Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)la...Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.展开更多
The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of ...The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.展开更多
External-cavity birefringence feedback effects of the microchip Nd：YAG laser are presented. When a birefringence element is placed in the external feedback cavity of the laser, two orthogonally polarized laser beams ...External-cavity birefringence feedback effects of the microchip Nd：YAG laser are presented. When a birefringence element is placed in the external feedback cavity of the laser, two orthogonally polarized laser beams with a phase difference are output. The phase difference is twice as large as the phase retardation in the external cavity along the two orthogonal directions. The variable extra-cavity birefringence, caused by rotation of the external-cavity birefringenee element, results in tunable phase difference between the two orthogonally polarized beams. This means that the roll angle information has been translated to phase difference of two output laser beams. A theoretical analysis based on the Fabry-Perot cavity equivalent model and refractive index ellipsoid is presented, which is in good agreement with the experimental results. This phenomenon has potential applications for roll angle measurement.展开更多
In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥...In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rtz.展开更多
The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is ...The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is used to reduce the governing partial differential equations （PDEs） to a set of non-linear coupled ordinary differential equations （ODEs） in the dimensionless form. The analytical solutions are obtained by employing the homotopy analysis method （HAM）. The effects of various physical param- eters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail.展开更多
Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
We presented a novel orthogonally linearly polarized Nd：YVO4 laser. Two pieces of a-cut grown-together composite YVO4/Nd：YVO4 crystals were placed in the resonant cavity with the c-axis of the two crystals orthogona...We presented a novel orthogonally linearly polarized Nd：YVO4 laser. Two pieces of a-cut grown-together composite YVO4/Nd：YVO4 crystals were placed in the resonant cavity with the c-axis of the two crystals orthogonally. The polarization and power performance of the orthogonally polarized laser were investigated. A 26.2-W orthogonally linearly polarized laser was obtained. The power ratio between the two orthogonally polarized lasers was varied with the pump power caused by the polarized mode coupling. The longitudinal modes competition and the corresponding variable optical beats were also observed from the orthogonally polarized laser. We also adjusted the crystals with their c-axis parallele to each other, and a 40.7-W linearly polarized TEM00 laser was obtained, and the beam quality factors were Mx^2 = 1.37 and My^2 = 1.25.展开更多
A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also...A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also considered in the research. The first order shear deformation theory is used to account for the transverse shear deformation. The motion of the equally spaced stiffeners is examined by considering their bending vibrations and torsional movements. Based on the periodic structure theory and the concepts of the equivalent dynamic flexibility of the plate, the generalized vibro-acoustic equation of the model is obtained by applying the Fourier transform method. The generalized model that can be solved numerically is validated by comparing model predictions with the existing results. Numerical calculations are performed to investigate the effects of the location of the excitation, the spacing of the stiffeners, the plate thickness, the strengthening form and the fiber orientation on the sound radiation characteristic of the orthogonaUy stiffened plate, and some practical conclusions are drawn from these parameter studies.展开更多
High-order harmonics from helium atom in the orthogonally two-color(OTC) laser field are investigated by solving the two-dimensional time-dependent Schrodinger equation.Non-integer high-order harmonics are obtained in...High-order harmonics from helium atom in the orthogonally two-color(OTC) laser field are investigated by solving the two-dimensional time-dependent Schrodinger equation.Non-integer high-order harmonics are obtained in some ratio of frequencies of two components.Pure odd and even harmonics from atoms could be separated in two components by adjusting the ratio of frequencies in OTC scheme,and the resolution of harmonics is improved at the same time.The physical mechanism is explained by the periodicity of dipole.With the same intensity of the incident laser,the intensity of the high-order harmonics from the OTC field scheme is improved by three orders of magnitude compared to the monochromatic laser field scheme.A theoretical scheme is provided for experimentally achieving improving energy resolution and separation of pure odd and even harmonics in atoms.Also,we provide a means for improving harmonic intensity.展开更多
A stable wavelength operation Ho:YAG laser dual-pumped by two orthogonally polarized Tm:YLF lasers is reported. Under the cw operation mode, a laser output power of 24 W is measured. The corresponding opticaloptical c...A stable wavelength operation Ho:YAG laser dual-pumped by two orthogonally polarized Tm:YLF lasers is reported. Under the cw operation mode, a laser output power of 24 W is measured. The corresponding opticaloptical conversion efficiency is 44.75% and the slope efficiency is 50.12%. Under the Q-switched operation mode,the output maximum average power is 22.8 W at the re-frequency of 6 kHz. The corresponding optical-optical conversion efficiency and slope efficiency are 42.64% and 48.01%, respectively. The output central wavelength is 2090.73 nm, the linewidth is 0.40 nm, and the beam quality is M^2< 1.6. Moreover, the shift of the output central wavelength is less than 0.01 nm, and the linewidth shift is also less than 0.01 nm.展开更多
