Method for adapting numerical simulations of vibrations on a mechanical structure using measured data

Abstract

The invention describes a method for verifying the vibration simulation of a mechanical structure and optimizing the elasticity and damping parameters used in the model using a vibration mode measured non-contact on the surface of an existing prototype of this mechanical structure. The agreement between the simulated and measured vibration modes is evaluated using an elasticity and damping metric, and optimized elasticity and damping parameters are determined in an iterative simulation process. The metrics capture independent properties of the vibration mode: The elasticity metric utilizes the local wavenumber on the surface of the structure, while the damping metric evaluates the decay of the envelope of the traveling waves moving away from and returning from the excitation point.The method is particularly advantageous for the adaptation of the complex Young's modulus in the numerical simulation of mechanical structures consisting of different material components and radiating sound over a wide frequency range (e.g., loudspeakers). The following figure represents the invention.

Description

FIELD OF THE INVENTION

[0001] The invention discloses a method for adapting and optimizing a vibration simulation (e.g., FEM) using a measuring device (e.g., a laser vibration scanner) that determines the vibration behavior of a structure on an accessible measuring surface without contact. The goal is to modify the free model parameters, which describe the geometry and material properties of the structure on the measuring surface, in such a way that the deviation between the simulated and measured vibration shape is minimized. This invention is particularly important for the design of loudspeakers and other structures that emit airborne sound over a wide frequency range and consist of multiple materials, the properties of which cannot currently be determined with the required accuracy using known methods. STATE OF THE ART

[0002] Numerical simulation methods have proven effective for the design of mechanical structures, particularly for the evaluation of vibration behavior and sound radiation. These methods are based on an abstract physical model whose free parameters P must be adapted to the specific mechanical structure. The analytical model with finite elements (FEM) fulfills the differential equation Kx(t)+Dx˙(t)+Mx¨(t)=f(t) where the state vectors x(t) and f(t) represent the local deflection and the external excitation forces acting on the structure, respectively. The free parameters P in this model are the three FEM matrices K, D, M, which generally describe the stiffness, damping, and mass of all elements in the FEM. These analytical parameters K, D, M are directly related to physical parameters that more precisely model the geometry of the structure and the properties of the materials.

[0003] One advantage of numerical simulation is the rapid evaluation of the fundamental functionality of new ideas based on geometric assumptions and estimated material parameters. Only after the first prototype has been built can the vibration behavior be measured using non-destructive and non-contact vibration measurement technology to verify the simulation.

[0004] US 2023 / 0304969 A1 (publication) describes a method for three-dimensional scanning of a vibration on a plate or dish using a laser vibration scanner that uses a demodulation technique.

[0005] Deviations between simulation and measurement can be reduced by adjusting the free parameters of the FEM. Various methods have been developed for adjusting these parameters, known as Finite Element Model Updating (FEMU), which optimize the analytical FEM matrices K, D, and M. A comparative study by V. Arora, "Comparative study of finite element model updating methods," Journal of Vibration Control 17(13), pages 2013-2039, describes the advantages and disadvantages of various methods.

[0006] Many FEMU methods use a modal analysis of the measured and simulated vibration data, subsequent assignment (pairing) of the calculated modes with a MAC measure (Modal Assurance Criterion) and a robust optimization procedure for the analytical FEM matrices K, D and MJ Matalevich describes in "Vibration and Modal Analysis Basics" URL: https: / / indico.jlab.org / event / 98 / contributions / 7450 / attachments / 6319 / 8367 / 6T_-_Vibration_and_Modal_Analysis_Basics.pdf the measurement of the transfer functions and the basics of modal analysis.

[0007] However, a laser vibration scanner according to the current state of the art can only measure the vibration behavior of the structure on an optically accessible measuring surface A Mwhich is usually only a part of the entire structural surface A. As a result, the experimentally determined modes do not always correspond to the analytical modes and cause errors in the pairing required for the optimization of the free parameters. Furthermore, modes with similar eigenfrequencies or low Q values ​​are sometimes impossible or only incorrectly separated.

