Mathematical and computer modeling of contactless ultrasonic sounding of layered anisotropic materials
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The correct interpretation of the results of contactless sounding requires the development of effective mathematical models that describe the processes of excitation and propagation of guided waves in a connected structure source-acoustic medium-submerged waveguide.Currently,for more accurate quantitative modeling of wave processes,as a rule,direct numerical methods based on a mesh approximation are used.However,this approach is numerically expensive and does not give a physically clear insight into the excitation of waves of various types.
The explicit integral representation of the solution of the considered connected boundary value problem can be obtained in terms of path integrals of the Fourier symbols of the Green's matrix of the immersed layered waveguide and the source parameters.The asymptotics of reflected and transmitted acoustic bulk waves and contactless excited guided elastic waves are derived from this representation using the stationary phase method and residue theory.These representations have physical clarity,and in addition to the dispersion characteristics and eigenmodes,they allow,with relatively low cost,to obtain quantitative amplitude-frequency characteristics for the excited waves.
In the course of previous studies carried out by the participation of the leader of the proposed project O.A.Ermolenko(until 2020 O.A.Miakisheva),in particular,the RSCF project No.17-11-01191 and thesis"Dynamic problems of the acoustic sounding of layered elastic materials"(2019),this approach has been implemented for the case of isotropic immersed layered waveguides.On this basis,studies of wave processes have been carried out,which allow us to determine the optimal regimes of excitation of the required modes and reveal some interesting wave effects.The proposed project aims to generalize this approach to the case of probed samples with an arbitrary anisotropy of elastic properties,which is the main factor determining the novelty of the expected results.
On this basis,it is planned to analyze various types of anisotropy(primarily characteristic of layered composite fiber-reinforced plastic plates with a certain scheme of laying prepreg layers)on the amplitude-frequency characteristics and directionality of traveling elastic waves,as well as reflected and transmitted acoustic bulk waves excited in connected system source-acoustic medium-immersed elastic waveguide.As a result,the work has already been developed and implemented in the form of computer programs for algorithms for calculating the elements of Green's matrix for a free multilayer anisotropic elastic waveguide,and experience has been gained in implementing integral and asymptotic representations obtained when solving problems similar to isotropic waveguides.
Expected results:The following results are expected:
-development and computer implementation of a mathematical model of the interaction of the wave field of a non-contact ultrasonic transducer with an elastic multilayer anisotropic waveguide immersed in an acoustic medium;
-analysis of the influence of the anisotropy of the elastic properties of the studied samples on the amplitude-frequency and energy characteristics of the traveling,flowing and bulk waves excited by a non-contact transducer;
-determination of the optimal parameters of excitation of various types of waves by a non-contact ultrasonic transducer;
-numerical construction of polar scan-images for the samples under study,which are obtained by varying the tilt of the non-contact source,analysis of the possibility of using them to identify the elastic material properties;
-experimental and numerical verification and evaluation of the limits of applicability of the developed model based on comparisons of calculated data with measurement results and finite element modeling.
The practical significance of the results is determined by the possibility of their use in the creation of systems for non-contact wave quality control of layered materials and diagnostic systems for ultrasonic non-destructive testing.
The correct interpretation of the results of contactless sounding requires the development of effective mathematical models that describe the processes of excitation and propagation of guided waves in a connected structure source-acoustic medium-submerged waveguide.Currently,for more accurate quantitative modeling of wave processes,as a rule,direct numerical methods based on a mesh approximation are used.However,this approach is numerically expensive and does not give a physically clear insight into the excitation of waves of various types.
The explicit integral representation of the solution of the considered connected boundary value problem can be obtained in terms of path integrals of the Fourier symbols of the Green's matrix of the immersed layered waveguide and the source parameters.The asymptotics of reflected and transmitted acoustic bulk waves and contactless excited guided elastic waves are derived from this representation using the stationary phase method and residue theory.These representations have physical clarity,and in addition to the dispersion characteristics and eigenmodes,they allow,with relatively low cost,to obtain quantitative amplitude-frequency characteristics for the excited waves.
In the course of previous studies carried out by the participation of the leader of the proposed project O.A.Ermolenko(until 2020 O.A.Miakisheva),in particular,the RSCF project No.17-11-01191 and thesis"Dynamic problems of the acoustic sounding of layered elastic materials"(2019),this approach has been implemented for the case of isotropic immersed layered waveguides.On this basis,studies of wave processes have been carried out,which allow us to determine the optimal regimes of excitation of the required modes and reveal some interesting wave effects.The proposed project aims to generalize this approach to the case of probed samples with an arbitrary anisotropy of elastic properties,which is the main factor determining the novelty of the expected results.
On this basis,it is planned to analyze various types of anisotropy(primarily characteristic of layered composite fiber-reinforced plastic plates with a certain scheme of laying prepreg layers)on the amplitude-frequency characteristics and directionality of traveling elastic waves,as well as reflected and transmitted acoustic bulk waves excited in connected system source-acoustic medium-immersed elastic waveguide.As a result,the work has already been developed and implemented in the form of computer programs for algorithms for calculating the elements of Green's matrix for a free multilayer anisotropic elastic waveguide,and experience has been gained in implementing integral and asymptotic representations obtained when solving problems similar to isotropic waveguides.
Expected results:The following results are expected:
-development and computer implementation of a mathematical model of the interaction of the wave field of a non-contact ultrasonic transducer with an elastic multilayer anisotropic waveguide immersed in an acoustic medium;
-analysis of the influence of the anisotropy of the elastic properties of the studied samples on the amplitude-frequency and energy characteristics of the traveling,flowing and bulk waves excited by a non-contact transducer;
-determination of the optimal parameters of excitation of various types of waves by a non-contact ultrasonic transducer;
-numerical construction of polar scan-images for the samples under study,which are obtained by varying the tilt of the non-contact source,analysis of the possibility of using them to identify the elastic material properties;
-experimental and numerical verification and evaluation of the limits of applicability of the developed model based on comparisons of calculated data with measurement results and finite element modeling.
The practical significance of the results is determined by the possibility of their use in the creation of systems for non-contact wave quality control of layered materials and diagnostic systems for ultrasonic non-destructive testing.