The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical ...The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.展开更多
We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is...We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is how to handle with the nonlocal nonlinear damping term.Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso(Evolution Equation and Control Theory,2017(6):437-470)and Narciso(Evolution Equations and Control Theory,2020,9(2):487-508).展开更多
This paper is concerned with the asymptotic behavior of a quasilinear vis-coelastic equation with nonlinear damping and memory.Assuming that the kernelμ(s)satisfies 3 u'(s)≤-kiμ^(m)(s),1≤m<3/2 we establish ...This paper is concerned with the asymptotic behavior of a quasilinear vis-coelastic equation with nonlinear damping and memory.Assuming that the kernelμ(s)satisfies 3 u'(s)≤-kiμ^(m)(s),1≤m<3/2 we establish the exponential stability result for m=1 and the polynomial stability result for1<m<3/2.展开更多
Strongly nonlinear characteristics of ship roll owing to viscous effect can be usually observed. To describe the nonlinear roll behavior, the CFD method has been frequently employed with obvious advantages compared wi...Strongly nonlinear characteristics of ship roll owing to viscous effect can be usually observed. To describe the nonlinear roll behavior, the CFD method has been frequently employed with obvious advantages compared with the traditional semi-empirical formula method in estimating the roll damping. Numerical simulations of free decay and forced rolling at various forward speeds and amplitudes for a 3-D ship hull are conducted in the present research to predict ship roll damping, in which a RANS solver is employed and a dynamic mesh technique is adopted and discussed in detail. Numerical results, including nonlinear flow characters around ships, rolling decay curves and damping coefficients, show that they are all in good agreement with available experimental data. The linear and nonlinear damping coefficients are estimated and analyzed by fitting with exponential functions for various rolling amplitudes, frequencies and speeds in the free decay simulations, and the damping coefficients are obtained by a polynomial fitting in the forced roll simulations. It is indicated that the damping coefficients increase with increasing rolling angle amplitude and velocity. It is also emphasized that the effect of forward speed is significant to roll damping and the nonlinear damping decreases with increasing velocity.展开更多
In this paper, we will show that under some smallness conditions, the planar diffusion wave v(x1/√+t)is stable for a quasilinear wave equation with nonlinear damping:vtt-△f(v)+vt+g(vt)=0_3 x=(x1,x2…,xn)...In this paper, we will show that under some smallness conditions, the planar diffusion wave v(x1/√+t)is stable for a quasilinear wave equation with nonlinear damping:vtt-△f(v)+vt+g(vt)=0_3 x=(x1,x2…,xn)∈Rn,where v(x1/√1+t)is the unique similar solution to the one dimensional nonlinear heat equa-tion:vt-f(v)x1 x1=0,f'(v)〉0,v+(∞,t)=v±,v+≠v_.We also obtain the L∞ time decay rate whichreads‖v-v‖L∞=О(1)(1+t)-r/4,where r=min(3,n).To get the main result, the energy method and a newinequality have been used.展开更多
A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance.In this paper,a generalized vibration isolation system is established with nonlinear stiffness,nonlinear ...A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance.In this paper,a generalized vibration isolation system is established with nonlinear stiffness,nonlinear viscous damping,and Bouc-Wen(BW)hysteretic damping.An approximate analytical analysis is performed based on a harmonic balance method(HBM)and an alternating frequency/time(AFT)domain technique.To evaluate the damping effect,a generalized equivalent damping ratio is defined with the stiffness-varying characteristics.A comprehensive comparison of different kinds of damping is made through numerical simulations.It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes.The linear damping,hysteretic damping,and nonlinear viscous damping are suitable for the small-amplitude,medium-amplitude,and large-amplitude conditions,respectively.The hysteretic damping has an extra advantage of broadband isolation.展开更多
In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetr...In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.展开更多
This paper deals with an initial boundary value problem for a class of nonlinear wave equation with nonlinear damping and source terms whose solution may blow up in finite time.An explicit lower bound for blow up time...This paper deals with an initial boundary value problem for a class of nonlinear wave equation with nonlinear damping and source terms whose solution may blow up in finite time.An explicit lower bound for blow up time is determined by means of a differential inequality argument if blow up occurs.展开更多
The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding p...The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation,the convergence rates of the new profile are better than that obtained by Nishihara(1997,J.Differential Equations 137,384-395) and H.-J.Zhao(2000,J.Differential Equations 167,467-494).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
In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom (MDOF) structures, in which an isolator with nonlinear anti-symmetri...In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom (MDOF) structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.展开更多
Bulk ion heating rate from nonlinear Landau damping of high mode number Toroidal Alfven Eigenmodes (TAEs) is calculated in the frame work of weak turbulence theory. The heating rate is lower than the nonlinear spect...Bulk ion heating rate from nonlinear Landau damping of high mode number Toroidal Alfven Eigenmodes (TAEs) is calculated in the frame work of weak turbulence theory. The heating rate is lower than the nonlinear spectral transfer rate to more stable modes, but relatively insensitive to the details of linear damping mechanisms.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations ...Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized (r, q) distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k +1, it reduces to the kappa distribution function.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p(t) and q(t) are allowed to change sign on [t0,∞).
