The temperature distribution in laminated beams underging thermal boundary conditions has been investigated.The thermal boundary conditions are general and include various combinations of prescribed heat fluxes and te...The temperature distribution in laminated beams underging thermal boundary conditions has been investigated.The thermal boundary conditions are general and include various combinations of prescribed heat fluxes and temperatures at the edges.An analytical solution of temperature for the laminated beam is present on the basis of the heat conduction theory in this paper.The proposed method is applicable to the beams with arbitrary thickness and layer numbers.Due to the complexity of the boundary conditions,the temperature field to be determined was considered from two sources.The first part was the temperature field from the complex temperature conditions at two edges of the laminated beam.The solution for the temperature of the first part was constructed to satisfy temperature boundary conditions at two edges.The second part was the temperature field from the upper and lower surface temperatures without taking account of the thermal conditions at two edges.In this part,the exact solution for the temperature was obtained based on the heat conduction theory.The convergence of the solution was examined by analyzing terms of Fourier series.The validity and feasibility of the proposed method was verified by comparing theoretical results with numerical results due to the equivalent single layer approach and the finite element method(FEM).The influences of surface temperatures,beam thicknesses,layer numbers and material properties with respects to the solution of the temperature field of the beam were investigated via a series of parametric studies.展开更多
Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which ca...Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.展开更多
If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become s...If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.展开更多
A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of tra...A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.展开更多
Beam structures are extensively used in many engineering branches.For marine engineering,the ship shafting system is generally simplified as a vibration model with single or multiple beam structures connected by the c...Beam structures are extensively used in many engineering branches.For marine engineering,the ship shafting system is generally simplified as a vibration model with single or multiple beam structures connected by the coupling stiffness.In engineering,multiple nonlinear energy sinks(NESs)can be arranged on the premise of sufficient installation space to ensure their vibration suppression effect.Considering engineering practice,this study investigates the dynamic behavior and vibration suppression of a generally restrained pre-pressure beam structure with multiple uniformly distributed NESs,where the prepressure is typically caused by thrust bearings,installation ways,and others.System governing equations are derived through the generalized Hamiltonian principle and the variational procedure.Dynamic responses of the pre-pressure beam structure are predicted by the Galerkin truncation method.The effect of NESs on dynamic responses and vibration suppression of the pre-pressure beam structure is studied and discussed.Suitable parameters of NESs have a beneficial effect on the vibration suppression at both ends of the pre-pressure beam structure.NESs can modify the vibration frequency and energy transmission characteristics of the vibration system.For different boundary conditions,the optimized parameters of NESs significantly suppress the vibration energy of the pre-pressure beam structure.展开更多
This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak so...This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.展开更多
In this article,we discuss the approach to solving a nonlinear PDE equation,specifically the p-Laplacian equation,with a general(nonlinear)boundary condition.We establish the existence and uniqueness of the solution,s...In this article,we discuss the approach to solving a nonlinear PDE equation,specifically the p-Laplacian equation,with a general(nonlinear)boundary condition.We establish the existence and uniqueness of the solution,subject to certain assumptions outlined in this paper.To solve our nonlinear problem using the Finite Element Method(FEM),we derive an appropriate variational formulation.Additionally,we introduce a study of the residual a posteriori-error indicator,establishing both upper and lower bounds to control the error.The upper bound is determined using averaging interpolators in some quasi-norms defined by Barrett and Liu.Furthermore,we prove the equivalence between the residual error and the true error e=u−u_(h).Lastly,we perform a simulation of the p-Laplacian problem in the L-shape domain using a Matlab program in two-dimensional space.展开更多
In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solutio...In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solution is solved using the Jacobi-Ritz method.The boundary conditions(BCs)at both ends of the CLCB are generalized by the application of artificial elastic springs,the CLCB is separated into two elements along the crack,the flexibility coefficient of fracture theory is used to model the essential continuous condition of the connective interface.All the allowable displacement functions used to analyze dynamic characteristics of CLCB are expressed by classical Jacobi orthogonal polynomials in a more general form.The accuracy of the proposed method is verified through the compare with results of the finite element method(software ABAQUS is used in this paper).On this basis,the parametric study for dynamic analysis characteristics of CLCB is performed to provide reference datum for engineers.展开更多
基金Projects(52108148,51878319,51578267)supported by the National Natural Science Foundation of ChinaProject(2021M701483)supported by the China Postdoctoral Research Funding Program+1 种基金Project(2021K574C)supported by the Jiangsu Postdoctoral Research Funding Program,ChinaProject(BK20190833)supported by the Natural Science Foundation of Jiangsu Province,China。
文摘The temperature distribution in laminated beams underging thermal boundary conditions has been investigated.The thermal boundary conditions are general and include various combinations of prescribed heat fluxes and temperatures at the edges.An analytical solution of temperature for the laminated beam is present on the basis of the heat conduction theory in this paper.The proposed method is applicable to the beams with arbitrary thickness and layer numbers.Due to the complexity of the boundary conditions,the temperature field to be determined was considered from two sources.The first part was the temperature field from the complex temperature conditions at two edges of the laminated beam.The solution for the temperature of the first part was constructed to satisfy temperature boundary conditions at two edges.The second part was the temperature field from the upper and lower surface temperatures without taking account of the thermal conditions at two edges.In this part,the exact solution for the temperature was obtained based on the heat conduction theory.The convergence of the solution was examined by analyzing terms of Fourier series.The validity and feasibility of the proposed method was verified by comparing theoretical results with numerical results due to the equivalent single layer approach and the finite element method(FEM).The influences of surface temperatures,beam thicknesses,layer numbers and material properties with respects to the solution of the temperature field of the beam were investigated via a series of parametric studies.