We investigate the nonadiabatic spectral redshift of high-order harmonic of He driven by two time-delayed orthogonally polarized laser fields. It is found that the nonadiabatic spectral redshift can be observed by pro...We investigate the nonadiabatic spectral redshift of high-order harmonic of He driven by two time-delayed orthogonally polarized laser fields. It is found that the nonadiabatic spectral redshift can be observed by properly adjusting the time delay of the two laser fields when the controlling pulse is added in the raising part of the driving pulse in the vertical direction. That is because the controlling pulse in the vertical direction prevents the ionized electrons from returning to the vicinity of parent ions and then reduces the recombination probability. This leads to the high-order harmonic generated mainly in the falling part of the driving pulse. Meanwhile,we also find that the quantity of redshift can be effectively controlled through accommodating the positive time delays. In addition, this scheme can also be used to produce nonadiabatic spectral blueshift.展开更多
We present the photoelectron momentum distributions(PMDs) and the photoelectron angular distributions(PADs) of He+ ions, aligned H2+ molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulatio...We present the photoelectron momentum distributions(PMDs) and the photoelectron angular distributions(PADs) of He+ ions, aligned H2+ molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schr?dinger equations(TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays Td, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N2 molecules.展开更多
We prot）ose a security-enhanced double-random phase encryption （DRPE） scheme using orthogonally encoded image and electronically synthesized key data to cope with the security problem of DRPE technique caused by fi...We prot）ose a security-enhanced double-random phase encryption （DRPE） scheme using orthogonally encoded image and electronically synthesized key data to cope with the security problem of DRPE technique caused by fixed double-random phase masks for eneryption. In the proposed scheme, we adopt the electronically synthesized key to frequently update the phase mask using a spatial light modulator, and also employ the orthogonal encoding technique to encode the image and electronically synthesized key data, which can enhance the security of both data. We provide detailed procedures for eneryption and decryption of the proposed scheme, and provide the simulation results to show the eneryption effects of the proposed scheme.展开更多
The cavity tuning characteristics of orthogonally polarized dual-frequency HeiNe laser at 1.15 μm are presented. Vectorial-extension model based on semi-classical laser theory reveals that cavity tuning characteristi...The cavity tuning characteristics of orthogonally polarized dual-frequency HeiNe laser at 1.15 μm are presented. Vectorial-extension model based on semi-classical laser theory reveals that cavity tuning characteristics are related to beat frequency, relative excitation, and type of Ne isotope. Distortions of cavity tuning curves become moderate with the increase of beat frequency because of the weakening of the cross- saturation effect. Distortions are enhanced with the increase of relative excitation because of the combined action of the self-saturation and cross-saturation effects. By adopting dual-isotope Ne instead of monoisotoplie Ne, distortions are reduced because of the misalignment between peaks of the self-saturation and net gain coefficients. The theoretical calculations are in good agreement with the corresponding experimental results.展开更多
In order to theoretically predict and analyze the vibration response and acoustic radiation characteristics of a periodical orthogonally rib-stiffened plate,its vibro-acoustic equations of an underwater infinite model...In order to theoretically predict and analyze the vibration response and acoustic radiation characteristics of a periodical orthogonally rib-stiffened plate,its vibro-acoustic equations of an underwater infinite model are established.The rib-stiffened plate is stimulated by a harmonic plane pressure.By using the Fourier transforms,Poisson’s summation formula and space harmonic method,the structural vibration response and acoustic radiation pressure are expressed as functions of displacement harmonic components.Efficient semi-analytical methods are proposed in this work,and then approximate solutions for finite terms of the harmonic components are obtained by employing the truncation technique.Effects of the vibration response,rib spacing and torsional moment of the ribs on the radiation pressure are examined,and the validity of the present methods is also verified.Theoretical results show that the torsional moment of the ribs affects the modal frequencies of the stiffened plate,which should not be neglected in engineering applications with high precision requirement.With attachment of the ribs to the thin plate,its far field radiation pressure can be reduced in the low frequency range by adjusting rib spacing and cross sectional size of the ribs.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12204132 and 12304376)Excellent Youth Science Foundation of Shandong Province (Overseas) (Grant No.2022HWYQ-073)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No.HIT.OCEF.2022042)Natural Science Foundation of Shandong Province (Grant No.ZR2023QA075)。
文摘Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11271158,61575077,and 11574117)
文摘The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.