[0008] R. Lin and D. Ewins, in “Analytical Model Improvement using Frequency Response Function,” Mechanical Systems and Signal Processing (1994) 8(4), 437-458, developed an alternative FEMU method (FRF) that dispenses with modal analysis and optimizes the FEM matrices directly using transfer functions that describe the relationship between an excitation force F and the displacement x at points r within the measurement area A Mdescribe. The deflection of all accessible elements of the structure is measured using a constant, stationary force input, whereby measurement data at individual measurement points inaccessible to the sensor can be replaced by modeled data. However, a significant error in the optimization arises if these approximated measurement data extend over a wide area of ​​the structure. One advantage of the FRF method is that it only requires measurement data at relatively few excitation frequencies, which are evenly distributed across the relevant frequency range. Like other perturbation methods, the FRF method requires that the relative deviations between the parameters P(i) used in the simulation and the optimal parameters P*, which explain the measured values, are relatively small. Problems with the conditioning and solution of the system of equations also arise for materials with high damping and for measurement data disturbed by noise.

[0009] The FRF and other well-known optimization methods can also be applied to individual physical parameters (e.g., Young's modulus), whereby the number of unknowns is reduced and thus the conditioning of the system of equations and the robustness of the method are improved, see RM Lin and J. Zhu in "Model updating of damped structures using FRF data", Mechanical systems and signal processing, Vol. 20, 2006, No. 8, pp. 2200-2218, ISSN 0888-3270.

[0010] Other physical parameters can also be assumed to be known or determined using other measurement methods. 3D laser scanners, with current technology, can already determine the geometric shape of the structure with a level of accuracy sufficient for many FEM applications. However, this may require disassembling and destroying the structure into individual components. Using a precision balance, the mass of the components can be measured and the density of the material calculated.

[0011] The dynamic determination of the complex Young's modulus according to ASTM Standard E 756-93 typically requires flat specimens clamped as beams and mechanically or acoustically excited to flexural vibrations. Unfortunately, this method is complex, error-prone, and only provides reliable measurement data for low frequencies. These values ​​can only be extrapolated to higher frequencies with considerable error for paper, fabric, rubber, polymers, and composite materials.

[0012] CN 1 11 751 200 B describes a method for the dynamic measurement of the Young's modulus of a material taking into account the average pressure and temperature of the sample.

[0013] Since the materials used in loudspeakers are used to radiate sound across the entire audible frequency range, W. Cardenas and W. Klippel developed a FEMU method in "Optimal Material Parameter Estimation by Fitting Finite Element Simulations to Loudspeaker Measurements," 144th Meeting of the Audio Eng. Society (May 2018), Number: 9928, https: / / www.aes.org / e-lib / browse.cfm?elib=19445, that directly determines the complex Young's modulus for loudspeaker development. This also requires a prototype of the loudspeaker in which the electrically driven voice coil generates the force. A laser sensor scans the mechanical vibration in the area of ​​the diaphragm and surround over a wide frequency range. This method extracts modes in the simulated and measured vibration data, pairs these modes, and minimizes the deviations in the complex eigenvalues ​​and MAC measures.However, the iterative optimization process can result in subminima of the error measure and this method fails for materials with high losses, which are used in loudspeaker construction. SUMMARY OF THE INVENTION

[0014] The aim of the invention is to develop a method that verifies a numerical simulation of the vibration behavior of an existing mechanical structure using a non-contact and non-destructive measuring device and determines the free elasticity parameters P E and damping parameter P D of the physical model used. These free elasticity parameters P E (r,f) and damping parameter P D (r,f) are for example the real part E R (r,f) or the imaginary part E I (r,j) of the complex elastic modulus E_(r,f)=ER(r,f)+jEI(r,f) of the materials used in the structure at point r and at the excitation frequency f. These free parameters cannot be determined using other known measurement methods at high frequencies and high damping levels, or can only be determined with large errors. The method can also be used to optimize the thickness and other geometric parameters of the structure that influence its elasticity. The influence of resonating air particles on the overall damping of the structure can also be verified using this method.

[0015] The measuring device determines a complex vibration shape x m (r,f) using a sensor that measures the deflection, velocity or other mechanical state variable on a measuring surface A M which in many cases is only a part of the surface of the structure. The measured vibration shape x m (r,f) is a complex function of the measuring point r and the excitation frequency f.