基金This subject was partly supported by the National Excellent Youth Foundation of China (Grant No. 49825161)
文摘Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51079082 and 40676053)the LRET through the joint centre involving University College London,Shanghai JiaoTong University and Harbin Engineering University
文摘If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.
基金Project supported by the National Natural Science Foundation of China(Nos.51805250 and 11602145)the Natural Science Foundation of Jiangsu Province of China(No.BK20180429)+1 种基金the China Postdoctoral Science Foundation(No.2019M660114)the Jiangsu Planned Projects for Postdoctoral Research Funds of China(No.2019K054)。
文摘A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.
基金supported by the National Natural Science Foundation of China(Grant No.11972125)the Fok Ying Tung Education Foundation(Grant No.161049).
文摘Beam structures are extensively used in many engineering branches.For marine engineering,the ship shafting system is generally simplified as a vibration model with single or multiple beam structures connected by the coupling stiffness.In engineering,multiple nonlinear energy sinks(NESs)can be arranged on the premise of sufficient installation space to ensure their vibration suppression effect.Considering engineering practice,this study investigates the dynamic behavior and vibration suppression of a generally restrained pre-pressure beam structure with multiple uniformly distributed NESs,where the prepressure is typically caused by thrust bearings,installation ways,and others.System governing equations are derived through the generalized Hamiltonian principle and the variational procedure.Dynamic responses of the pre-pressure beam structure are predicted by the Galerkin truncation method.The effect of NESs on dynamic responses and vibration suppression of the pre-pressure beam structure is studied and discussed.Suitable parameters of NESs have a beneficial effect on the vibration suppression at both ends of the pre-pressure beam structure.NESs can modify the vibration frequency and energy transmission characteristics of the vibration system.For different boundary conditions,the optimized parameters of NESs significantly suppress the vibration energy of the pre-pressure beam structure.
文摘This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.
基金the National Natural Science Foundation of China(No.51505445)the Key Subject“Computational Solid Mechanics”of the China Academy of Engineering Physics
文摘In this article,we discuss the approach to solving a nonlinear PDE equation,specifically the p-Laplacian equation,with a general(nonlinear)boundary condition.We establish the existence and uniqueness of the solution,subject to certain assumptions outlined in this paper.To solve our nonlinear problem using the Finite Element Method(FEM),we derive an appropriate variational formulation.Additionally,we introduce a study of the residual a posteriori-error indicator,establishing both upper and lower bounds to control the error.The upper bound is determined using averaging interpolators in some quasi-norms defined by Barrett and Liu.Furthermore,we prove the equivalence between the residual error and the true error e=u−u_(h).Lastly,we perform a simulation of the p-Laplacian problem in the L-shape domain using a Matlab program in two-dimensional space.
文摘In this paper,a semi-analytical method for the forced vibration analysis of cracked laminated composite beam(CLCB)is investigated.One computational model is formulated by Timoshenko beam theory and its dynamic solution is solved using the Jacobi-Ritz method.The boundary conditions(BCs)at both ends of the CLCB are generalized by the application of artificial elastic springs,the CLCB is separated into two elements along the crack,the flexibility coefficient of fracture theory is used to model the essential continuous condition of the connective interface.All the allowable displacement functions used to analyze dynamic characteristics of CLCB are expressed by classical Jacobi orthogonal polynomials in a more general form.The accuracy of the proposed method is verified through the compare with results of the finite element method(software ABAQUS is used in this paper).On this basis,the parametric study for dynamic analysis characteristics of CLCB is performed to provide reference datum for engineers.
