axial forces along the six supports 116 and the torque of the forces applied to the plate 114 on which the object 10 is fixed.

[0049] The method 50 therefore begins in step 52 by actuating the drive device 14 so as to impart to the object 10 a predefined periodic movement at a cycle frequency in a predefined frequency range, as described above. During the actuation, the variations of one or more quantities representative of a dynamic behavior of the object 10 (for example representative of resonance conditions) are collected using the sensors. The actuation of the drive device 14 and the recording of the dynamic behavior of the object are carried out at various cycle frequencies each time for at least one period of the periodic movement. The various cycle frequencies are within a predefined frequency range.

[0050] [Fig.4] shows an example of temporal variation of a dynamic quantity of the object (displacement), in this case a quantity likely to cause the resonance frequencies of the object to appear, for a periodic movement at a cycle frequency of 0.4 Hz.

[0051] Thus in step 52, this temporal variation is obtained for various cycle frequencies.

[0052] In step 54, a calculation unit (which may be the central processing unit UC), which has access to the data from the sensors C, calculates the Fourier transform of each sensor on the elementary frequencies of each cycle. Each Fourier transform corresponding to an elementary frequency is called an "elementary component". The calculation unit determines a dynamic behavior of the object by analyzing the variations of the elementary components as a function of the elementary frequencies.

[0053] The calculation unit calculates for each of the cycle frequencies at which the object 10 has undergone the periodic movement, the components of a Fourier transform of the variation of the resonance quantity(ies) for each elementary frequency. The components obtained are called “elementary components”. They include an elementary intensity component and an elementary phase component.

[0054] According to one embodiment, determining the dynamic behavior of the object comprises determining that the object is at least partly non-rigid. Mathematically this can be translated by a comparison between the variation of the elementary components of the forces applied to the object and a square of the cycle frequency (or of each elementary frequency). Thus, if it is found that the variation of the elementary components of the forces is not a linear function of the square of the cycle frequency, then it is deduced that the object is at least partly non-rigid. This determination can be interesting in cases where it is not certain that the object is non-rigid. For example, an object may have some non-rigid parts such as suspensions, cables or liquid tanks. If these parts have a very low mass compared to the total mass of the object, their impact on the overall forces applied to the object may be negligible. In this case, the elementary components of the overall forces have a behavior very close to a linear law as a function of the square of the cycle frequency.However, specific sensors placed on the non-rigid parts can identify resonant behavior.

[0055] According to one embodiment, the determination of the dynamic behavior of the object 10 comprises the determination of the resonance frequencies and optionally the resonance modes of the object 10 among the frequencies of the frequency range of the periodic movement to which the object has been subjected. These determinations can be made whether the determination that the object is at least partly non-rigid has been made beforehand or not.

[0056] [Fig.5] shows an example of elementary components obtained as a function of the cycle frequency. In this example, the periodic motion is that illustrated in [Fig.3], that is to say, it is a combination of two elementary motions: a roll motion r defined by r = a.sin(2.u), and a pitch motion t defined by t = a.sin(3.u), where u= 2.ir.ft, f is the cycle frequency, a the angular amplitude and t the time. The period of the periodic motion is T=l / f. The angular amplitude is, for example, a=100 mrd. The elementary components obtained are therefore, for this example, elementary roll intensity component (Ir), elementary roll phase component (Rr), elementary pitch intensity component (It), elementary pitch phase component (Rt). [Fig.5] shows the evolution of the elementary components Rr, Ir, Rt, It as a function of the cycle frequency, and [Fig.6] shows the evolution of the same elementary components but as a function of the elementary frequency corresponding to each elementary component.

[0057] Obtaining the variation of the elementary components as a function of the elementary frequency will make it possible to identify one or more resonance frequencies of the object 10. Thus, in step 56, at least one resonance frequency is identified for each elementary movement from the variations according to the elementary frequencies of the elementary components of each elementary movement. For this, according to one embodiment, for each elementary movement, an extremum of the elementary intensity component. In the example of [Fig.6], there are two extremums for the roll and two extremums for the pitch (for each at the elementary frequency 0.6Hz and 1.5Hz). These extremums make it possible to define the resonance frequencies. Indeed, when a parameter is sensitive to a resonance mode of an object or a part of this object, the amplitude of variation of this parameter varies according to the frequency of the periodic movement applied to it, and has a maximum at the resonance frequency.

[0058] In contrast, for a rigid object, the variations of the elementary components as a function of the frequency (cycle or elementary) depend only on the weight and the inertial forces. The weight is independent of the cycle frequency and the inertial forces are proportional to the square of the cycle frequency. As a result, the elementary components do not exhibit any extremum as a function of this frequency for a rigid object. The appearance of an extremum of an elementary component as a function of the frequency therefore essentially reflects the existence of a resonance mode of at least one part of the object. In certain configurations, it is possible to isolate this part of the object.For example, in the case of a tank, it is possible to measure the elementary components with the tank empty or completely filled so that there is no liquid movement (measured by applying the same periodic movement at the same frequencies but on the empty tank). In this case, it is advantageous to subtract the elementary components measured with the empty tank, for example, from those measured with the partially filled tank. This method makes it possible to isolate the elementary components linked to the moving liquid alone and thus to identify its resonance modes more clearly.