[0016] The simulation calculates the complex vibration shape x m (r,f) on the measuring surface A M using classical FEM methods or other numerical models that, for example, describe wave propagation, damping, and acoustic load in more detail. The mechanical vibration is excited by external forces or moments that are applied at the same excitation point r during measurement and simulation. e and fed with constant strength.

[0017] The verification of the numerical simulation and the adjustment of the free elasticity parameters P E (r,f,i) and damping parameter P D(r,f,i) is carried out in an iterative process, whereby elasticity values ​​E(r,f, i) and damping values ​​D(r,f, i) are calculated from the measured and simulated vibration shapes, the discrepancy between the measured and simulated values ​​is evaluated with error measures and correction factors are derived from this for the calculation of optimized elasticity parameters P E (r,f,i+1) and damping parameter P D (r,f,i+1) can be generated.

[0018] According to the invention, the elasticity and damping values ​​are calculated using metrics that capture essential and, above all, independent characteristics of the complex vibration mode in wave space. The real part of the complex wavenumber (indirectly proportional to the wavelength) is used as a characteristic of elasticity, and the imaginary part as a characteristic of energy loss (dissipation) in the mechanical structure. The imaginary part of the wavenumber describes the exponential decay of the envelope of the traveling waves over space. These metrics are largely independent of the amplitude of the vibration mode. In this respect, the invention differs from experimental modal analysis, which decomposes the overall vibration into modes with complex eigenfrequencies and orthogonal eigenvectors, and the resonance peaks in the amplitude frequency response are used to identify the modal eigenfrequencies and loss factors.In the present invention, the amplitude frequency response is not used as a metric, since both elasticity and damping determine the amplitude. However, the amplitude of the waveform can be used for other purposes, such as evaluating the signal-to-noise ratio and suppressing noisy measurement data in the calculated metrics.

[0019] It is a further feature of the invention that the complex waveform x(r,f) on the measuring surface A M is decomposed into a standing vibration form and a residual, propagating vibration form.

[0020] The standing oscillation form x sw In the steady state, (r,f) consists of two wave components propagating in opposite directions with equal amplitude. They generate a position-independent phase in the complex oscillation form and effectively transport no energy across the spatial coordinate r.

[0021] The residual, propagating oscillation form x pw (r,f) describes the remaining part of the complex oscillation form, whose phase varies over space and contains traveling waves with decreasing amplitude. These traveling waves transport energy from the excitation point r e (source), where, for example, the voice coil in the loudspeaker introduces a force into the structure, to the damping resistors distributed on the structure (sink), where the mechanical energy is converted into heat. This circumstance is used in the invention for the formulation of the local damping metric, which determines the amplitude drop over r using the local gradient of the envelopes of the traveling waves. It is expedient to use the envelopes of the excitation point r eto calculate the traveling waves departing from and returning to the same location r and to use their difference to calculate the attenuation values. This allows the influences of the structural geometry, reflection at material boundaries and the near field around the excitation point r to be taken into account. e on the envelopes of the traveling waves.

[0022] The elasticity metric is formed using the local real wavenumber, which is calculated from the local gradient of the imaginary phase of a complex-analytic waveform. Analogous to the complex-analytic signal in signal theory, the complex-analytic waveform is a complex-valued function of position, whose imaginary part is the Hilbert transform of the real part. The complex-analytic waveform contains only partial waves that propagate in the same direction. It is advisable to select the propagation direction where the total power of all partial waves is greater and the signal-to-noise ratio is improved.

[0023] Thus, the two metrics for elasticity and damping utilize orthogonal information, establishing a monotonic relationship to the elasticity or damping parameter at location r and frequency f. While monotonicity is an essential requirement for avoiding subminima in iterative optimization, a nearly linear relationship is useful for minimizing the number of required simulations. Through further nonlinear transformations, particularly the elasticity metric, the relationship between metrics and the Young's modulus can be linearized, thus accelerating the convergence of the iterative procedure to the error minimum.

