Drill string vibration during drilling plays a vital and potentially decisive role in maintaining wellbore stability,as repeated impacts may lead to fatigue and borehole collapse.While drilling through geological laye...Drill string vibration during drilling plays a vital and potentially decisive role in maintaining wellbore stability,as repeated impacts may lead to fatigue and borehole collapse.While drilling through geological layers,a material contrast may act as a localization point for wellbore damage.The hypothesis tested in this paper is that wellbore instability is focused on the boundary between the layers and that mechanical contrasts accelerate the wellbore collapse.In this study,an elastic-plastic damage model was employed to investigate the effects of repeated mechanical impacts on wellbore stability.A 2-dimensional(2D)model of a wellbore surrounded by contrasting materials was developed,and the accumulated damage caused by repeated lateral impacts was monitored.It was found that damage develops not only around the wall of the wellbore but also along the material boundaries.A sensitivity analysis was carried out to identify the impact of contrasts in both elastic(Young's modulus and Poisson's ratio)and plastic(cohesion,friction angle,and dilation angle)parameters between layers.Four damage patterns were identifiedin the simulated models.The results also suggested that the number of impacts required to reach the critical damage was highly affected by the contrast in elastic parameters,while cohesion and friction angle contrasts had a lesser effect.Additionally,increasing the contrast in the dilation angle localized the damage,thus reducing the number of impacts required to trigger wellbore failure.展开更多
The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected s...The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.展开更多
Detailed information is provided for the design and construction of nitrogen drilling in a coal seam.Two prototype wells are considered.The Guo model is used to calculate the required minimum gas injection rate,while ...Detailed information is provided for the design and construction of nitrogen drilling in a coal seam.Two prototype wells are considered.The Guo model is used to calculate the required minimum gas injection rate,while the Finnie,Sommerfeld,and Tulsa models are exploited to estimate the ensuing erosion occurring in pipe strings.The calculated minimum gas injection rates are 67.4 m^(3)/min(with water)and 49.4 m^(3)/min(without water),and the actual field of use is 90–120 m^(3)/min.The difference between the calculated injection pressure and the field value is 6.5%–15.2%(formation with water)and 0.65%–7.32%(formation without water).The results show that the Guo model can more precisely represent the situation of the no water formation in the nitrogen drilling of a coal seam.The Finnie,Sommerfeld,and Tulsa models have different sensitivities to cutting densities,particle size,impact velocity and angle,and pipe string hardness.展开更多
This paper develops a functional relation between Digital Libraries and Confucion Integrated Curriculum Learning systems. We show that under certain properties of Learning Systems which can implement laissez-faire mar...This paper develops a functional relation between Digital Libraries and Confucion Integrated Curriculum Learning systems. We show that under certain properties of Learning Systems which can implement laissez-faire markets under uncertainty, the systems integration is possible in entropy space.展开更多
Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-represent...Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-representation is either a string representation or a band representation by using the coefficient quivers.It is worth noting that for a given band and a positive integer,there exists a unique band representation up to isomorphism.展开更多
A new phenomenological model(axionic QCD string)is constructed to study the topological issues of the QCD vacuum and hadron structure.It provides an alternative way of tackling the Strong CP problem,which is different...A new phenomenological model(axionic QCD string)is constructed to study the topological issues of the QCD vacuum and hadron structure.It provides an alternative way of tackling the Strong CP problem,which is different from the traditional Peccei–Quinn approach.Neither new particle nor extra symmetry is introduced,and the role of the Peccei–Quinn axion is played by a quasiparticle arising from the phase of the quark condensate,dubbed as axionic excitation.The derivative of this excitation field is decomposed into a regular part and a singular part,and the latter contains vorticity from the string configuration.A hidden gauge symmetry is revealed in this decomposition and vorticity is represented by an emergent gauge field associated with anomalies.These components,together with the anomaly-inflow mechanism,complete the effective Lagrangian description for the axionic QCD string.展开更多
In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the...In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes(QNMs)and shadow cast.To do this,we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins:massless scalar field,electromagnetic field and gravitational field.Then,using the sixth-order Wentzel-Kramers-Brillouin approximation,we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies.The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored.We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius.Interestingly,the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius.Finally,we employ observational data from Sgr A^(*) and M87^(*) to set limitations on the BH parameters.展开更多
In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue...In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.展开更多
During drilling operations,cyclic loading is exerted on the wellbore wall by the vibrations of the drill string.This loading could lead to rock fatigue,which in turn might result in wellbore failure.In this study,a nu...During drilling operations,cyclic loading is exerted on the wellbore wall by the vibrations of the drill string.This loading could lead to rock fatigue,which in turn might result in wellbore failure.In this study,a numerical model is developed to simulate the effects of repeated loading on rock fatigue and failure.The simulation is based on an elasto-plastic constitutive model coupled with a damage mechanics approach,which allows us to examine the wellbore instability due to drill string vibrations.The model is verified with the existing data in the literature related to experiments on impact of a steel ball against a curved wall.The findings indicate that cyclic loading increases the development of plastic strain around the wellbore significantly compared to static conditions,promoting rock fatigue.Furthermore,the cyclic loading expands the radius of the yielded zone substantially,a critical factor for maintaining wellbore integrity.The proposed model can be used to evaluate the wellbore stability under repetitive loading caused by the drill string action.展开更多