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia...In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E(0) 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E(0) 〈 0.展开更多
Nonlinearity can take an important and critical role in engineering systems,and thus cannot be simply ignored in structural design,dynamic response analysis,and parameter selection.A key issue is how to analyze and de...Nonlinearity can take an important and critical role in engineering systems,and thus cannot be simply ignored in structural design,dynamic response analysis,and parameter selection.A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study.This is a must-do task in many practical applications involving vibration control,energy harvesting,sensor systems,robotic technology,etc.This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years,named as the X-structure/mechanism approach.The method is inspired from animal leg/limb skeletons,and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness(high static&ultra-low dynamic),nonlinear damping(dependent on resonant frequency and/or relative vibration displacement),and nonlinear inertia(low static&high dynamic)individually or simultaneously.The X-structure/mechanism is a generic and basic structure/mechanism,representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion,can be flexibly realized through commonly-used mechanical components,and have many different forms(with a basic unit taking a shape like X/K/Z/S/V,quadrilateral,diamond,polygon,etc.).Importantly,all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration.Moreover,they are generally flexible in design and easy to implement.This paper systematically reviews the research background,motivation,essential bio-inspired ideas,advantages of this novel method,the beneficial nonlinear properties in stiffness,damping,and inertia,and the potential applications,and ends with some remarks and conclusions.展开更多
In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonli...In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.展开更多
An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve. The fourth order Runge-Kutta was applied to calculate th...An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve. The fourth order Runge-Kutta was applied to calculate the damper axial velocity in time domain. Fourier series based moving block analysis was applied to calculate equivalent linear damping in terms of transient responses of damper axial velocity. Results indicate that equivalent linear damping will be significantly reduced if pitch/flap/lag kinematic coupling introduced for notional model and flight conditions.展开更多
The minimization of spurious wave reflection is a challenge in multiscale coupling due to the difference of spatial resolution between atomistic and continuum regions. In this study, a new damping condition is present...The minimization of spurious wave reflection is a challenge in multiscale coupling due to the difference of spatial resolution between atomistic and continuum regions. In this study, a new damping condition is presented for eliminating spurious wave reflection at the interface between atomistic and continuum regions. This damping method starts by a coarse–fine decomposition of the atomic velocity based on the bridging scale method. The fine scale velocity of the atoms in the damping region is reduced by applying nonlinear damping coefficients. The effectiveness of this damping method is verified by one-and two-dimensional simulations.展开更多
基金National Natural Science Foundation of ChinaUnder Grant No. 50578047, 50338020 China Ministry ofEducation (Program for New Century Excellent Talents inUniversity) China Ministry of Science and Technology UnderGrant No.2003AA602150
文摘The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.
基金Supported by National Natural Science Foundation of China(11601122,11801145)。
文摘We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is how to handle with the nonlocal nonlinear damping term.Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso(Evolution Equation and Control Theory,2017(6):437-470)and Narciso(Evolution Equations and Control Theory,2020,9(2):487-508).
