Normal mode extraction has attracted extensive attention over the past few decades due to its practical value in enhancing the performance of underwater acoustic signal processing.Singular value decomposition(SVD)is a...Normal mode extraction has attracted extensive attention over the past few decades due to its practical value in enhancing the performance of underwater acoustic signal processing.Singular value decomposition(SVD)is an effective method to extract modal depth functions using vertical line arrays(VLA),particularly in scenarios when no prior environment information is available.However,the SVD method requires rigorous orthogonality conditions,and its performance severely degenerates in the presence of mode degeneracy.Consequently,the SVD approach is often not feasible in practical scenarios.This paper proposes a full rank decomposition(FRD)method to address these issues.Compared to the SVD method,the FRD method has three distinct advantages:1)the conditions that the FRD method requires are much easier to be fulfilled in practical scenarios;2)both modal depth functions and wavenumbers can be simultaneously extracted via the FRD method;3)the FRD method is not affected by the phenomenon of mode degeneracy.Numerical simulations are conducted in two types of waveguides to verify the FRD method.The impacts of environment configurations and noise levels on the precision of the extracted modal depth functions and wavenumbers are also investigated through simulation.展开更多
In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on t...In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear stress.Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue.Then,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems.Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved together.The obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures.In addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies.Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.展开更多
Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, un...Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12304504,12304506 and U22 A2012)the Youth Innovation Promotion Association,Chinese Academy of Sciences(No.2021023)+1 种基金the Strategy Priority Research Program(Category B)of Chinese Academy of Sciences(Nos.XDB0700100 and XDB0700000)the Natural Science Foundation of Tianjin(No.22JCYBJC00070).
文摘Normal mode extraction has attracted extensive attention over the past few decades due to its practical value in enhancing the performance of underwater acoustic signal processing.Singular value decomposition(SVD)is an effective method to extract modal depth functions using vertical line arrays(VLA),particularly in scenarios when no prior environment information is available.However,the SVD method requires rigorous orthogonality conditions,and its performance severely degenerates in the presence of mode degeneracy.Consequently,the SVD approach is often not feasible in practical scenarios.This paper proposes a full rank decomposition(FRD)method to address these issues.Compared to the SVD method,the FRD method has three distinct advantages:1)the conditions that the FRD method requires are much easier to be fulfilled in practical scenarios;2)both modal depth functions and wavenumbers can be simultaneously extracted via the FRD method;3)the FRD method is not affected by the phenomenon of mode degeneracy.Numerical simulations are conducted in two types of waveguides to verify the FRD method.The impacts of environment configurations and noise levels on the precision of the extracted modal depth functions and wavenumbers are also investigated through simulation.
基金supported by the National key Research and Development Plan of Ministry of Science and Technology of the People’s Republic of China(2017YFC0404903).
文摘In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear stress.Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue.Then,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems.Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved together.The obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures.In addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies.Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.
基金supported by the National Natural Science Foundation of China (Grants 11402126, 11502122, and 11290152)the Scientific Research Foundation of the Inner Mongolia University of Technology (Grant ZD201410)
文摘Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.