The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of dril...The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.展开更多
This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing(2006)and an expanded version of these lectures given at the Third Summer School on Strings,...This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing(2006)and an expanded version of these lectures given at the Third Summer School on Strings,Fields and Holography in Nanjing(2023).It aims to provide both a historical and pedagogical account of developments in finding 1/2 Bogomol?nyi–Prasad–Sommerfield(BPS)extended string solitons during the early stage of the so-called second string revolution,before which these objects were thought to be unrelated to strings.Nonsupersymmetric solutions related to brane/anti brane systems or non-BPS systems are also discussed.展开更多
In this work we study gravitational lensing of the wormhole in the Eddington-inspired Born–Infeld(EiBI)spacetime that incorporates with a cosmic string.It is found that the presence of a cosmic string can enhance the...In this work we study gravitational lensing of the wormhole in the Eddington-inspired Born–Infeld(EiBI)spacetime that incorporates with a cosmic string.It is found that the presence of a cosmic string can enhance the light deflection in the strong-field limit,compared to the Ellis–Bronnikov wormhole.The magnification effects of this composite structure could cause some substantial impacts on the angle separation between the first and the rest of the images,and their relative brightness.Furthermore,based on these observables,we model some observable aspects in the strong-and the weak-field limits.The presence of a cosmic string can affect some distinguishable observables compared to the wormhole without cosmic string.This work could deepen our understanding of the spacetime structure of the wormhole in EiBI spacetime with one-dimensional topological defects.展开更多
The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated.It is shown that the phase boundaries of the three phases in th...The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated.It is shown that the phase boundaries of the three phases in the model can be determined precisely,in line with the precision of its ground-state energy.Numerical calculations using the regularized time-evolving block decimation(rTEBD)algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits.Moreover,we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure,which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.展开更多
提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特...提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特征索引表设计了一个分类器,待检查的句子通过此分类器被分配到某个负实例特征表里进行匹配搜索,而此特征表的特征属性数和记录数要远远小于原始负实例数据库中的相应数目,从而大大提高了检查的速度,同时不影响语法检查的精度。通过比较测试,可看出提出的方法在保证语法检查精确度的同时有更快的速度。展开更多
This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation...This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.展开更多
基金support from the Research Council of Norway,Equinor,and Sekal with NFR project(Grant No.308826).
文摘Drill string vibration during drilling plays a vital and potentially decisive role in maintaining wellbore stability,as repeated impacts may lead to fatigue and borehole collapse.While drilling through geological layers,a material contrast may act as a localization point for wellbore damage.The hypothesis tested in this paper is that wellbore instability is focused on the boundary between the layers and that mechanical contrasts accelerate the wellbore collapse.In this study,an elastic-plastic damage model was employed to investigate the effects of repeated mechanical impacts on wellbore stability.A 2-dimensional(2D)model of a wellbore surrounded by contrasting materials was developed,and the accumulated damage caused by repeated lateral impacts was monitored.It was found that damage develops not only around the wall of the wellbore but also along the material boundaries.A sensitivity analysis was carried out to identify the impact of contrasts in both elastic(Young's modulus and Poisson's ratio)and plastic(cohesion,friction angle,and dilation angle)parameters between layers.Four damage patterns were identifiedin the simulated models.The results also suggested that the number of impacts required to reach the critical damage was highly affected by the contrast in elastic parameters,while cohesion and friction angle contrasts had a lesser effect.Additionally,increasing the contrast in the dilation angle localized the damage,thus reducing the number of impacts required to trigger wellbore failure.
文摘The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the stares of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.
基金National Science and Technology Major Special Project,2016ZX05044CBM Development Technology and Pilot Test in East Yunnan and Western Guizhou.
文摘Detailed information is provided for the design and construction of nitrogen drilling in a coal seam.Two prototype wells are considered.The Guo model is used to calculate the required minimum gas injection rate,while the Finnie,Sommerfeld,and Tulsa models are exploited to estimate the ensuing erosion occurring in pipe strings.The calculated minimum gas injection rates are 67.4 m^(3)/min(with water)and 49.4 m^(3)/min(without water),and the actual field of use is 90–120 m^(3)/min.The difference between the calculated injection pressure and the field value is 6.5%–15.2%(formation with water)and 0.65%–7.32%(formation without water).The results show that the Guo model can more precisely represent the situation of the no water formation in the nitrogen drilling of a coal seam.The Finnie,Sommerfeld,and Tulsa models have different sensitivities to cutting densities,particle size,impact velocity and angle,and pipe string hardness.
文摘This paper develops a functional relation between Digital Libraries and Confucion Integrated Curriculum Learning systems. We show that under certain properties of Learning Systems which can implement laissez-faire markets under uncertainty, the systems integration is possible in entropy space.