[0024] The signal-to-noise ratio can be improved by averaging the sensor signals during the measurement, as well as by averaging the local metrics over the spatial extent of the structural components in the measurement area. The influence of noise can also be reduced by additionally averaging the correction factors in selected frequency bands. BRIEF DESCRIPTION OF THE DRAWINGS Fig. shows a generalized block diagram for the optimal adaptation of the complex Young's modulus in a numerical simulation of the vibration behavior according to the invention. Fig. shows a generalized block diagram for the generation of elasticity values ​​using an elasticity metric according to the invention. Fig. shows a generalized block diagram for generating attenuation values ​​using an attenuation metric according to the present invention. Fig. shows the real and imaginary parts as well as the envelope of a simulated waveform of a loudspeaker. Fig. shows the real and imaginary parts as well as the envelope of the stationary part of the simulated vibration form of a loudspeaker. Fig. shows examples of the real and imaginary parts, as well as the envelope of the traveling waves of a loudspeaker propagating in the positive r-direction. Fig. shows examples of the envelopes of the traveling waves of a loudspeaker propagating in positive and negative directions. DETAILED DESCRIPTION OF THE INVENTION

[0025] Fig. shows the most important steps of the method for the optimal adaptation of the complex Young's modulus E(r,f) or other free model parameters in the numerical simulation of the vibration behavior of a mechanical structure according to the invention. The first step after starting (1) the method is the provision of a real prototype of the mechanical structure (3), whose surface vibrations on the measuring surface A M In the second step (5), the mechanical structure is measured using external forces or moments under defined conditions (e.g. frequency f, amplitude and position r e ) is excited, and the deflection x, velocity v or another physical state variable is sampled with sufficient spatial resolution, taking into account the wavelengths involved and the Nyqvist criterion. From the measured values, the oscillation form x m(r,f) which is calculated as a complex transfer function between a constant excitation force F(r e ) and the measured state variable x m (r,f) at the measurement point r. This mode is usually complex, and the imaginary part is a characteristic of the damping in the structure.

[0026] In a further step (7), the measured waveform x m (r,f) local measured values ​​are calculated using metrics, where elasticity values ​​E m (r,f) the elasticity and the damping values ​​D m (r,f) describe the losses at location r on the structure. According to the inventive concept, the elasticity metric and damping metric describe different properties of the measured vibration mode, which are used as independent characteristics of elasticity and damping, respectively, in the adaptation of the free model parameters.

[0027] In the following step (9), the iterative adaptation process is initialized (i = 0) and the starting parameters P E (i = 0) and P D (i = 0) of the modeling. The starting parameters contain information (e.g., geometry, density) that can be measured with high accuracy on the prototype and estimates for other material properties (e.g., the complex Young's modulus) that are neither known nor easily measurable.

[0028] These starting parameters are used in the following process step (11) for the calculation of the simulated vibration shape x s (r,f,i) using a numerical model (FEA).

[0029] In the next step (13), the simulated waveform x s (r,f,i) simulated elasticity values ​​E s (r,f) and damping values ​​D s (r,fi) is calculated using the metrics used for the measured elasticity values ​​E m (r,f) or damping values ​​D m(r,f,i) can be used in step (7).

[0030] In the following step (15), local error measures ε s (r,f,i) are formed, which evaluate the discrepancy between the simulated and measured vibration form in decibels, for example as the relative ratio of the elasticity values εE(r,f,i)=20 log(Es(r,f,i)Em(r,f)) and the damping values εD(r,f,i)=20 log(Es(r,f,i)Em(r,f)).

[0031] These error measures are used to evaluate the iteration process in step (17). For example, the mean square error (MSE) ε¯(f,i)=12Nt∑∀r(εE(r,f,i))2+(εD(r,f,i))2 calculated and evaluated using a termination criterion. Once the MSE value has sufficiently approached the minimum, it is appropriate to terminate the iterative process (19).

[0032] However, if the reduction of the MSE value in the last iteration step was significant, a further iteration is performed with incremented index i := i + 1 (21).

[0033] In the following step (23), correction factors for the previously used elasticity parameters P E (i - 1) and free damping parameter P D (i - 1) determined from the local error measures CE(r,f,i)=10−εE(r,f,i−1) / 20 CD(r,f,i)=10−εD(r,f,i−1) / 20 and in the following step (25) to generate optimized parameters P E (i) or P D (i) used: PE(r,f,i)=CE(r,f,i)PE(r,f,i−1) PD(r,f,i)=CE(r,f,i)PD(r,f,i−1)

[0034] For example, optimized values ​​for the real and imaginary part of the Young’s modulus E can be calculated ER(r,f)=CE(r,f,i)ER(r,f,i−1) EI(r,f,i)=CD(r,f,i)EI(r,f,i−1) and used in a further iteration starting with the numerical simulation (11).