基金supported by the Basic Research Project of Guangzhou Science and Technology Plan(No.202201011341).
文摘This paper is concerned with the asymptotic behavior of a quasilinear vis-coelastic equation with nonlinear damping and memory.Assuming that the kernelμ(s)satisfies 3 u'(s)≤-kiμ^(m)(s),1≤m<3/2 we establish the exponential stability result for m=1 and the polynomial stability result for1<m<3/2.
基金Project supported by the National Natural Science Foundation of China(Grant No.50639020)the National High Technology Research and Development Program of China(863Program,Grant No.2006AA09Z332)
文摘Strongly nonlinear characteristics of ship roll owing to viscous effect can be usually observed. To describe the nonlinear roll behavior, the CFD method has been frequently employed with obvious advantages compared with the traditional semi-empirical formula method in estimating the roll damping. Numerical simulations of free decay and forced rolling at various forward speeds and amplitudes for a 3-D ship hull are conducted in the present research to predict ship roll damping, in which a RANS solver is employed and a dynamic mesh technique is adopted and discussed in detail. Numerical results, including nonlinear flow characters around ships, rolling decay curves and damping coefficients, show that they are all in good agreement with available experimental data. The linear and nonlinear damping coefficients are estimated and analyzed by fitting with exponential functions for various rolling amplitudes, frequencies and speeds in the free decay simulations, and the damping coefficients are obtained by a polynomial fitting in the forced roll simulations. It is indicated that the damping coefficients increase with increasing rolling angle amplitude and velocity. It is also emphasized that the effect of forward speed is significant to roll damping and the nonlinear damping decreases with increasing velocity.
基金Supported by the National Natural Science Foundation of China(No.11201301)Shanghai University Young Teacher Training Program(No.slg12026)
文摘In this paper, we will show that under some smallness conditions, the planar diffusion wave v(x1/√+t)is stable for a quasilinear wave equation with nonlinear damping:vtt-△f(v)+vt+g(vt)=0_3 x=(x1,x2…,xn)∈Rn,where v(x1/√1+t)is the unique similar solution to the one dimensional nonlinear heat equa-tion:vt-f(v)x1 x1=0,f'(v)〉0,v+(∞,t)=v±,v+≠v_.We also obtain the L∞ time decay rate whichreads‖v-v‖L∞=О(1)(1+t)-r/4,where r=min(3,n).To get the main result, the energy method and a newinequality have been used.
基金Project supported by the National Natural Science Foundation of China(No.11902097)the China Postdoctoral Science Foundation(No.2019M661266)。
文摘A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance.In this paper,a generalized vibration isolation system is established with nonlinear stiffness,nonlinear viscous damping,and Bouc-Wen(BW)hysteretic damping.An approximate analytical analysis is performed based on a harmonic balance method(HBM)and an alternating frequency/time(AFT)domain technique.To evaluate the damping effect,a generalized equivalent damping ratio is defined with the stiffness-varying characteristics.A comprehensive comparison of different kinds of damping is made through numerical simulations.It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes.The linear damping,hysteretic damping,and nonlinear viscous damping are suitable for the small-amplitude,medium-amplitude,and large-amplitude conditions,respectively.The hysteretic damping has an extra advantage of broadband isolation.
基金supported by the National Science Fund for Distinguished Young Scholars (11125209)the National Natural Science Foundation of China (10732060, 10902068)the EPSRC (UK)
文摘In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.
基金supported by big data and Educational Statistics Application Laboratory(2017WSYS001)Guangdong University of Finance and Economics。
文摘This paper deals with an initial boundary value problem for a class of nonlinear wave equation with nonlinear damping and source terms whose solution may blow up in finite time.An explicit lower bound for blow up time is determined by means of a differential inequality argument if blow up occurs.