基金supported by the National Natural Science Foundation of China (Grant No 50575110)
文摘External-cavity birefringence feedback effects of the microchip Nd：YAG laser are presented. When a birefringence element is placed in the external feedback cavity of the laser, two orthogonally polarized laser beams with a phase difference are output. The phase difference is twice as large as the phase retardation in the external cavity along the two orthogonal directions. The variable extra-cavity birefringence, caused by rotation of the external-cavity birefringenee element, results in tunable phase difference between the two orthogonally polarized beams. This means that the roll angle information has been translated to phase difference of two output laser beams. A theoretical analysis based on the Fabry-Perot cavity equivalent model and refractive index ellipsoid is presented, which is in good agreement with the experimental results. This phenomenon has potential applications for roll angle measurement.
基金Supported by Opening Foundation of Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing(Grant No.2017CSOBDP0103)Guangxi Universitys Science and Technology Research Project(Grant No.201012MS185)Science and Technology Foundation of Guizhou Province(Grant No.LKS[2012]34)
文摘In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rtz.
基金Project supported by the National Natural Science Foundation of China (Nos. 51004013,50936003,51174028,and 50905013)the Research Foundation of Engineering Research Institute of University of Science and Technology Beijing (No. Yj2011-015)the Fundamental Research Funds for the Central Universities (No. T-RF-TP-12-108A)
文摘The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is used to reduce the governing partial differential equations （PDEs） to a set of non-linear coupled ordinary differential equations （ODEs） in the dimensionless form. The analytical solutions are obtained by employing the homotopy analysis method （HAM）. The effects of various physical param- eters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail.
基金supported by Basic Science Research Program through National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant No. NRF-2012R1A1A2004299)
文摘Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50721004 and 60978032)
文摘We presented a novel orthogonally linearly polarized Nd：YVO4 laser. Two pieces of a-cut grown-together composite YVO4/Nd：YVO4 crystals were placed in the resonant cavity with the c-axis of the two crystals orthogonally. The polarization and power performance of the orthogonally polarized laser were investigated. A 26.2-W orthogonally linearly polarized laser was obtained. The power ratio between the two orthogonally polarized lasers was varied with the pump power caused by the polarized mode coupling. The longitudinal modes competition and the corresponding variable optical beats were also observed from the orthogonally polarized laser. We also adjusted the crystals with their c-axis parallele to each other, and a 40.7-W linearly polarized TEM00 laser was obtained, and the beam quality factors were Mx^2 = 1.37 and My^2 = 1.25.
基金financially supported by the Science Fund for Outstanding Youth of the National Natural Science Foundation of China(Grant No.51222904)the National Security Major Basic Research Program of China(Grant No.613157)+1 种基金the Key Program of National Natural Science Foundation of China(Grant No.0939002)the National Natural Science Foundation of China(Grant No.51209052)
文摘A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also considered in the research. The first order shear deformation theory is used to account for the transverse shear deformation. The motion of the equally spaced stiffeners is examined by considering their bending vibrations and torsional movements. Based on the periodic structure theory and the concepts of the equivalent dynamic flexibility of the plate, the generalized vibro-acoustic equation of the model is obtained by applying the Fourier transform method. The generalized model that can be solved numerically is validated by comparing model predictions with the existing results. Numerical calculations are performed to investigate the effects of the location of the excitation, the spacing of the stiffeners, the plate thickness, the strengthening form and the fiber orientation on the sound radiation characteristic of the orthogonaUy stiffened plate, and some practical conclusions are drawn from these parameter studies.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974229 and 11504221)the Natural Science Foundation of Shanxi Province+4 种基金China(Grant No.201901D111288)the Scientific and Technological Innovation Programs of Higher Education Institutions in ShanxiChina(Grant No.2019L0452)the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi ProvinceChina。
文摘High-order harmonics from helium atom in the orthogonally two-color(OTC) laser field are investigated by solving the two-dimensional time-dependent Schrodinger equation.Non-integer high-order harmonics are obtained in some ratio of frequencies of two components.Pure odd and even harmonics from atoms could be separated in two components by adjusting the ratio of frequencies in OTC scheme,and the resolution of harmonics is improved at the same time.The physical mechanism is explained by the periodicity of dipole.With the same intensity of the incident laser,the intensity of the high-order harmonics from the OTC field scheme is improved by three orders of magnitude compared to the monochromatic laser field scheme.A theoretical scheme is provided for experimentally achieving improving energy resolution and separation of pure odd and even harmonics in atoms.Also,we provide a means for improving harmonic intensity.
