As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function...As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function, and short life cycle, which go against the principles of energy conservation and the environmental protection intensive design concept. In this paper, a rational multi-function method of design through functional superposition, transformation, and technical implementation is proposed. An organic combination of frog-style scooter and children’s tricycle is developed using the multi-function method. From the ergonomic perspective, the paper elaborates on the body size of children aged 5 to 12 and effectively extracts data for a multi-function children’s bike, which can be used for gliding and riding. By inverting the body, parts can be interchanged between the handles and the pedals of the bike. Finally, the paper provides a detailed analysis of the components and structural design, body material, and processing technology of the bike. The study of Industrial Product Innovation Design provides an effective design method to solve the bicycle problems, extends the function problems, improves the product market situation, and enhances the energy saving feature while implementing intensive product development effectively at the same time.展开更多
The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric a...The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.展开更多
In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a s...In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.展开更多
This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. T...This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.展开更多
Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process...Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.展开更多
In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G)?-expansion method is a special case of the generalized tanh-...In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G)?-expansion method is a special case of the generalized tanh-function type method, so the (G'/G)?-expansion method is considered as a special deformation application of the transformed rational function method. We demonstrate that all solutions obtained by the (G'/G)?-expansion method were found by the generalized tanh-function type method. As applications, we consider mKdV equation. Compared with the (G'/G) -expansion method, the generalized tanh-function type method gives new and more abundant solutions.展开更多
In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe s...In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obta/ned and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the （N ＋ 1）-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N 〉 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.展开更多
In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material propert...In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.展开更多
海冰密集度数据是开展全球海洋监测和应对气候变化研究的重要数据源,为了研制出分辨率更高,误差更小的北极海冰密集度融合资料,本文使用了多源海冰密集度资料,以OSTIA(Operational Sea Surface Temperature and Ice Analysis)数据集为...海冰密集度数据是开展全球海洋监测和应对气候变化研究的重要数据源,为了研制出分辨率更高,误差更小的北极海冰密集度融合资料,本文使用了多源海冰密集度资料,以OSTIA(Operational Sea Surface Temperature and Ice Analysis)数据集为融合背景场,采用以下方案开展融合研究。首先,对现有5种海冰资料进行质量控制;其次,以OSI SAF(Ocean and Sea Ice Satellite Application Facility)资料为基准,采用概率密度匹配法订正各资料的系统误差;然后,利用小波分解将各资料分解为低频信息和高频信息,对低频信息和高频信息分别计算融合权重和卡尔曼滤波处理;最后,利用小波重构将各资料进行融合,生成0.05°分辨率的北极逐日海冰密集度融合资料。通过对比国际上广泛认可的OISST(Optimum Interpolation Sea Surface Temperature)、OSTIA海冰密集度资料,验证结果显示:融合资料与OISST、OSTIA海冰密集度资料在北极的空间分布上高度一致,相关系数均超过0.967。相对于前人的研究,本融合资料与OISST的偏差由–1.170%减少到–0.108%,与OSTIA的偏差由0.276%减少到–0.156%;与OISST和OSTIA的均方根误差分别由9.835%减少为8.010%以及由7.427%减少为5.140%。本融合资料的偏差以及均方根误差都得到了显著的提升,具有较高的质量。展开更多
The free vibration of functionally graded material （FGM） beams is studied based on both the classical and the first-order shear deformation beam theories. The equations of motion for the FGM beams are derived by con...The free vibration of functionally graded material （FGM） beams is studied based on both the classical and the first-order shear deformation beam theories. The equations of motion for the FGM beams are derived by considering the shear deforma- tion and the axial, transversal, rotational, and axial-rotational coupling inertia forces on the assumption that the material properties vary arbitrarily in the thickness direction. By using the numerical shooting method to solve the eigenvalue problem of the coupled ordinary differential equations with different boundary conditions, the natural frequen- cies of the FGM Timoshenko beams are obtained numerically. In a special case of the classical beam theory, a proportional transformation between the natural frequencies of the FGM and the reference homogenous beams is obtained by using the mathematical similarity between the mathematical formulations. This formula provides a simple and useful approach to evaluate the natural frequencies of the FGM beams without dealing with the tension-bending coupling problem. Approximately, this analogous transition can also be extended to predict the frequencies of the FGM Timoshenko beams. The numerical results obtained by the shooting method and those obtained by the analogous transformation are presented to show the effects of the material gradient, the slenderness ratio, and the boundary conditions on the natural frequencies in detail.展开更多