基金National Natural Science Foundation of China(No.11301443,11171340)Specialized Research Fund for the Doctoral Program of Higher Education(No.20124301120002)+1 种基金Natural Science Foundation of Hunan Provincial(No.2015JJ3125)Scientific Research Fund of Hunan Provincial Education Department(No.13C935)
文摘The quasilinear hyperbolic equation with nonlinear damping is considered in this paper,a new asymptotic profile for the solution to the equation is obtained by suitably choosing the initial data of the corresponding parabolic equation,the convergence rates of the new profile are better than that obtained by Nishihara(1997,J.Differential Equations 137,384-395) and H.-J.Zhao(2000,J.Differential Equations 167,467-494).
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.
基金supported by the EPSRC (UK)the National Science Fund for Distinguished Young Scholars (11125209)the National Natural Science Foundation of China (10902068 and 51121063)
文摘In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom (MDOF) structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.
基金supported by the Seoul National University Research GrantR&D Program through the National Fusion Research Institute of Korea(NFRI) Funded by the Government Funds
文摘Bulk ion heating rate from nonlinear Landau damping of high mode number Toroidal Alfven Eigenmodes (TAEs) is calculated in the frame work of weak turbulence theory. The heating rate is lower than the nonlinear spectral transfer rate to more stable modes, but relatively insensitive to the details of linear damping mechanisms.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
基金Project supported by the Pakistan Science Foundation Project No.PSF/Res/P-GCU/Phys.(143)the National Natural Science Foundation of China(Grant Nos.41074114 and 41274146)the Specialized Research Fund for State Key Laboratories of China
文摘Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized (r, q) distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k +1, it reduces to the kappa distribution function.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p(t) and q(t) are allowed to change sign on [t0,∞).
文摘In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E(0) 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E(0) 〈 0.
基金the Hong Kong Construction Industry Council R&D Fund of China(No.EPS 202017)the Innovation and Technology Fund of Hong Kong Innovation and Technology Commission of China(No.ITP/020/19AP)。
文摘Nonlinearity can take an important and critical role in engineering systems,and thus cannot be simply ignored in structural design,dynamic response analysis,and parameter selection.A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study.This is a must-do task in many practical applications involving vibration control,energy harvesting,sensor systems,robotic technology,etc.This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years,named as the X-structure/mechanism approach.The method is inspired from animal leg/limb skeletons,and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness(high static&ultra-low dynamic),nonlinear damping(dependent on resonant frequency and/or relative vibration displacement),and nonlinear inertia(low static&high dynamic)individually or simultaneously.The X-structure/mechanism is a generic and basic structure/mechanism,representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion,can be flexibly realized through commonly-used mechanical components,and have many different forms(with a basic unit taking a shape like X/K/Z/S/V,quadrilateral,diamond,polygon,etc.).Importantly,all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration.Moreover,they are generally flexible in design and easy to implement.This paper systematically reviews the research background,motivation,essential bio-inspired ideas,advantages of this novel method,the beneficial nonlinear properties in stiffness,damping,and inertia,and the potential applications,and ends with some remarks and conclusions.
基金Birzeit UniversitySharjah University for their supportsponsored by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.Grant No.2002144089,2019-2020。
文摘In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.
文摘An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve. The fourth order Runge-Kutta was applied to calculate the damper axial velocity in time domain. Fourier series based moving block analysis was applied to calculate equivalent linear damping in terms of transient responses of damper axial velocity. Results indicate that equivalent linear damping will be significantly reduced if pitch/flap/lag kinematic coupling introduced for notional model and flight conditions.
基金the financially support from the Japan Society for the promotion of Science (JSPS) for his fellowship
文摘The minimization of spurious wave reflection is a challenge in multiscale coupling due to the difference of spatial resolution between atomistic and continuum regions. In this study, a new damping condition is presented for eliminating spurious wave reflection at the interface between atomistic and continuum regions. This damping method starts by a coarse–fine decomposition of the atomic velocity based on the bridging scale method. The fine scale velocity of the atoms in the damping region is reduced by applying nonlinear damping coefficients. The effectiveness of this damping method is verified by one-and two-dimensional simulations.