The application of the dynamic stiffness method(DSM)for free-vibration analysis of beams is surveyed in this paper.The historical development of the DSM,which has taken place in several stages,is discussed in detail w...The application of the dynamic stiffness method(DSM)for free-vibration analysis of beams is surveyed in this paper.The historical development of the DSM,which has taken place in several stages,is discussed in detail with reference to the free-vibration problems of beams.In particular,the suitability of the DSM in solving the free-vibration problems of beams through the application of the well-known Wittrick–Williams algorithm as a solution technique is highlighted.The literature concerning homogeneous isotropic metallic beams,for which the DSM is well established,is reviewed first,after which,with the rapid and ongoing emergence of advanced composite materials,the development of the DSM in solving the free-vibration problems of anisotropic beams is discussed.The free-vibration analysis of functionally graded beams using the DSM is also highlighted.The survey covers the DSM application for free-vibration analysis of a wide range of beams,including sandwich beams,rotating beams,twisted beams,moving beams and bending-torsion coupled beams,amongst others.Some aspects of the contributions made by the author and his research team are also highlighted.Finally,the future potential of the DSM in solving complex engineering problems is projected.展开更多
The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape...The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.展开更多
This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analyti...This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method(DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and effi ciency are verifi ed in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the infl uences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coeffi cient. Results show that the modal damping ratio is signifi cantly infl uenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.展开更多
In this paper,the stability of a periodic heterogeneous nanotube conveying fluid is investigated.The governing equations of the nanotube system are derived based on the nonlocal Euler-Bernoulli beam theory.The dynamic...In this paper,the stability of a periodic heterogeneous nanotube conveying fluid is investigated.The governing equations of the nanotube system are derived based on the nonlocal Euler-Bernoulli beam theory.The dynamic stiffness method is employed to analyze the natural frequencies and critical flow velocities of the heteronanotube.The results and discussions are presented from three aspects which reveal the influences of period number,material length ratio and boundary conditions.In particular,we make comparisons between the heterogeneous nanotubes with periodic structure and the homogeneous ones with the same integral values of material properties along the longitudinal direction to isolate the influences of periodic distribution.According to the simulation results,we can conclude that with a proper selection of period number in terms of length ratio,the stability of the constructed nanotube can be improved.展开更多
In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material propert...In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.展开更多
The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and acc...The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and accuracy of this model are investigated. Parameter studies are performed; in these studies, the stiffness coefficient, the fluid time step and the processor number are varied under conditions with different numbers of particles and different particle diameters. The obtained results are compared with measurements to derive the optimum parameters for CFD/DEM simulations. The results suggest that the application of higher stiffness coefficients slightly improves the simulation accuracy. However, the average computing time increases exponentially. At larger fluid time steps, the results show that the average computation time is independent of the applied fluid time step whereas the simulation accuracy decreases greatly with increasing the fluid time step. The use of smaller time steps leads to negligible improvements in the simulation accuracy but results in an exponential rise in the average computing time. The parallelization accelerates the DEM simulations if the critical number for the domain decomposition is not reached. Above this number, the performance is no longer proportional to the number of processors. The critical number for the domain decomposition depends on the number of particles. An increase in solid contents results in a shift of the critical decomposition number to higher numbers of CPUs.展开更多
基金the EPSRC(UK)for funding several research projects on dynamic stiffness formulation for structural elements(Grant Refs:GR/R21875/01,EP/F03606X/1,EP/I004904/1 and EP/J007706/1),from which a majority of his publications resulted.
文摘The application of the dynamic stiffness method(DSM)for free-vibration analysis of beams is surveyed in this paper.The historical development of the DSM,which has taken place in several stages,is discussed in detail with reference to the free-vibration problems of beams.In particular,the suitability of the DSM in solving the free-vibration problems of beams through the application of the well-known Wittrick–Williams algorithm as a solution technique is highlighted.The literature concerning homogeneous isotropic metallic beams,for which the DSM is well established,is reviewed first,after which,with the rapid and ongoing emergence of advanced composite materials,the development of the DSM in solving the free-vibration problems of anisotropic beams is discussed.The free-vibration analysis of functionally graded beams using the DSM is also highlighted.The survey covers the DSM application for free-vibration analysis of a wide range of beams,including sandwich beams,rotating beams,twisted beams,moving beams and bending-torsion coupled beams,amongst others.Some aspects of the contributions made by the author and his research team are also highlighted.Finally,the future potential of the DSM in solving complex engineering problems is projected.
基金Project (No. 9040831) supported by the Hong Kong Research GrantCouncil, China
文摘The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.
基金973 Program under Grant under Grant No.2012CB723304It was partially supported by the Major Research Plan of the National Natural Science Foundation of China under Grant No.91315301-07+2 种基金in part by Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT13057the Ministry of Education Program for New Century Excellent Talents in University under Grant No.NCET-11-0914the Guangzhou Ram Scholar Program Grant No.10A032D
文摘This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method(DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and effi ciency are verifi ed in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the infl uences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coeffi cient. Results show that the modal damping ratio is signifi cantly infl uenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.
文摘In this paper,the stability of a periodic heterogeneous nanotube conveying fluid is investigated.The governing equations of the nanotube system are derived based on the nonlocal Euler-Bernoulli beam theory.The dynamic stiffness method is employed to analyze the natural frequencies and critical flow velocities of the heteronanotube.The results and discussions are presented from three aspects which reveal the influences of period number,material length ratio and boundary conditions.In particular,we make comparisons between the heterogeneous nanotubes with periodic structure and the homogeneous ones with the same integral values of material properties along the longitudinal direction to isolate the influences of periodic distribution.According to the simulation results,we can conclude that with a proper selection of period number in terms of length ratio,the stability of the constructed nanotube can be improved.
基金Project supported by the Vietnam National Foundation for Science and Technology Development(No.107.02-2017.301)。
文摘In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.
文摘The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and accuracy of this model are investigated. Parameter studies are performed; in these studies, the stiffness coefficient, the fluid time step and the processor number are varied under conditions with different numbers of particles and different particle diameters. The obtained results are compared with measurements to derive the optimum parameters for CFD/DEM simulations. The results suggest that the application of higher stiffness coefficients slightly improves the simulation accuracy. However, the average computing time increases exponentially. At larger fluid time steps, the results show that the average computation time is independent of the applied fluid time step whereas the simulation accuracy decreases greatly with increasing the fluid time step. The use of smaller time steps leads to negligible improvements in the simulation accuracy but results in an exponential rise in the average computing time. The parallelization accelerates the DEM simulations if the critical number for the domain decomposition is not reached. Above this number, the performance is no longer proportional to the number of processors. The critical number for the domain decomposition depends on the number of particles. An increase in solid contents results in a shift of the critical decomposition number to higher numbers of CPUs.