文摘Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-representation is either a string representation or a band representation by using the coefficient quivers.It is worth noting that for a given band and a positive integer,there exists a unique band representation up to isomorphism.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2022J011130)the Research Starting Grant from Minjiang University(Grant No.30804317)。
文摘A new phenomenological model(axionic QCD string)is constructed to study the topological issues of the QCD vacuum and hadron structure.It provides an alternative way of tackling the Strong CP problem,which is different from the traditional Peccei–Quinn approach.Neither new particle nor extra symmetry is introduced,and the role of the Peccei–Quinn axion is played by a quasiparticle arising from the phase of the quark condensate,dubbed as axionic excitation.The derivative of this excitation field is decomposed into a regular part and a singular part,and the latter contains vorticity from the string configuration.A hidden gauge symmetry is revealed in this decomposition and vorticity is represented by an emergent gauge field associated with anomalies.These components,together with the anomaly-inflow mechanism,complete the effective Lagrangian description for the axionic QCD string.
基金supported by the National Natural Science Foundation of China under Grant No.11675143the National Key Research and Development Program of China under Grant No.2020YFC2201503。
文摘In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes(QNMs)and shadow cast.To do this,we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins:massless scalar field,electromagnetic field and gravitational field.Then,using the sixth-order Wentzel-Kramers-Brillouin approximation,we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies.The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored.We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius.Interestingly,the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius.Finally,we employ observational data from Sgr A^(*) and M87^(*) to set limitations on the BH parameters.
文摘In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.
基金funded by the Research council of Norway,Equinor and Sekal with NFR(Grant No.308826).
文摘During drilling operations,cyclic loading is exerted on the wellbore wall by the vibrations of the drill string.This loading could lead to rock fatigue,which in turn might result in wellbore failure.In this study,a numerical model is developed to simulate the effects of repeated loading on rock fatigue and failure.The simulation is based on an elasto-plastic constitutive model coupled with a damage mechanics approach,which allows us to examine the wellbore instability due to drill string vibrations.The model is verified with the existing data in the literature related to experiments on impact of a steel ball against a curved wall.The findings indicate that cyclic loading increases the development of plastic strain around the wellbore significantly compared to static conditions,promoting rock fatigue.Furthermore,the cyclic loading expands the radius of the yielded zone substantially,a critical factor for maintaining wellbore integrity.The proposed model can be used to evaluate the wellbore stability under repetitive loading caused by the drill string action.
基金supported by the National Natural Science Foundation of China(52174003,52374008).
文摘The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.
基金the support by grants from the NNSF of China with Grant Nos.12275264 and 12247103。
文摘This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing(2006)and an expanded version of these lectures given at the Third Summer School on Strings,Fields and Holography in Nanjing(2023).It aims to provide both a historical and pedagogical account of developments in finding 1/2 Bogomol?nyi–Prasad–Sommerfield(BPS)extended string solitons during the early stage of the so-called second string revolution,before which these objects were thought to be unrelated to strings.Nonsupersymmetric solutions related to brane/anti brane systems or non-BPS systems are also discussed.
基金supported by the Youth Program of the Natural Science Foundation of Guangxi(Grant No.2021GXNSFBA075049)the Doctor Start-up Foundation of Guangxi University of Science and Technology(Grant No.19Z21)+3 种基金supported by the National Natural Science Foundation of China(Grant No.12165009)supported by the National Natural Science Foundation of China(Grant No.11865005)Hunan Natural Provincial Science Foundation(Grant No.2023JJ30487)supported by the starting Foundation of Guangxi University of Science and Technology(Grant No.24Z17)。
文摘In this work we study gravitational lensing of the wormhole in the Eddington-inspired Born–Infeld(EiBI)spacetime that incorporates with a cosmic string.It is found that the presence of a cosmic string can enhance the light deflection in the strong-field limit,compared to the Ellis–Bronnikov wormhole.The magnification effects of this composite structure could cause some substantial impacts on the angle separation between the first and the rest of the images,and their relative brightness.Furthermore,based on these observables,we model some observable aspects in the strong-and the weak-field limits.The presence of a cosmic string can affect some distinguishable observables compared to the wormhole without cosmic string.This work could deepen our understanding of the spacetime structure of the wormhole in EiBI spacetime with one-dimensional topological defects.
基金supported by the National Natural Science Foundation of China(Grant No.12471443).
文摘The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated.It is shown that the phase boundaries of the three phases in the model can be determined precisely,in line with the precision of its ground-state energy.Numerical calculations using the regularized time-evolving block decimation(rTEBD)algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits.Moreover,we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure,which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.
文摘提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特征索引表设计了一个分类器,待检查的句子通过此分类器被分配到某个负实例特征表里进行匹配搜索,而此特征表的特征属性数和记录数要远远小于原始负实例数据库中的相应数目,从而大大提高了检查的速度,同时不影响语法检查的精度。通过比较测试,可看出提出的方法在保证语法检查精确度的同时有更快的速度。
文摘This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.