[0035] Fig. shows a generalized block diagram of the joint elasticity metric, which calculates the elasticity values ​​E m (r,f) and E s (r,j) is generated from the measured or simulated vibration form x(r,f) (27).

[0036] In the first step (29), the respective measured or simulated oscillation form x(r,f) is converted into a wave spectrum X(k,f) as a function of the wave number k using a discrete Fourier transformation (DFT): X_(k,f)=DFT{x_(r,f)}

[0037] In the next step (31) the wave spectrum X(k,f) is decomposed into two partial spectra with positive and negative wavenumbers X_(k,f)=X_+(k,f)+X_−(k,f) where X_+(k,f)=X_(k,f)(1+sign(k)) / 2 X_−(k,f)=X_(k,f)(1−sign(k)) / 2

[0038] In the next step (33) the sub-spectrum with the higher total power is selected X_t(k,f)={X_+(k,f) fu¨r ∫∀kX_+(k,f)2dk>∫∀kX_−(k,f)2dkX_−(k,f) fu¨r ∫∀kX_+(k,f)2dk≤∫∀kX_−(k,f)2dk and the complex-analytical vibration form x t (r,f) calculated using the inverse DFT: x_t(r,f)=DFT−1{X_t(k,f)}

[0039] Then the local real wavenumber k t (r, f) in step (35) by local differentiation of the phase of the complex waveform: kt(r,f)=|d arg(x_t(r,f))dr|

[0040] In the last step (37) the local real wave number k t (r,f) under the assumption that bending vibrations dominate the vibration shape, into an elasticity metric which is proportional to the real part E near an operating point R of the E-modulus is: E(r,f)=kt(r,f)−4∝ER(r,f)

[0041] Fig. shows a generalized block diagram of the damping metric used to generate the damping values ​​D m (r,f) and D s (r,f) from the measured or simulated vibration shape (39) is used.

[0042] The respective measured or simulated oscillation form x(r,f) is converted in the first step (41) into a standing oscillation form x sw (r,f) and a residual propagating mode x pw (r,f) decomposed: x_(r,f)=x_sw(r,f)+x_pw(r,f)

[0043] For this purpose, for example, the correlation technique developed by BF Feeny, “A Complex Orthogonal Decomposition for Wave Motion Analysis”, J. of Sound and Vibration 310 (1-2) 77-90 (2008) can be used.

[0044] In the next step (43) the residual propagating oscillation form x pw (r,f) is transformed into a wave spectrum: X_pw(k,f)=DFT{x_pw(r,f)}

[0045] Then, in step (45), the propagating wave spectrum X pw (k,f) decomposed into two partial spectra X_pw(k,f)=X_pw+(k,f)+X_pw−(k,f), where the spectrum X_pw+(k,f)=X_pw(k,f)(1+sign(k)) / 2 the propagation of residual traveling waves in positive r-direction and the spectrum X_pw−(k,f)=X_pw(k,f)(1−sign(k)) / 2 which describes the spread in a negative direction.

[0046] In the subsequent step (47), the two partial spectra are transformed into complex-analytical vibration forms using an inverse DFT x_pw+(r,f)=DFT−1{X_pw+(k,f)} x_pw−(r,f)=DFT−1{X_pw−(k,f)} and the envelopes of these traveling waves in positive and negative r-direction are calculated by forming the absolute values: hpw+(r,f)=|x_pw+(r,f)| hpw−(r,f)=|x_pw−(r,f)|

[0047] Taking into account the position of the excitation point r e, where a force is fed into the mechanical structure and the source of the traveling waves is located, in the next step (49) the gradient of the envelope of the waves traveling away from the source Ge(r,f)={dhpw+(r,f)drr>redhpw−(r,f)drr≤re and the gradient of the envelope of the waves returning to the source can be determined: Gr(r,f)={dhpw−(r,f)drr>redhpw+(r,f)drr≤re

