As an evaluation index,the natural frequency has the advantages of easy acquisition and quantitative evaluation.In this paper,the natural frequency is used to evaluate the performance of external cable reinforced brid...As an evaluation index,the natural frequency has the advantages of easy acquisition and quantitative evaluation.In this paper,the natural frequency is used to evaluate the performance of external cable reinforced bridges.Numerical examples show that compared with the natural frequencies of first-order modes,the natural frequencies of higher-order modes are more sensitive and can reflect the damage situation and external cable reinforcement effect of T-beam bridges.For damaged bridges,as the damage to the T-beam increases,the natural frequency value of the bridge gradually decreases.When the degree of local damage to the beam reaches 60%,the amplitude of natural frequency change exceeds 10%for the first time.The natural frequencies of the firstorder vibration mode and higher-order vibration mode can be selected as indexes for different degrees of the damaged T-beam bridges.For damaged bridges reinforced with external cables,the traditional natural frequency of the first-order vibration mode cannot be used as the index,which is insensitive to changes in prestress of the external cable.Some natural frequencies of higher-order vibration modes can be selected as indexes,which can reflect the reinforcement effect of externally prestressed damaged T-beam bridges,and its numerical value increases with the increase of external prestressed cable force.展开更多
Based on mathematical orthogonality and mechanical equilibrium,a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials...Based on mathematical orthogonality and mechanical equilibrium,a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials.By aid of this method,the comprehensive deformation energy of planar discrete elastomers can be decomposed into five basic deformation energies,and the comprehensive deformation energy of spatial discrete elastomers can be decomposed into eighteen basic deformation energies.The quantification and visualization of structural deformation performance can be realized.According to the magnitude of different deformation energy in the same element,the decomposition diagram is drawn,which can visually display the area dominated by each basic deformation energy.The cloud diagram is drawn based on the distribution of specific deformation energy in different elements,which can be used to analyze the gradient change of deformation energy in the structure.Finally,the deformation properties of cantilever beam and four-sided consolidation plate are analyzed by deformation energy decomposition method.The correctness and superiority of this method are verified by comparing with the results of strain energy decomposition.展开更多
基金supported by Henan Province Science and Technology Research Funding Project(No.222102320129)the Key Research Project of Henan Higher Education Institutions(Grant Nos.22A560004,22A56005).
文摘As an evaluation index,the natural frequency has the advantages of easy acquisition and quantitative evaluation.In this paper,the natural frequency is used to evaluate the performance of external cable reinforced bridges.Numerical examples show that compared with the natural frequencies of first-order modes,the natural frequencies of higher-order modes are more sensitive and can reflect the damage situation and external cable reinforcement effect of T-beam bridges.For damaged bridges,as the damage to the T-beam increases,the natural frequency value of the bridge gradually decreases.When the degree of local damage to the beam reaches 60%,the amplitude of natural frequency change exceeds 10%for the first time.The natural frequencies of the firstorder vibration mode and higher-order vibration mode can be selected as indexes for different degrees of the damaged T-beam bridges.For damaged bridges reinforced with external cables,the traditional natural frequency of the first-order vibration mode cannot be used as the index,which is insensitive to changes in prestress of the external cable.Some natural frequencies of higher-order vibration modes can be selected as indexes,which can reflect the reinforcement effect of externally prestressed damaged T-beam bridges,and its numerical value increases with the increase of external prestressed cable force.
基金supported by the National Natural Science Foundation of China(Grant Nos.52208322 and 51878621)the Postdoctoral Science Foundation of China(Grant No.2022M712905)the Key Research Projects of Henan Higher Education Institutions(Grant No.22A560005).
文摘Based on mathematical orthogonality and mechanical equilibrium,a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials.By aid of this method,the comprehensive deformation energy of planar discrete elastomers can be decomposed into five basic deformation energies,and the comprehensive deformation energy of spatial discrete elastomers can be decomposed into eighteen basic deformation energies.The quantification and visualization of structural deformation performance can be realized.According to the magnitude of different deformation energy in the same element,the decomposition diagram is drawn,which can visually display the area dominated by each basic deformation energy.The cloud diagram is drawn based on the distribution of specific deformation energy in different elements,which can be used to analyze the gradient change of deformation energy in the structure.Finally,the deformation properties of cantilever beam and four-sided consolidation plate are analyzed by deformation energy decomposition method.The correctness and superiority of this method are verified by comparing with the results of strain energy decomposition.
