For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matr...For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matrix which is a highly nonlinear function of the eigenvalues.Therefore,classical strategies for sensitivity analysis of eigenvalues w.r.t.system parameters cannot be applied.The paper develops two specific strategies for this situation,a direct differentiation strategy and an adjoint variable method,where especially the latter is easy to use and applicable to arbitrarily complex chain or branched multibody systems.Like the system analysis itself,it is able to break down the sensitivity analysis of the overall system to analytically determinable derivatives of element transfer matrices and recursive formula which can be applied along the transfer path of the topology figure.Several examples of different complexity validate the proposed approach by comparing results to analytical calculations and numerical differentiation.The obtained procedure may support gradient‐based optimization and robust design by delivering exact sensitivities.展开更多
In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typica...In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t.various types of outboard body's output links.This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper.Systematic procedures for chain,tree,closed-loop,and arbitrary general systems are defined,respectively,to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process.As a result,accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.展开更多
文摘For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matrix which is a highly nonlinear function of the eigenvalues.Therefore,classical strategies for sensitivity analysis of eigenvalues w.r.t.system parameters cannot be applied.The paper develops two specific strategies for this situation,a direct differentiation strategy and an adjoint variable method,where especially the latter is easy to use and applicable to arbitrarily complex chain or branched multibody systems.Like the system analysis itself,it is able to break down the sensitivity analysis of the overall system to analytically determinable derivatives of element transfer matrices and recursive formula which can be applied along the transfer path of the topology figure.Several examples of different complexity validate the proposed approach by comparing results to analytical calculations and numerical differentiation.The obtained procedure may support gradient‐based optimization and robust design by delivering exact sensitivities.
基金This work was performed at the Brandenburg University of Technology(BTU Cottbus-Senftenberg)and supported by the National Major Project of the Chinese Government(No.2017JCJQ-ZD-005)the National Natural Science Foundation of China(No.11472135)+1 种基金a Scholarship by the Chinese Scholarship Council of the Ministry of Education of China(No.201708080083)the Nanjing University of Science and Technology International Joint Training Scholarship.
文摘In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t.various types of outboard body's output links.This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper.Systematic procedures for chain,tree,closed-loop,and arbitrary general systems are defined,respectively,to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process.As a result,accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.
