Free-interface Mode Synthesis Method Research Articles

Model order reduction and dynamic characteristic analysis of the bolted flange structure with free-free boundaries

The problem of model order reduction and dynamic characteristic analysis of the bolted flange structure with free-free boundary conditions is studied by proposing a novel simplified modeling method. The proposed simplified modeling method is able to reduce the finite element model of the linear components through free-interface mode synthesis method and condense the number of degree-of-freedom of the joint interface through coordinate condensation, which can fix the model size not to increase with the number of bolts and greatly reduce the computational cost. Rigid-body mode elimination is also considered to further reduce the order of the integrated dynamic equation and avoid the problem of computational instability in the proposed simplified modeling method. An experimental bolted flange structure with free-free boundary conditions is built and the corresponding modal testing is carried out to verify the accuracy of the proposed simplified modeling method. Comparative results of modal testing and simulation indicate that gravity leads to unequal bending frequencies of the same order in X and Y directions, which also proves that the proposed simplified modeling method is able to analyze the dynamic characteristic of the bolted flange structure with free-free boundary conditions.

Condensation modeling of the linear structure with nonlinear boundary conditions

The problem of modeling for the linear structure with nonlinear boundary conditions in a more efficient manner is considered by proposing a novel condensation modeling method. The key idea of the proposed method is to reduce the overall number of degrees-of-freedom (DOFs) for the nonlinear jointed structure being analyzed, which can be implemented in the following two steps. Firstly, linear DOFs of the structure are truncated via finite element model reduction by using the free-interface mode synthesis method, as numerical integration of governing equations of structures with large numbers of DOFs is always time-consuming. Secondly, nonlinear DOFs at the boundary interface are reduced via coordinate condensation, so as to further minimize the model size of the structure being analyzed and make the subsequent analysis computationally efficient and memory economical. The performance of the proposed condensation modeling method is validated via case studies focused on an experimental structure with adjustable boundary conditions. Comparative results demonstrate that the computational efficiency can be extremely improved while the accuracy is simultaneously guaranteed by using the proposed method to model the linear structure with nonlinear boundary conditions.

Hybrid Modeling of Nonlinear-Jointed Structures via Finite-Element Model Reduction and Deep Learning Techniques

In engineering practice many structures are assembled by several linear components through nonlinear joints. A novel hybrid modeling method based on finite element model reduction and deep learning techniques is proposed to meet the ever-increasing requirements of efficient and accurate modeling for nonlinear jointed structures. The main idea of the hybrid modeling method for nonlinear jointed structures is summarized as follows: Firstly, finite element models of linear components are reduced to improve the computing efficiency using the free-interface mode synthesis method, as numerical integration of governing equations of nonlinear structures with large numbers of degrees-of-freedom is always time-consuming. Secondly, deep neural networks are used to equivalently represent the nonlinear joints which are difficult to describe by accurate and physically-motivated models, so as to avoid the errors caused by traditional mechanism modeling or system identification. Nonlinear joints are finally replaced with their equivalent neural networks and connected with the substructure models of linear components through the compatibility of displacements and equilibrium of forces at the interfaces. The performance of the proposed hybrid modeling method is tested and assessed via a case study focused on a cantilever plate with nonlinear joints. Comparative results demonstrate the capability of the proposed method for efficient and accurate modeling of nonlinear jointed structures and predicting their intrinsic nonlinear behavior.

Influence Factors Analysis on the Modal Characteristics of Irregularly-Shaped Bridges Based on a Free-Interface Mode Synthesis Algorithm

In order to relieve traffic congestion, irregularly-shaped bridges have been widely used in urban overpasses. However, the analysis on modal characteristics of irregularly-shaped bridges is not exhaustive, and the effect of design parameters on modal characteristics will be deeply investigated in future studies. In this paper, a novel strategy based on a free-interface mode synthesis algorithm is proposed to evaluate the parameters’ effect on the modal characteristics of irregularly-shaped bridges. First, a complicated, irregularly-shaped bridge is divided into several substructures based on its properties. Then, the modal characteristics of the overall structure can be obtained, only by a few low-order modal parameters of each substructure, using a free-interface mode synthesis method. A numerical model of a typical irregularly-shaped bridge is employed to verify the effectiveness of the proposed strategy. Simulation results reveal that the free-interface mode synthesis method possesses favorable calculation accuracy for analyzing the modal characteristics of irregularly-shaped bridges. The effect of design parameters such as ramp curve radius, diaphragm beam stiffness, cross-section feature, and bearing conditions on the modal characteristics of an irregularly-shaped bridge is evaluated in detail. Analysis results can provide references for further research into and the design of irregularly-shaped bridges.