基金Supported by the Cooperation Foundation of Changchun Science and Technology Bureau under Grant No 17DY027the Foundation of Education Department of Jilin Province under Grant No JJKH20181105KJthe Foundation of Jilin Province Science and Technology Department under Grant No 20180101033JC
文摘A stable wavelength operation Ho:YAG laser dual-pumped by two orthogonally polarized Tm:YLF lasers is reported. Under the cw operation mode, a laser output power of 24 W is measured. The corresponding opticaloptical conversion efficiency is 44.75% and the slope efficiency is 50.12%. Under the Q-switched operation mode,the output maximum average power is 22.8 W at the re-frequency of 6 kHz. The corresponding optical-optical conversion efficiency and slope efficiency are 42.64% and 48.01%, respectively. The output central wavelength is 2090.73 nm, the linewidth is 0.40 nm, and the beam quality is M^2< 1.6. Moreover, the shift of the output central wavelength is less than 0.01 nm, and the linewidth shift is also less than 0.01 nm.
基金supported by the National Natural Science Foundation of China(NSFC)(Nos.11404153,11135002,11604119,and 11405077)the Fundamental Research Funds for the Central Universities of China(No.lzujbky-2017-14)
文摘We investigate the nonadiabatic spectral redshift of high-order harmonic of He driven by two time-delayed orthogonally polarized laser fields. It is found that the nonadiabatic spectral redshift can be observed by properly adjusting the time delay of the two laser fields when the controlling pulse is added in the raising part of the driving pulse in the vertical direction. That is because the controlling pulse in the vertical direction prevents the ionized electrons from returning to the vicinity of parent ions and then reduces the recombination probability. This leads to the high-order harmonic generated mainly in the falling part of the driving pulse. Meanwhile,we also find that the quantity of redshift can be effectively controlled through accommodating the positive time delays. In addition, this scheme can also be used to produce nonadiabatic spectral blueshift.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12074146,21827805,11974007,and 12074142)the Natural Science Foundation of Jilin Province of China(Grant No.20180101225JC)。
文摘We present the photoelectron momentum distributions(PMDs) and the photoelectron angular distributions(PADs) of He+ ions, aligned H2+ molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schr?dinger equations(TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays Td, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N2 molecules.
基金supported in part by the Basic Science Research Program through the National Research Foundation of Korea Funded by the Ministry of Science,ICT & Future Planning(No.2011-0030079)the Ministry of Education(No.NRF-2013R1A1A2057549)
文摘We prot）ose a security-enhanced double-random phase encryption （DRPE） scheme using orthogonally encoded image and electronically synthesized key data to cope with the security problem of DRPE technique caused by fixed double-random phase masks for eneryption. In the proposed scheme, we adopt the electronically synthesized key to frequently update the phase mask using a spatial light modulator, and also employ the orthogonal encoding technique to encode the image and electronically synthesized key data, which can enhance the security of both data. We provide detailed procedures for eneryption and decryption of the proposed scheme, and provide the simulation results to show the eneryption effects of the proposed scheme.
基金supported by the National Natural Science Foundation of China under Grant Nos.60827006 and 60723004
文摘The cavity tuning characteristics of orthogonally polarized dual-frequency HeiNe laser at 1.15 μm are presented. Vectorial-extension model based on semi-classical laser theory reveals that cavity tuning characteristics are related to beat frequency, relative excitation, and type of Ne isotope. Distortions of cavity tuning curves become moderate with the increase of beat frequency because of the weakening of the cross- saturation effect. Distortions are enhanced with the increase of relative excitation because of the combined action of the self-saturation and cross-saturation effects. By adopting dual-isotope Ne instead of monoisotoplie Ne, distortions are reduced because of the misalignment between peaks of the self-saturation and net gain coefficients. The theoretical calculations are in good agreement with the corresponding experimental results.
基金supported by the National Natural Science Foundation of China(51405276,51505261,50875030)the Natural Science Foundation of Shandong Province,China(ZR2014EEQ019)the Foundation for Young Teacher Development Program of Shandong University of Technology
文摘In order to theoretically predict and analyze the vibration response and acoustic radiation characteristics of a periodical orthogonally rib-stiffened plate,its vibro-acoustic equations of an underwater infinite model are established.The rib-stiffened plate is stimulated by a harmonic plane pressure.By using the Fourier transforms,Poisson’s summation formula and space harmonic method,the structural vibration response and acoustic radiation pressure are expressed as functions of displacement harmonic components.Efficient semi-analytical methods are proposed in this work,and then approximate solutions for finite terms of the harmonic components are obtained by employing the truncation technique.Effects of the vibration response,rib spacing and torsional moment of the ribs on the radiation pressure are examined,and the validity of the present methods is also verified.Theoretical results show that the torsional moment of the ribs affects the modal frequencies of the stiffened plate,which should not be neglected in engineering applications with high precision requirement.With attachment of the ribs to the thin plate,its far field radiation pressure can be reduced in the low frequency range by adjusting rib spacing and cross sectional size of the ribs.
