Based on a multiobjective approach whose objective function (OF) vector collects stochastic reliability performance and structural cost indices, a structural optimization criterion for mechanical systems subject to ra...Based on a multiobjective approach whose objective function (OF) vector collects stochastic reliability performance and structural cost indices, a structural optimization criterion for mechanical systems subject to random vibrations is presented for supporting engineer’s design. This criterion differs from the most commonly used conventional optimum design criterion for random vibrating structure, which is based on minimizing displacement or acceleration variance of main structure responses, without considering explicitly required performances against failure. The proposed criterion can properly take into account the design-reliability required performances, and it becomes a more efficient support for structural engineering decision making. The multiobjective optimum (MOO) design of a tuned mass damper (TMD) has been developed in a typical seismic design problem, to control structural vibration induced on a multi-storey building structure excited by nonstationary base acceleration random process. A numerical example for a three-storey building is developed and a sensitivity analysis is carried out. The results are shown in a useful manner for TMD design decision support.展开更多
During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envel...During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.展开更多
Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower tri...Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.展开更多
A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified ...A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multioutput kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.展开更多
Demand for large vibrating screen is huge in the mineral processing industry. As bending and random vibration are not considered in a traditional design method for beam structures of a large vibrating screen, fatigue ...Demand for large vibrating screen is huge in the mineral processing industry. As bending and random vibration are not considered in a traditional design method for beam structures of a large vibrating screen, fatigue damage occurs frequently to affect the screening performance. This work aims to conduct a systematic mechanics analysis of the beam structures and improve the design method. Total motion of a beam structure in screening process can be decomposed into the traditional followed rigid translation(FRT), bending vibration(BV) and axial linear-distributed random rigid translation(ALRRT) excited by the side-plates. When treated as a generalized single-degree-of-freedom(SDOF) elastic system analytically, the BV can be solved by the Rayleigh's method. Stochastic analysis for random process is conducted for the detailed ALRRT calculation. Expressions for the mechanics property, namely, the shearing force and bending-moment with respect to BV and ALRRT, are derived, respectively. Experimental and numerical investigations demonstrate that the largest BV exists at the beam center and can be nearly ignored in comparison with the FRT during a simplified engineering design. With the BV and FRT considered, the mechanics property accords well with the practical situation with the maximum error of 6.33%, which is less than that obtained by traditional method.展开更多
The performance in vibration environment of switching apparatus containing mechanical contact is an important element when judging the apparatus’s reliability. A piecewise linear two-degrees-of-freedom mathematical m...The performance in vibration environment of switching apparatus containing mechanical contact is an important element when judging the apparatus’s reliability. A piecewise linear two-degrees-of-freedom mathematical model considering contact loss was built in this work, and the vibration performance of the model under random external Gaussian white noise excitation was investigated by using Monte Carlo simulation in Matlab/Simulink. Simulation showed that the spectral content and statistical characters of the contact force coincided strongly with reality. The random vibration character of the contact system was solved using time (numerical) domain simulation in this paper. Conclusions reached here are of great importance for reliability design of switching apparatus.展开更多
Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and t...Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation,the intensity of which is larger than 7,acts in train-bridge system.Firstly,the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established,where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom,while the single-span simple supported bridge subsystem is composed of 102D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support.Secondly,Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system.The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method,respectively solved by precise integral method and Newmark-βmethod through the inter-system iterative procedure.Finally,the results are compared with the case under the weak seismic excitation,and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution.In a high probability,the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.展开更多
The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordin...The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-9 schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.展开更多
The seismic analysis of long-span bridges subjected to multiple ground excitations is an important problem. The conventional response spectrum method neglects the spatial effects of ground motion,and therefore may res...The seismic analysis of long-span bridges subjected to multiple ground excitations is an important problem. The conventional response spectrum method neglects the spatial effects of ground motion,and therefore may result in questionable conclusions.The random vibration approach has been regarded as more reliable.Unfortunately,so far, computational difficulties have not yet been satisfactorily resolved.In this paper,an accurate and efficient random vibration approach—pseudo excitation method (PEM),by which the above difficulties are overcome,is presented.It has been successfully used in the three dimensional seismic analysis of a number of long-span bridges with thousands of degrees of freedom and dozens of supports.The numerical results of a typical bridge show that the seismic spatial effects~ particularly the wave passage effect,are sometimes quite important in evaluating the safety of long-span bridges.展开更多
The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric pote...The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.展开更多
A stochastic optimal control method for nonlinear hysteretic systems under externally and/or parametrically random excitations is presented and illustrated with an example of hysteretic column system. A hysteretic sys...A stochastic optimal control method for nonlinear hysteretic systems under externally and/or parametrically random excitations is presented and illustrated with an example of hysteretic column system. A hysteretic system subject to random excitation is first replaced by a nonlinear non-hysteretic stochastic system. An It$\hat {\rm o}$ stochastic differential equation for the total energy of the system as a one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. A dynamical programming equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the responses of uncontrolled and controlled systems are evaluated to determine the control efficacy. It is shown by numerical results that the proposed stochastic optimal control method is more effective and efficient than other optimal control methods.展开更多