[0048] In the last step (51), the difference between the two gradients is converted into a damping metric which, near an operating point, is proportional to the imaginary part E I of the E-modulus is: D(r,f)=Gr(r,f)−Ge(r,f)∝EI(r,f)

[0049] In order to improve the signal-to-noise ratio of the measured values ​​and the robustness of the iterative process, it is useful to estimate the local and frequency-dependent elasticity errors ε E (r,f,i) and damping error ε D(r,f,i) in a local area r(m c ) with homogeneous material properties on the measuring surface A M and in a frequency band f ∈ f b (e.g. an octave) to average: ε¯E(r(mc),fb,i)=1Nt(mc)Nb(fb)∑j=1Nt(mc)∑m=1Nb(fb)EE(rj,fm,i) ε¯D(r(mc),fb,i)=1Nt(mc)Nb(fb)∑j=1Nt(mc)∑m=1Nb(fb)ED(rj,fm,i)

[0050] With these mean values, the corresponding correction factors C E (r(m c ), f b , i) or C D (r(m c ),f b ,i) and used to adjust the elasticity and damping parameters. For a loudspeaker, for example, the spatial averaging is carried out separately in three areas m c = 1, 2, 3, namely the rubber surround, the paper membrane and the dust cap.

[0051] Fig. shows an example of the simulated vibration shape x(r,f) on the sound-radiating components of an axially symmetric loudspeaker in the radial direction r. The center (53) of the dust dome is located at radius r = 0 mm. The voice coil (55) generates at the transition point between the dust dome and the paper membrane at location r e = 28 mm. At a radius of r = 75 mm (57), the paper cone is glued to a rubber surround, which is clamped to the chassis (59) at r = 95 mm. The real part (61) and the imaginary part (63) determine the envelope (65) of the vibration shape.

[0052] Fig. shows the standing wave component x sw (r,f) of the simulated waveform x(r,f) of the loudspeaker of Fig. The real part (67), the imaginary part (69), and the envelope (71) share a maximum (antibody, 73) at radius r = 38 mm and a minimum (node, 75) at radius r = 45 mm. Thus, the standing wave effectively transports no power in the steady state.

[0053] Fig. shows the wave component propagating in the positive direction x pw +(r,f) of the simulated waveform x(r,f) of the loudspeaker in Fig. The real part (77), the imaginary part (78), and the envelope (79) have their maxima at different points. Thus, these propagating waves transport power in the positive radial direction.

[0054] Fig. shows the envelopes h e (r) and h r(r) of the waves (83, 81) traveling away from the voice coil and the waves (85, 87) returning therefrom. The difference between these two envelopes describes the power loss of the propagating waves caused by material damping and is used to calculate the damping metric in the invention. ADVANTAGES OF THE INVENTION

[0055] The new method for optimizing the free elasticity and damping parameters of a numerical vibration simulation does not require detailed information about the physical model used. In particular, no restrictive assumptions are made regarding the type of damping (e.g., viscous, proportional, linear, homogeneous, isotropic) and its physical causes (e.g., material, interfaces, hysteresis, air motion). Thus, the method can be applied both to adapting the complex Young's modulus for various material components and to the elasticity and damping parameters of other models of any complexity and accuracy (e.g., number and distribution of nodes in the mesh).

[0056] The required input information is limited to vibration data as a function of one or two spatial coordinates and the frequency, and the position of the component boundaries and the excitation point r eConfidential information of a new product development, such as complete 3D geometry data and material properties, is not required for parameter optimization.

[0057] The invention can be applied to mechanical structures that only offer access to a limited measuring area for non-contact and non-destructive vibration measurements.

[0058] Numerical simulation of vibration data can be performed quickly using commercially available FEA products, as only a very coarse frequency resolution of the vibration data (e.g., one-third octave spacing) is required in the relevant frequency range. Such a resolution is generally insufficient for modal analysis.

[0059] The invention determines the elasticity and damping parameters as a function of frequency and can be used for materials where these parameters are not constants. For mechanical structures consisting solely of a homogeneous material with frequency-independent elasticity and damping, optimization of the free material parameters is possible using a few measurement points and at a single excitation frequency.