This paper revisits the characteristics of windowing techniques with various window functions involved,and successively investigates spectral leakage mitigation utilizing the Welch method.The discrete Fourier transfor...This paper revisits the characteristics of windowing techniques with various window functions involved,and successively investigates spectral leakage mitigation utilizing the Welch method.The discrete Fourier transform(DFT)is ubiquitous in digital signal processing(DSP)for the spectrum analysis and can be efciently realized by the fast Fourier transform(FFT).The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is employed.Windowing is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened out.Therefore,windowing processing reduces the amplitude of the samples at the beginning and end of the window.In addition to selecting appropriate window functions,a pretreatment method,such as the Welch method,is effective to mitigate the spectral leakage.Due to the noise caused by imperfect,nite data,the noise reduction from Welch’s method is a desired treatment.The nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio(SNR)is high and mitigates noise in the estimated power spectra in exchange for frequency resolution reduction.The periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately selected.The design of nite impulse response(FIR)digital lter using the window technique is rstly addressed.The inuence of various window functions on the Fourier transform spectrum of the signals is discussed.Comparison on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.展开更多
The differential transformation method (DTM) is applied to investigate free vibration of functionally graded beams supported by arbitrary boundary conditions, including various types of elastically end constraints. Th...The differential transformation method (DTM) is applied to investigate free vibration of functionally graded beams supported by arbitrary boundary conditions, including various types of elastically end constraints. The material properties of functionally graded beams are assumed to obey the power law distribution. The main advantages of this method are known for its excellence in high accuracy with small computational expensiveness. The DTM also provides all natural frequencies and mode shapes without any frequency missing. Fundamental frequencies as well as their higher frequencies and mode shapes are presented. The significant aspects such as boundary conditions, values of translational and rotational spring constants and the material volume fraction index on the natural frequencies and mode shapes are discussed. For elastically end constraints, some available results of special cases for isotropic beams are used to validate the present results. The new frequency results and mode shapes of functionally graded beams resting on elastically end constraints are presented.展开更多
Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-...Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.展开更多
基金supported by Social Science Fund for Young Scholar of Ministry of Education of China(Grant No. 12YJC760092)Changzhou Key Digital Manufacturing Technology Laboratory Foundation of China(Grant No. CM2007301)
文摘As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function, and short life cycle, which go against the principles of energy conservation and the environmental protection intensive design concept. In this paper, a rational multi-function method of design through functional superposition, transformation, and technical implementation is proposed. An organic combination of frog-style scooter and children’s tricycle is developed using the multi-function method. From the ergonomic perspective, the paper elaborates on the body size of children aged 5 to 12 and effectively extracts data for a multi-function children’s bike, which can be used for gliding and riding. By inverting the body, parts can be interchanged between the handles and the pedals of the bike. Finally, the paper provides a detailed analysis of the components and structural design, body material, and processing technology of the bike. The study of Industrial Product Innovation Design provides an effective design method to solve the bicycle problems, extends the function problems, improves the product market situation, and enhances the energy saving feature while implementing intensive product development effectively at the same time.
基金Supported by the Marine Engineering Equipment Scientific Research Project of Ministry of Industry and Information Technology of PRCthe National Science and Technology Major Project of China(Grant No.2016ZX05057020)National Natural Science Foundation of China(Grant No.51809067)
文摘The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.
文摘In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.
文摘This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.
基金the National High.Technology Research and Development Programme of China(2004AA404013)
文摘Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.