Seismic random vibration analysis of stochastic truss structures is presented.A new method called random factor method is used for dynamic analysis of structures with uncertain parameters,due to variability in their m...Seismic random vibration analysis of stochastic truss structures is presented.A new method called random factor method is used for dynamic analysis of structures with uncertain parameters,due to variability in their material properties and geometry.Using the random factor method,the natural frequencies and modeshapes of a stochastic structure can be respectively described by the product of two parts,corresponding to the random factors of the structural parameters with uncertainty,and deterministic values of the natural frequencies and modeshapes obtained by conventional finite element analysis.The stochastic truss structure is subjected to stationary or non-stationary random earthquake excitation.Computational expressions for the mean and standard deviation of the mean square displacement and mean square stress are developed by means of the random variable's functional moment method and the algebra synthesis method.An antenna and a truss bridge are used as practical engineering examples to illustrate the application of the random factor method in the seismic response analysis of random structures under stationary or non-stationary random earthquake excitation.展开更多
In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standa...In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered.The stationary probability density function(SPDF)of the harvester is obtained by the improved stochastic averaging.Then,with the adiabatic approximation theory,the analytical expression of signal-to-noise ratio(SNR)for the TEH is deduced to characterize stochastic resonance(SR).To enhance direct current(DC)power delivery from a rotational TEH,the influences of system parameters on SR is discussed.The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system.The TEH has higher harvesting performance under the optimal SR.That is,the optimal parameter combinations can induce optimal SR and maximize harvesting performance.Thus,the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.展开更多
For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtaine...For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.展开更多
The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are bot...The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to be an effective supplement of the traditional random vibration theory. In this paper, we further extend the nonrandom vibration analysis into the general viscous damping system, and formulate a method to calculate the dynamic response bounds of a viscous damping vibration system under uncertain excitations. Firstly, the unit impulse response matrix of the system is obtained by using a complex mode superposition method. Secondly, an analytic formulation of the system dynamic response middle point and radius under uncertain excitations is derived based on the Duhamel’s integral, and thus the upper and lower response bounds of the system can be obtained. Finally, two numerical examples are investigated to demonstrate the effectiveness of the proposed method.展开更多
In this research the tail equivalent linearization method(TELM)has been extended to study structures with degrading materials.The responses of such structures to excitations are non-stationary,even if the excitations ...In this research the tail equivalent linearization method(TELM)has been extended to study structures with degrading materials.The responses of such structures to excitations are non-stationary,even if the excitations are stationary.Non-stationary behavior of the system cannot be considered by conventional TELM.Applying the conventional TELM,the only distinction in the design point excitation for two stationary excitations with diff erent durations is in the addition of a zero value part at the beginning of the design point of the longer excitation.This means that the failure probability is the same for the non-stationary systems under excitations with diff erent durations.Therefore,this solution cannot be correct.In this study,in using TELM for systems with degrading materials,hysteretic energy is replaced by average hysteretic energy,calculated by averaging the obtained hysteretic energy of the structure subjected to a few random sample load realization.In this way,the degradation parameters under design point coincide with those under sample load realizations.Since the average of the hysteretic energy is converges very fast,the modifi ed TELM only requires about tens to hundreds solutions of the response in addition to the ordinary calculations of conventional TELM.展开更多
This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this w...This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean-square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.展开更多
An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acousti...An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.展开更多
A nonlinear seismic analysis method for complex frame structures subjected to sta- tionary random ground excitations is proposed.The nonlinear elasto-plastic behaviors may take place only on a small part of the struct...A nonlinear seismic analysis method for complex frame structures subjected to sta- tionary random ground excitations is proposed.The nonlinear elasto-plastic behaviors may take place only on a small part of the structure.The Bouc-Wen differential equation model is used to model the hysteretic characteristics of the nonlinear components.The Pseudo Excitation Method (PEM)is used in solving the linearized random differential equations to replace the solution of the less efficient Lyapunov equation.Numerical results of a real bridge show that the method proposed is effective for practical engineering analysis.展开更多
Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and b...Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.展开更多
文摘Based on a multiobjective approach whose objective function (OF) vector collects stochastic reliability performance and structural cost indices, a structural optimization criterion for mechanical systems subject to random vibrations is presented for supporting engineer’s design. This criterion differs from the most commonly used conventional optimum design criterion for random vibrating structure, which is based on minimizing displacement or acceleration variance of main structure responses, without considering explicitly required performances against failure. The proposed criterion can properly take into account the design-reliability required performances, and it becomes a more efficient support for structural engineering decision making. The multiobjective optimum (MOO) design of a tuned mass damper (TMD) has been developed in a typical seismic design problem, to control structural vibration induced on a multi-storey building structure excited by nonstationary base acceleration random process. A numerical example for a three-storey building is developed and a sensitivity analysis is carried out. The results are shown in a useful manner for TMD design decision support.