[0060] In contrast to the prior art, no restrictive assumptions are made regarding the number and properties of the material components in the structure. This allows for unknown influences from shaping, the use of adhesive bonds, and other manufacturing techniques to be taken into account. The invention can also be applied to materials with extreme properties, such as textiles impregnated with a viscous impregnation to achieve very high damping in the vibrating structure. These materials are used, for example, in loudspeakers to achieve a smooth frequency response and high sound quality.

[0061] Furthermore, the invention can also be used to optimize the geometry of the mechanical structure, the density and other properties of the materials used.

Claims

[1] Method for the verification of vibration simulations of a mechanical structure and optimization of used free elasticity parameters P E (r,f) and damping parameters P D (r,f) in an iterative process; the procedure consists of the following steps: I. Provision (3) of a real prototype of the mechanical structure and measurement (5) of a complex vibration mode x m (r,f) as a function of a location r and an excitation frequency f using a non-contact measuring device that measures a physical state variable within a measuring area A M recorded on a surface A of the prototype; II. Generation (7) of measured elasticity values ​​E m (r,f) based on the measured vibration shape x m (r,f) with an elasticity metric that provides a monotonic relationship between the elasticity values ​​E m(r,f) and local elasticity of the structure at location r on the measuring surface A M and at frequency f; III. Generation (7) of measured damping values ​​D m (r,f) based on the measured vibration shape x m (r,f) with a damping metric that provides a monotonic relationship between the damping values ​​D m (r,f) and local damping of the structure at location r on the measuring surface A M and at frequency f, where the elasticity metric and the damping metric are independent features of the complex vibration shape x m capture (r,f); IV. Initialization (9) of the iterative optimization process and initial determination of the elasticity parameters P E (r,f,i = 0) and damping parameter P D (r,f,i = 0) using existing knowledge about the geometry and material properties of the mechanical structure; V. Numerical simulation (11) of the physical state variable and determination of a simulated vibration form x s (r,f,i) on the measuring surface A M using the elasticity parameters P E (r,f,i) and the damping parameter P D (r f , i) in an iteration i; VI. Generation (13) of simulated elasticity values ​​E s (r,f,i) based on the simulated vibration shape x s (r,f,i) with the elasticity metric in step II; VII. Generation (15) of local elasticity errors ε E (r,f,i), which represents the discrepancy between the measured elasticity values ​​E m (r,f) and the simulated elasticity values ​​E s describe (r,f,i); VIII. Generation (13) of simulated damping values ​​D s (r,f,i) based on the simulated state variable x s (r,f,i) with the attenuation metric in step III; IX. Generation (15) of local damping errors εD (r,f,i), which represents the discrepancy between the measured damping values ​​D m (r,f,i) and simulated damping values ​​D s describe (r,f,i); X. Completion (19) of the iterative process when the local elasticity errors ε E (r,f,i) and damping error ε D (r,f,i) satisfy predefined conditions; otherwise, the calculation (25) of optimized elasticity parameters P E (r,f,i+1) and optimized damping parameters P D (r,f,i+1) based on the elasticity errors ε E (r,f,i) or damping error ε D (r,f,i) in a further iteration i := i+1, which starts with the numerical simulation (11) in step V. [2] The method according to claim 1, wherein the elasticity metric a local wavenumber k t (r,f) at least one point on the measuring surface A M or a quantity derived therefrom; and the attenuation metric the local losses due to the local change of an envelope h(r,f) of at least one residual traveling wave at at least one point on the measuring surface A M describes. [3] The method according to claim 1, wherein the elasticity parameters P E (r,f,i) and damping parameter P D (r,f,i) a real part or an imaginary part of a complex elastic modulus E(r,f,i) at the location r within the measuring area A M at the excitation frequency f and the iteration i; and a correction factor C E (r,f,i) from the elasticity error ε E (r,f,i) and applied to the elasticity parameters P E (r,f,i) is applied; a correction factor C D (r,f,i) from the damping error ε D (r,f,i) and applied to the damping parameters P D (r,f,i) is applied. [4] The method of claim 2, wherein the elasticity metric comprises the measured and simulated elasticity values ​​E m (r,f) or E s (r,f,i) is determined from the measured or simulated vibration form (27) according to the following steps: