The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a pi...The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.展开更多
This study describes the seismic performance of an existing five storey reinforced concrete building which represents the typical properties of low-rise non-ductile buildings in Turkey. The effectiveness of shear wall...This study describes the seismic performance of an existing five storey reinforced concrete building which represents the typical properties of low-rise non-ductile buildings in Turkey. The effectiveness of shear walls and the steel bracings in retrofitting the building was examined through nonlinear static and dynamic analyses. By using the nonlinear static analysis, retrofitted buildings seismic performances under lateral seismic load were compared with each other. Moreover, the performance points and response levels of the existing and retrofitting cases were determined by way of the capacity-spectrum method described in ATC-40 (1996). For the nonlinear dynamic analysis the records were selected to represent wide ranges of duration and frequency content. Considering the change in the stiffness and the energy dissipation capacities, the performance of the existing and retrofitted buildings were evaluated in terms of story drifts and damage states. It was found that each earthquake record exhibited its own peculiarities, dictated by frequency content, duration, sequence of peaks and their amplitude. The seismic performance of retrofitted buildings resulted in lower displacements and higher energy dissipation capacity depending mainly on the properties of the ground motions and the retrofitting strategies. Moreover, severe structural damage (irreparable or collapse) was observed for the existing building. However, buildings with retrofit alternatives exhibited lower damage levels changing from no damage to irreparable damage states.展开更多
Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key c...Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.展开更多
For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arrange...For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arranged on the outer surface of nucleus. Then, by taking into account the nucleus-electron interaction (attractive and repulsive) and the mutual electron-electron repulsions, and by a simple step-by-step nonlinear static analysis program, all the electrons are found to equilibrate on the outer surface of the same sphere, which is concentric and larger than nucleus. In a second stage, starting from an equilibrium sphere of electrons, one of the electrons is subjected to gradual forced removal, radially and outwards with respect to nucleus. Within each removal step, the produced work increment is determined and the increments are summed. When no more significant attraction is exerted by nucleus to removed electron, the total work gives the Ionization Energy. After removing of single electron, the remaining electrons fall on a lower shell, that is, they equilibrate on the outer surface of a smaller concentric sphere. For nucleus-electron interaction, an L-J (Lennard-Jones) type curve, attractive and repulsive, is adopted. When the parameter of this curve is n > 1.0, the Ionization Energy exhibits an upper bound. As parameter n increases from 1.0 up to 2.0, the attractive potential of L-J curve is gradually weakened. The proposed model is applied on Argon. It is observed that, as the number of electrons increases, the radius of equilibrium sphere increases, too, whereas the attractive nucleus-electron potential is reduced;thus the Ionization Energy is reduced, too. Particularly, as the number of electrons and the radius of equilibrium sphere exceed some critical values, the above two last quantities exhibit abrupt falls. A regular polyhedron is revealed, which can accommodate Elements up to atomic number Z = 146, that is 28 more than Z = 118 of existing last Element, as guide for initial locations of electrons in the above first program.展开更多
In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-...In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.展开更多
The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-ma...The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.展开更多
The Duffing equation describes the oscillations of a damped nonlinear oscillator [1]. Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited ...The Duffing equation describes the oscillations of a damped nonlinear oscillator [1]. Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited e.g. oscillations of a theoretical weightless-spring. We propose generalizing the mathematical features of the Duffing equation by including in addition to the cubic term unlimited number of odd powers of coordinate-dependent terms. The proposed generalization describes a true mass-less magneto static-spring capable of performing highly non-linear oscillations. The equation describing the motion is a super non-linear ODE. Utilizing Mathematica [2] we solve the equation numerically displaying its time series. We investigate the impact of the proposed generalization on a handful of kinematic quantities. For a comprehensive understanding utilizing Mathematica animation we bring to life the non-linear oscillations.展开更多
This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric laye...This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.展开更多
A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herei...A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.展开更多
This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that...This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.展开更多