基金supported by Aviation Science Foundation of China (No. 20100251006)the Technological Foundation Project (No. J132012C001)
文摘During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.
基金National Natural Science Foundation of China （10972104） The Fundamental Research Funds for NUAA（NS2010007）
文摘Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_0234)
文摘A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multioutput kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.
基金Project(51221462) supported by the National Natural Science Foundation of ChinaProject(20120095110001) supported by the Ph D Programs Foundation of Ministry of Education of China
文摘Demand for large vibrating screen is huge in the mineral processing industry. As bending and random vibration are not considered in a traditional design method for beam structures of a large vibrating screen, fatigue damage occurs frequently to affect the screening performance. This work aims to conduct a systematic mechanics analysis of the beam structures and improve the design method. Total motion of a beam structure in screening process can be decomposed into the traditional followed rigid translation(FRT), bending vibration(BV) and axial linear-distributed random rigid translation(ALRRT) excited by the side-plates. When treated as a generalized single-degree-of-freedom(SDOF) elastic system analytically, the BV can be solved by the Rayleigh's method. Stochastic analysis for random process is conducted for the detailed ALRRT calculation. Expressions for the mechanics property, namely, the shearing force and bending-moment with respect to BV and ALRRT, are derived, respectively. Experimental and numerical investigations demonstrate that the largest BV exists at the beam center and can be nearly ignored in comparison with the FRT during a simplified engineering design. With the BV and FRT considered, the mechanics property accords well with the practical situation with the maximum error of 6.33%, which is less than that obtained by traditional method.
基金Project (No. FEBQ24409102) supported by the Space Technology Innovation Fund, China
文摘The performance in vibration environment of switching apparatus containing mechanical contact is an important element when judging the apparatus’s reliability. A piecewise linear two-degrees-of-freedom mathematical model considering contact loss was built in this work, and the vibration performance of the model under random external Gaussian white noise excitation was investigated by using Monte Carlo simulation in Matlab/Simulink. Simulation showed that the spectral content and statistical characters of the contact force coincided strongly with reality. The random vibration character of the contact system was solved using time (numerical) domain simulation in this paper. Conclusions reached here are of great importance for reliability design of switching apparatus.
基金Project(52178101) supported by the National Natural Science Foundation of China。
文摘Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation,the intensity of which is larger than 7,acts in train-bridge system.Firstly,the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established,where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom,while the single-span simple supported bridge subsystem is composed of 102D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support.Secondly,Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system.The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method,respectively solved by precise integral method and Newmark-βmethod through the inter-system iterative procedure.Finally,the results are compared with the case under the weak seismic excitation,and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution.In a high probability,the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.
基金NSFC (No. 10472023)Doctoral Research Fund of the Chinese Ministry of Education (No. 20040141020)
文摘The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-9 schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.
基金NSFC (No.10472023) and Doctoral Research Fund of the Chinese Ministry of Education
文摘The seismic analysis of long-span bridges subjected to multiple ground excitations is an important problem. The conventional response spectrum method neglects the spatial effects of ground motion,and therefore may result in questionable conclusions.The random vibration approach has been regarded as more reliable.Unfortunately,so far, computational difficulties have not yet been satisfactorily resolved.In this paper,an accurate and efficient random vibration approach—pseudo excitation method (PEM),by which the above difficulties are overcome,is presented.It has been successfully used in the three dimensional seismic analysis of a number of long-span bridges with thousands of degrees of freedom and dozens of supports.The numerical results of a typical bridge show that the seismic spatial effects~ particularly the wave passage effect,are sometimes quite important in evaluating the safety of long-span bridges.
基金supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y607087)
文摘The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.
基金Project supported by the National Natural Science Foundation of China(No.19972059)Zhejiang Provincial Natural Science Foundation(No.101046)
文摘A stochastic optimal control method for nonlinear hysteretic systems under externally and/or parametrically random excitations is presented and illustrated with an example of hysteretic column system. A hysteretic system subject to random excitation is first replaced by a nonlinear non-hysteretic stochastic system. An It$\hat {\rm o}$ stochastic differential equation for the total energy of the system as a one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. A dynamical programming equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the responses of uncontrolled and controlled systems are evaluated to determine the control efficacy. It is shown by numerical results that the proposed stochastic optimal control method is more effective and efficient than other optimal control methods.