I. Fourier transformation (29) of the respective oscillation form x(r,f) as a function of the location r into a wave spectrum X(k,f) as a function of a wave number k using exponential basis functions; II. Calculation (33) of a complex-analytical vibration form x t (r,f) as a function of the location r from the wave spectrum X(k,f); III. Calculation (35) of a local wavenumber k t (r,f) as a local gradient of a phase of the complex-analytic oscillation form x t (r,f); IV. Transformation (37) of the local wavenumber k t (r,f) into the corresponding elasticity value E(r,f). [5] Method according to claim 4, wherein the complex analytical waveform x t (r,f) is calculated according to the following steps: I. Decomposition (31) of the wave spectrum X(k,f) into sub-spectra X+(k,f) and X(k,f), where the sub-spectra describe the wave propagation in opposite directions. II. Calculation (33) of a complex-analytical vibration form x t (r,f) as a function of the location r by applying an inverse Fourier transform to the subspectrum with the higher total power. [6] The method of claim 2, wherein the attenuation metric comprises the measured attenuation value D m (r,f) or the simulated damping value D s (r,f,i) is generated from the measured or simulated waveform (39) according to the following steps: I. Decomposition (41) of the respective oscillation form x(r,f) into a standing oscillation form x sw(r,f) with a position-independent phase and into a propagating oscillation form x pw (r,f) with a spatially variable phase, where the propagating oscillation form x pw (r,f) describes the residual traveling waves on the structure; II. Fourier transformation (43) of the propagating oscillation form x pw (r,f) into a propagating wave spectrum X pw (k,f); III. Calculation (51) of the corresponding attenuation value D(r,f) from the propagating wave spectrum X pw (k,f). [7] Method according to claim 6, wherein the calculation of the respective attenuation value D(r,f) from the propagating wave spectrum X pw (k,f) is carried out with the following steps: I. Provision of a stimulus point r e , where the excitation point r e describes the location (55) at which power is supplied to the structure from an external source; II. Decomposition (45) of the propagating wave spectrum X pw (k,f) into two partial spectra X pw+ (k,f) and X pw -(k,f) and inverse Fourier transformation of these partial spectra into complex-analytic oscillation forms x pw+ (r,f) or x pw -(r,f), which describe the propagation of the traveling waves in positive and negative directions respectively; III. Calculation (47) of an envelope h e (r,f) of the residual traveling wave, which moves from the excitation point r e removed from the complex-analytical vibration forms x pw +(r,f) and x pw -(r,f); IV. Calculation (47) of an envelope h r (r,f) of the residual traveling wave traveling to the excitation point r e returns from the complex-analytical oscillation forms x pw +(r,f) and x pw -(r,f); V. Calculation (49) of a local gradient G e (r,f) of the envelope h e (r,f) of the excitation point r etraveling wave and a local gradient G r (r,f) of the envelope h r (r,f) of the returning traveling wave; VI. Calculation (51) of the local damping values ​​D(r,f) as the difference between the local gradients G e (r,f) and G r (r,j) of the departing or returning traveling wave at the same location r. [8] Method according to claim 3, wherein a correction of the elasticity parameters P E (r,f,i) and the damping parameter P D (r,f,i) of the numerical simulation is carried out with the following steps: I. Averaging of local elasticity errors ε E (r,f,i) in a local area r(m c ) with homogeneous material properties on the measuring surface A M and use of the mean value to calculate a correction factor C E (r,f,i), which is based on the elasticity parameters P E (r,f,i) is applied in this area; II. Averaging of the attenuation error ε D (r,f,i) in a local area r(m c ) with homogeneous material properties on the measuring surface A M and use of the mean value to calculate a correction factor C D (r,f,i), which is based on the damping parameter P D (r,f,i) is applied in this area; III. Averaging of the local elasticity error ε E (r,f,i) in a frequency band f b , in which a frequency dependence of the material on the measuring surface A M can be neglected, and use of the mean value for the calculation of the correction factor C E (r,f,i), which is based on the elasticity parameter P E (r,f,i) is applied in this frequency band; IV. Averaging of the attenuation error ε D (r,f,i) in a frequency band f b , in which the frequency dependence of the material on the measuring surface A Mcan be neglected, and use of the mean value for the calculation of the correction factor C D (r,f,i), which is based on the damping parameter P D (r,f,i) is applied in this frequency band.

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