The compliant vertical access riser (CVAR) is a new riser concept with good compliance;it can significantly reduce operating costs by eliminating the need for additional machines to operate wells directly on the platf...The compliant vertical access riser (CVAR) is a new riser concept with good compliance;it can significantly reduce operating costs by eliminating the need for additional machines to operate wells directly on the platform.In this study,we determined the optimal riser parameters in terms of the stress and riser weight by optimizing the CVAR,and we compared the optimization resuits.A two-dimensional nonlinear static CVAR model was deduced according to the principles of virtual work and variation,and the model was verified using MATLAB.Design of experiments and Kriging method were used to reduce the number of sample calculations and improve the modeling accuracy.An appropriate selection of the multi-objective optimization problem (MOP) and the non-dominated sorting genetic algorithm helped to optimize the CVAR design.The non-dominated sorting genetic algorithm Ⅱ was used to solve the Pareto frontier of the optimization model in order to provide decision makers with more choices for the optimization results.After optimizing the riser parameters,the geometry of the riser was smoother,and the stress and stress differences were greatly reduced;the maximum equivalent stresses at the top and bottom were reduced by 36.6% and 44%,respectively.In addition,the stress difference in the buoyancy block area was reduced by 20.9%,and the weight of the riser was increased significantly by 28.1%.展开更多
According to the purpose of the opening and the structural designer, the shape of the web opening is decided. It is too easy to choose the shape of openings from regular shape whether it is circular or rectangular sha...According to the purpose of the opening and the structural designer, the shape of the web opening is decided. It is too easy to choose the shape of openings from regular shape whether it is circular or rectangular shape. The presence of openings in the web of steel beams decreases stiffness of the beam and introducing a larger deflection than in the steel web opening with solid opening. A steel beam with web opening is analyzed in this paper. ABAQUS software is using for analyzing nonlinear static and dynamic opening of steel beam with different position and supporting conditions.展开更多
The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapuno...The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.展开更多
An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequentl...An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.展开更多
The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly ...The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.展开更多
For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is dif...For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.展开更多
This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation the...This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.展开更多
基金The National Natural Science Foundation of China(No.10772086,10772085)
文摘The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.
文摘This study describes the seismic performance of an existing five storey reinforced concrete building which represents the typical properties of low-rise non-ductile buildings in Turkey. The effectiveness of shear walls and the steel bracings in retrofitting the building was examined through nonlinear static and dynamic analyses. By using the nonlinear static analysis, retrofitted buildings seismic performances under lateral seismic load were compared with each other. Moreover, the performance points and response levels of the existing and retrofitting cases were determined by way of the capacity-spectrum method described in ATC-40 (1996). For the nonlinear dynamic analysis the records were selected to represent wide ranges of duration and frequency content. Considering the change in the stiffness and the energy dissipation capacities, the performance of the existing and retrofitted buildings were evaluated in terms of story drifts and damage states. It was found that each earthquake record exhibited its own peculiarities, dictated by frequency content, duration, sequence of peaks and their amplitude. The seismic performance of retrofitted buildings resulted in lower displacements and higher energy dissipation capacity depending mainly on the properties of the ground motions and the retrofitting strategies. Moreover, severe structural damage (irreparable or collapse) was observed for the existing building. However, buildings with retrofit alternatives exhibited lower damage levels changing from no damage to irreparable damage states.
基金Supported by National Key R&D Program of China(Grant No.2018YFB1702503)National Program on Key Basic Research Project of China(973 Program,Grant No.2013CB035403)Startup Fund for Youngman Research at SJTU(SFYR at SJTU)
文摘Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.
文摘For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arranged on the outer surface of nucleus. Then, by taking into account the nucleus-electron interaction (attractive and repulsive) and the mutual electron-electron repulsions, and by a simple step-by-step nonlinear static analysis program, all the electrons are found to equilibrate on the outer surface of the same sphere, which is concentric and larger than nucleus. In a second stage, starting from an equilibrium sphere of electrons, one of the electrons is subjected to gradual forced removal, radially and outwards with respect to nucleus. Within each removal step, the produced work increment is determined and the increments are summed. When no more significant attraction is exerted by nucleus to removed electron, the total work gives the Ionization Energy. After removing of single electron, the remaining electrons fall on a lower shell, that is, they equilibrate on the outer surface of a smaller concentric sphere. For nucleus-electron interaction, an L-J (Lennard-Jones) type curve, attractive and repulsive, is adopted. When the parameter of this curve is n > 1.0, the Ionization Energy exhibits an upper bound. As parameter n increases from 1.0 up to 2.0, the attractive potential of L-J curve is gradually weakened. The proposed model is applied on Argon. It is observed that, as the number of electrons increases, the radius of equilibrium sphere increases, too, whereas the attractive nucleus-electron potential is reduced;thus the Ionization Energy is reduced, too. Particularly, as the number of electrons and the radius of equilibrium sphere exceed some critical values, the above two last quantities exhibit abrupt falls. A regular polyhedron is revealed, which can accommodate Elements up to atomic number Z = 146, that is 28 more than Z = 118 of existing last Element, as guide for initial locations of electrons in the above first program.