[0059] According to one embodiment, these extrema are defined as representative of a resonance frequency if the corresponding elementary phase component has a rapid variation. Indeed, another characteristic of a resonance mode is that the phase of the response of the sensor C with respect to the stress varies more rapidly in the vicinity of the resonance frequency than towards the other frequencies. By rapid is meant by comparing it to the rest of the variation. For example, for the example of [Fig.6], it is noted that at the elementary frequencies of 0.6Hz and 1.5Hz (corresponding to the extrema of the elementary intensity component), the elementary roll phase component has a rapid decrease. Therefore, the frequencies of 0.6Hz and 1.5Hz are resonance frequencies for the roll and pitch movements.Similarly, we notice that at the elementary frequency of 0.6 Hz, the elementary pitch phase component has a rapid increase, and at the elementary frequency of 1.5 Hz, the elementary pitch phase component has a rapid decrease.

[0060] Thus, according to one embodiment, the method further comprises identifying a resonance mode of the resonance quantity. A resonance mode is associated with each of the resonant frequencies identified for each elementary motion. There can therefore be multiple modes if there are multiple frequencies identified. Each resonant mode is characterized by the identified resonant frequency, an amplitude of the elementary component intensity at the identified resonant frequency, and a direction associated with the elementary motion for which the resonant frequency was identified.

[0061] According to one embodiment, if one of the resonance frequencies identified for each of the elementary movements is identical for several elementary movements, then the resonance mode is characterized by the combination of these elementary movements (for example rolling and pitching).

Claims

1. Claims Method for identifying the dynamic behavior of a non-rigid object (10), the object being securely fixed to a platform (12) which can be set in motion by an actuating device (14), the method comprising: a. Actuating the drive device (14) so ​​as to impart to the object a predefined periodic movement at a frequency, called the "cycle frequency", the periodic movement being a combination of at least two geometrically independent periodic elementary movements, said at least two elementary movements each having a frequency, called the "elementary frequency", an integer multiple of the cycle frequency, at most two of said at least two elementary movements being of the same elementary frequency, if the periodic movement comprises two elementary movements of the same elementary frequency then they are of different phase, preferably in phase quadrature, the actuation being carried out during at least one period of the periodic movement; b. Record during actuation the variation of at least one quantity representative of dynamic behavior, called “dynamic quantity”, collected by at least one sensor (C) placed on the platform and / or the object; c. Repeating the actuation of the drive device and the recording of the variation of said at least one dynamic quantity at various cycle frequencies each time during at least one period of the periodic movement, the various cycle frequencies being within a predefined frequency range; d. Calculate, by a calculation unit, for each of the cycle frequencies of the predefined frequency range the components of a Fourier transform of the variation of said at least one dynamic quantity for each elementary frequency, the components, called “elementary components s”, including a component elementary intensity and an elementary phase component; and e. Determine, based on the variation of the elementary components, a dynamic behavior of the object.

2. Method according to the preceding claim, in which said at least two elementary movements have two different elementary frequencies, preferably of ratios 2 and 3 or 3 and 4 relative to the cycle frequency, or said at least two elementary movements have three different elementary frequencies, preferably of ratios 4, 5 and 6 relative to the cycle frequency.

3. A method according to claim 1 or 2, wherein determining the dynamic behavior of the object comprises noting that the variation of the elementary components is not a linear function of the square of the frequency of the cycle.

4. Method according to one of the preceding claims, in which said at least one quantity representative of a dynamic behavior is representative of a resonance condition of the object, and this quantity is called "resonance quantity", and determining the dynamic behavior of the object comprises identifying at least one resonance frequency for each of said at least two elementary movements from the variations according to the elementary frequencies of the elementary components of each of said at least two elementary movements.

5. Method according to the preceding claim, in which identifying at least one resonance frequency for each of said at least two elementary movements, includes identifying an extremum of the elementary intensity component for each of said at least two elementary movements.

6. Method according to any one of claims 4 or 5, further comprising determining an amplitude of said at least one resonance quantity for said at least one resonance frequency, this determination being made from the variations of said at least one resonance quantity according to the elementary frequencies of the elementary components for each of said at least two elementary movements.

7. Method according to claim 6, wherein the amplitude of said at least one resonance quantity is the amplitude of the extremum of the elementary intensity component of said at least one resonance quantity at said at least one identified resonance frequency.

8. Method according to one of claims 4 to 7, further comprising the identification for each of said identified resonance frequencies of a resonance mode of said at least one resonance quantity, the resonance mode being further characterized by an amplitude of the elementary intensity component at said resonance frequency considered, and a direction associated with the elementary movement for said resonance frequency considered.

9. Method according to the preceding claim, in which if one of said resonance frequencies identified for each of said at least two elementary movements is identical for several elementary movements, then the resonance mode is characterized by the combination of these elementary movements.

10. Method according to any one of the preceding claims, in which the object is a tank containing a liquid, and the determination of the dynamic behavior comprising a step of measuring the dynamic quantities with the tank empty, and deducing therefrom, by subtraction of the elementary components, only the effects of the liquid.

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