文摘In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G)?-expansion method is a special case of the generalized tanh-function type method, so the (G'/G)?-expansion method is considered as a special deformation application of the transformed rational function method. We demonstrate that all solutions obtained by the (G'/G)?-expansion method were found by the generalized tanh-function type method. As applications, we consider mKdV equation. Compared with the (G'/G) -expansion method, the generalized tanh-function type method gives new and more abundant solutions.
基金Supported by NSFC for Young Scholars under Grant No.11101166Tianyuan Youth Foundation of Mathematics under Grant No.11126244+1 种基金Youth PhD Development Fund of CUFE 121 Talent Cultivation Project under Grant No.QBJZH201002Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No.KM201110772017
文摘In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obta/ned and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the （N ＋ 1）-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N 〉 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.
基金Project supported by the Vietnam National Foundation for Science and Technology Development(No.107.02-2017.301)。
文摘In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.
基金Project supported by the National Natural Science Foundation of China(No.11272278)
文摘The free vibration of functionally graded material （FGM） beams is studied based on both the classical and the first-order shear deformation beam theories. The equations of motion for the FGM beams are derived by considering the shear deforma- tion and the axial, transversal, rotational, and axial-rotational coupling inertia forces on the assumption that the material properties vary arbitrarily in the thickness direction. By using the numerical shooting method to solve the eigenvalue problem of the coupled ordinary differential equations with different boundary conditions, the natural frequen- cies of the FGM Timoshenko beams are obtained numerically. In a special case of the classical beam theory, a proportional transformation between the natural frequencies of the FGM and the reference homogenous beams is obtained by using the mathematical similarity between the mathematical formulations. This formula provides a simple and useful approach to evaluate the natural frequencies of the FGM beams without dealing with the tension-bending coupling problem. Approximately, this analogous transition can also be extended to predict the frequencies of the FGM Timoshenko beams. The numerical results obtained by the shooting method and those obtained by the analogous transformation are presented to show the effects of the material gradient, the slenderness ratio, and the boundary conditions on the natural frequencies in detail.
基金supported by the Ministry of Science and Technology,Taiwan[Grant Numbers MOST 104-2221-E-019-026-MY2 and MOST 108-2221-E019-013].
文摘This paper revisits the characteristics of windowing techniques with various window functions involved,and successively investigates spectral leakage mitigation utilizing the Welch method.The discrete Fourier transform(DFT)is ubiquitous in digital signal processing(DSP)for the spectrum analysis and can be efciently realized by the fast Fourier transform(FFT).The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is employed.Windowing is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened out.Therefore,windowing processing reduces the amplitude of the samples at the beginning and end of the window.In addition to selecting appropriate window functions,a pretreatment method,such as the Welch method,is effective to mitigate the spectral leakage.Due to the noise caused by imperfect,nite data,the noise reduction from Welch’s method is a desired treatment.The nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio(SNR)is high and mitigates noise in the estimated power spectra in exchange for frequency resolution reduction.The periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately selected.The design of nite impulse response(FIR)digital lter using the window technique is rstly addressed.The inuence of various window functions on the Fourier transform spectrum of the signals is discussed.Comparison on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.
文摘The differential transformation method (DTM) is applied to investigate free vibration of functionally graded beams supported by arbitrary boundary conditions, including various types of elastically end constraints. The material properties of functionally graded beams are assumed to obey the power law distribution. The main advantages of this method are known for its excellence in high accuracy with small computational expensiveness. The DTM also provides all natural frequencies and mode shapes without any frequency missing. Fundamental frequencies as well as their higher frequencies and mode shapes are presented. The significant aspects such as boundary conditions, values of translational and rotational spring constants and the material volume fraction index on the natural frequencies and mode shapes are discussed. For elastically end constraints, some available results of special cases for isotropic beams are used to validate the present results. The new frequency results and mode shapes of functionally graded beams resting on elastically end constraints are presented.
基金supported by the National Natural Science Foundation of China (Nos. 10732100, 10572155)the Science and Technology Planning Project of Guangdong Province of China (No. 2006A11001002)the Ph. D. Programs Foundation of Ministry of Education of China (No. 2006300004111179)
文摘Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.