文摘In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.
文摘The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.
文摘The Duffing equation describes the oscillations of a damped nonlinear oscillator [1]. Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited e.g. oscillations of a theoretical weightless-spring. We propose generalizing the mathematical features of the Duffing equation by including in addition to the cubic term unlimited number of odd powers of coordinate-dependent terms. The proposed generalization describes a true mass-less magneto static-spring capable of performing highly non-linear oscillations. The equation describing the motion is a super non-linear ODE. Utilizing Mathematica [2] we solve the equation numerically displaying its time series. We investigate the impact of the proposed generalization on a handful of kinematic quantities. For a comprehensive understanding utilizing Mathematica animation we bring to life the non-linear oscillations.
基金supported by the National Natural Science Foundation of China (11172138, 10727201)
文摘This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.
基金National Natural Science Foundation of China(Nos.11172025,91116005)Research Fund for the Doctoral Program of Higher Education of China(No.20091102110015)
文摘A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.
文摘This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.
基金funded by the National Natural Science Foundation of China (No. 51579245)the National Key R&D Program of China (No. 2016YFC0303 800)
文摘The compliant vertical access riser (CVAR) is a new riser concept with good compliance;it can significantly reduce operating costs by eliminating the need for additional machines to operate wells directly on the platform.In this study,we determined the optimal riser parameters in terms of the stress and riser weight by optimizing the CVAR,and we compared the optimization resuits.A two-dimensional nonlinear static CVAR model was deduced according to the principles of virtual work and variation,and the model was verified using MATLAB.Design of experiments and Kriging method were used to reduce the number of sample calculations and improve the modeling accuracy.An appropriate selection of the multi-objective optimization problem (MOP) and the non-dominated sorting genetic algorithm helped to optimize the CVAR design.The non-dominated sorting genetic algorithm Ⅱ was used to solve the Pareto frontier of the optimization model in order to provide decision makers with more choices for the optimization results.After optimizing the riser parameters,the geometry of the riser was smoother,and the stress and stress differences were greatly reduced;the maximum equivalent stresses at the top and bottom were reduced by 36.6% and 44%,respectively.In addition,the stress difference in the buoyancy block area was reduced by 20.9%,and the weight of the riser was increased significantly by 28.1%.
文摘According to the purpose of the opening and the structural designer, the shape of the web opening is decided. It is too easy to choose the shape of openings from regular shape whether it is circular or rectangular shape. The presence of openings in the web of steel beams decreases stiffness of the beam and introducing a larger deflection than in the steel web opening with solid opening. A steel beam with web opening is analyzed in this paper. ABAQUS software is using for analyzing nonlinear static and dynamic opening of steel beam with different position and supporting conditions.
基金supported by the National Natural Science Foundation of China (60574011)
文摘The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.
文摘利用线性弹簧斜向布置的几何非线性产生非线性恢复力,提出了引入非线性恢复力的水下涡激振动(VIV)发电系统.该系统通过单向轴承、齿轮齿条机构、增速箱和转子发电机,将钝体横向往复运动转变为发电机的单向旋转运动.建立了综合考虑流-固-电耦合的水下涡激振动发电系统动力学方程,利用非线性振动理论,获得了钝体非线性振动的静态平衡点分岔和不同稳态运动的区间,重点研究了PF-2SN和2PF-2SN两种静态分岔情况下钝体的非线性动力学行为,获得了不同流速下钝体振动的Poincaré映射、相图和幅频图,分析了钝体在单周期小幅运动、大幅混沌运动和准周期大幅运动等运动模式下的振动行为及运动规律,并计算了在钝体处于不同稳态运动时的发电机功率.结果表明:在PF-2SN分岔方式中,系统处于二稳态运动时的振动和发电具有明显优势,平均振幅比为2.18、发电功率最大值为24.45 W.而在2PF-2SN分岔方式中,系统处于三稳态运动时的振动和发电更具优势,平均振幅比为1.98、发电功率最大值为18.32 W.
文摘An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.
基金Project(KYLX15_0256)supported by the Funding of Jiangsu Innovation Program for Graduate Education,ChinaProject(SV2015-KF-01)supported by the Open Project of State Key Laboratory for Strength and Vibration of Mechanical Structures,ChinaProject(XZA15003)supported by the Fundamental Research Funds for the Central Universities,China
文摘The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.
文摘For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.
文摘This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.