文摘Seismic random vibration analysis of stochastic truss structures is presented.A new method called random factor method is used for dynamic analysis of structures with uncertain parameters,due to variability in their material properties and geometry.Using the random factor method,the natural frequencies and modeshapes of a stochastic structure can be respectively described by the product of two parts,corresponding to the random factors of the structural parameters with uncertainty,and deterministic values of the natural frequencies and modeshapes obtained by conventional finite element analysis.The stochastic truss structure is subjected to stationary or non-stationary random earthquake excitation.Computational expressions for the mean and standard deviation of the mean square displacement and mean square stress are developed by means of the random variable's functional moment method and the algebra synthesis method.An antenna and a truss bridge are used as practical engineering examples to illustrate the application of the random factor method in the seismic response analysis of random structures under stationary or non-stationary random earthquake excitation.
基金This work has been supported by the National Natural Science Foundation of China(Grant No.12072025)Beijing Natural Science 5 Foundation(Grant No.1222015)the Natural Science Basic Research Program of Shaanxi Province(Grant No.2022JQ-044).
文摘In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered.The stationary probability density function(SPDF)of the harvester is obtained by the improved stochastic averaging.Then,with the adiabatic approximation theory,the analytical expression of signal-to-noise ratio(SNR)for the TEH is deduced to characterize stochastic resonance(SR).To enhance direct current(DC)power delivery from a rotational TEH,the influences of system parameters on SR is discussed.The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system.The TEH has higher harvesting performance under the optimal SR.That is,the optimal parameter combinations can induce optimal SR and maximize harvesting performance.Thus,the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.
基金supported by Aeronautical Science Foundation of China (No. 20100251006)Technological Foundation Project of China (No. J132012C001)
文摘For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.
基金supported by the Science Challenge Project of China (No. TZ2018007)the National Science Fund for Distinguished Young Scholars (No. 51725502)+1 种基金the National Key R&D Program of China (No. 2016YFD0701105)the Open Project Program of Key Laboratory for Precision & Non-traditional Machining of Ministry of Education, Dalian University of Technology of China (No. JMTZ201701)
文摘The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to be an effective supplement of the traditional random vibration theory. In this paper, we further extend the nonrandom vibration analysis into the general viscous damping system, and formulate a method to calculate the dynamic response bounds of a viscous damping vibration system under uncertain excitations. Firstly, the unit impulse response matrix of the system is obtained by using a complex mode superposition method. Secondly, an analytic formulation of the system dynamic response middle point and radius under uncertain excitations is derived based on the Duhamel’s integral, and thus the upper and lower response bounds of the system can be obtained. Finally, two numerical examples are investigated to demonstrate the effectiveness of the proposed method.
文摘In this research the tail equivalent linearization method(TELM)has been extended to study structures with degrading materials.The responses of such structures to excitations are non-stationary,even if the excitations are stationary.Non-stationary behavior of the system cannot be considered by conventional TELM.Applying the conventional TELM,the only distinction in the design point excitation for two stationary excitations with diff erent durations is in the addition of a zero value part at the beginning of the design point of the longer excitation.This means that the failure probability is the same for the non-stationary systems under excitations with diff erent durations.Therefore,this solution cannot be correct.In this study,in using TELM for systems with degrading materials,hysteretic energy is replaced by average hysteretic energy,calculated by averaging the obtained hysteretic energy of the structure subjected to a few random sample load realization.In this way,the degradation parameters under design point coincide with those under sample load realizations.Since the average of the hysteretic energy is converges very fast,the modifi ed TELM only requires about tens to hundreds solutions of the response in addition to the ordinary calculations of conventional TELM.
文摘This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean-square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.
基金supported by the National Natural Science Foundations of China(Nos.11872079,11572109)the Science and Technology Project of Hebei Education Department(No.QN2019135)Advanced Talents Incubation Program of the Hebei University(No.521000981285)。
文摘An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.
基金Project supported by the National Natural Science Foundation of China(No.10072015)the National Key Base Research Special Foundation(No.G1999032805).
文摘A nonlinear seismic analysis method for complex frame structures subjected to sta- tionary random ground excitations is proposed.The nonlinear elasto-plastic behaviors may take place only on a small part of the structure.The Bouc-Wen differential equation model is used to model the hysteretic characteristics of the nonlinear components.The Pseudo Excitation Method (PEM)is used in solving the linearized random differential equations to replace the solution of the less efficient Lyapunov equation.Numerical results of a real bridge show that the method proposed is effective for practical engineering analysis.
基金National Natural Science Foundation of China under Grant Nos.11972379 and 42377184,Hunan 100-Talent PlanNatural Science Foundation of Hunan Province under Grant No.2022JJ10079+1 种基金Hunan High-Level Talent Plan under Grant No.420030004Central South University Research Project under Grant Nos.202045006(Innovation-Driven Project)and 502390001。
文摘Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.
