In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thi...In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.展开更多
An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the rea...An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.展开更多
Using the axial symmetry results of marker and cell (MAC) method as initial value in this paper, two numerical calculating methods are presented for the late wavemaking response induced by explosion in harbour. One of...Using the axial symmetry results of marker and cell (MAC) method as initial value in this paper, two numerical calculating methods are presented for the late wavemaking response induced by explosion in harbour. One of the methods is the superposition method of the vibration mode based on fluid slosh in container. Another one is the joining method of the MAC results with the shallow wave theory calculation in time domain. As a practical example, it is conducted to the numerical calculation about 1000 ton TNT equivalent explosion within touch of water surface. The results show that it can be rationally described with the methods to the wavemaking progress and character. The numerical results are identical with the observed scene on the spot experiment. The methods are simple and applicable in the engineering design.展开更多
In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The init...In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The initial values of the impact forces are exactly determined by the momentum conservation law. The propagation of the longitudinal and transverse waves along the beam, especially, the effects of boundary conditions on the characteristics of the reflected waves, are investigated in detail. Some results are compared with those by MSC/NASTRAN.展开更多
The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals ov...The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damp- ing model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.展开更多
This study presents a conceptual design for a cost-effective submersible gravity-type fish cage with a single-point mooring design.The performance of the new design in reducing environmental loads under extreme sea co...This study presents a conceptual design for a cost-effective submersible gravity-type fish cage with a single-point mooring design.The performance of the new design in reducing environmental loads under extreme sea con-ditions is demonstrated using an in-house numerical code package.The effectiveness of the submerging and surfacing operations of the fish cages is validated through numerical simulations.In the present code package,irregular wave modelling is employed to generate the wave elevations,velocities and accelerations,and the hydrodynamic forces acting on the fish cages and mooring system are calculated using the Morison model.A submersible model for the floating collar is developed to simulate the submerging and surfacing operations of the fish cages.The deformations of the fish cage system are calculated using a modified extended position based dynamics(XPBD)method combined with a mode superposition method.Results show that tension in the mooring system is significantly reduced when fish cages are submerged in the water layer with lower current speeds,and extending the buoy line to lower the conjunction point helps maintain fish cages in the desired water layer under extreme sea conditions.Flooding the outer tubes of the floating collar allows the fish cages to smoothly submerge to the desired water depth.The surfacing designs based on the compressed air and the lifting operation of the bottom sinker can enable the cages to ascend to the water surface.The submerging and surface operations are proved to be completed within six minutes.The new design based on the lifting operation of the bottom sinker,is safer and more cost-effective than the design based on compressed air for the surfacing operation.The design of the submersible single-point mooring gravity-type fish cage is thereby validated through the present numerical methods,offering valuable insights for future aquaculture design and implementation.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11872090 and 12172023).
文摘In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.
基金Fund of China National Industrial Building Diagnosis and Reconstruction Engineering Technology Research Center under Grant No.YZA2017Ky03the Beijing Natural Science Foundation under Grant No.JQ18029the National Natural Science Foundation of China under Grant No.52078277。
文摘An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.
基金Subsidized subject financially supported by the National Natural Science Foundation of China
文摘Using the axial symmetry results of marker and cell (MAC) method as initial value in this paper, two numerical calculating methods are presented for the late wavemaking response induced by explosion in harbour. One of the methods is the superposition method of the vibration mode based on fluid slosh in container. Another one is the joining method of the MAC results with the shallow wave theory calculation in time domain. As a practical example, it is conducted to the numerical calculation about 1000 ton TNT equivalent explosion within touch of water surface. The results show that it can be rationally described with the methods to the wavemaking progress and character. The numerical results are identical with the observed scene on the spot experiment. The methods are simple and applicable in the engineering design.
文摘In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The initial values of the impact forces are exactly determined by the momentum conservation law. The propagation of the longitudinal and transverse waves along the beam, especially, the effects of boundary conditions on the characteristics of the reflected waves, are investigated in detail. Some results are compared with those by MSC/NASTRAN.
基金This research was supported by the National Natural Science Foundation of China （Grant No. 51375184）.
文摘The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damp- ing model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.
基金supported by the Research Council of Norway through the project“Unleashing the sustainable value creation potential of offshore ocean aquaculture”(Project number:328724).
文摘This study presents a conceptual design for a cost-effective submersible gravity-type fish cage with a single-point mooring design.The performance of the new design in reducing environmental loads under extreme sea con-ditions is demonstrated using an in-house numerical code package.The effectiveness of the submerging and surfacing operations of the fish cages is validated through numerical simulations.In the present code package,irregular wave modelling is employed to generate the wave elevations,velocities and accelerations,and the hydrodynamic forces acting on the fish cages and mooring system are calculated using the Morison model.A submersible model for the floating collar is developed to simulate the submerging and surfacing operations of the fish cages.The deformations of the fish cage system are calculated using a modified extended position based dynamics(XPBD)method combined with a mode superposition method.Results show that tension in the mooring system is significantly reduced when fish cages are submerged in the water layer with lower current speeds,and extending the buoy line to lower the conjunction point helps maintain fish cages in the desired water layer under extreme sea conditions.Flooding the outer tubes of the floating collar allows the fish cages to smoothly submerge to the desired water depth.The surfacing designs based on the compressed air and the lifting operation of the bottom sinker can enable the cages to ascend to the water surface.The submerging and surface operations are proved to be completed within six minutes.The new design based on the lifting operation of the bottom sinker,is safer and more cost-effective than the design based on compressed air for the surfacing operation.The design of the submersible single-point mooring gravity-type fish cage is thereby validated through the present numerical methods,offering valuable insights for future aquaculture design and implementation.
