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The simulation of bolt joints affects the analysis accuracy of the dynamic characteristics of the whole structure in the dynamic modeling of bolted connection structures. In this study, the mechanical properties of the bolted thin-plate lap joint were simulated based on a nonuniformly distributed virtual material. The parameters of the virtual material were expressed based on a complex modulus, and the complex stiffness matrix can be directly generated to express the stiffness and damping characteristics of the lap joint. The steps used to generate a joint damping matrix in conventional modeling were omitted, and the modeling process was simplified to ensure model accuracy. We established a semianalytical model of a bolted thin plate structure to enable its dynamic analysis. In this study, we first described the modeling concept. The virtual material was assumed to have three types of nonuniform complex modulus distributions to simulate the mechanical properties of the bolted lap joint. We proposed a method for determining the storage modulus and energy dissipation modulus of the virtual material using a reverse identification technique. Based on the energy method and the assumed modes of orthogonal polynomials, we derived a semianalytical model of bolted thin plates and develop an innovative formula for solving the frequency response function at any hammering point and the vibration point of the semianalytical model. Finally, we conducted a case study on a bolted thin plate structure. Results show that the deviation between the simulated natural frequencies calculated using the semianalytical model and the experimental natural frequencies are less than 5%. Further, the calculated model shapes and frequency-response-function curves are close to those obtained based on the measured values. These results prove that a virtual material with a nonuniform complex modulus distribution can effectively simplify the modeling of a bolted joint and achieve high simulation accuracy.

In order to effectively simulate the vibration behavior of bolted structures, it is necessary to consider the non-uniform distribution of pressure and the nonlinear characteristics of variable stiffness and damping at bolted joints. In this paper, the virtual material model is used to simulate the above two characteristics of the bolted lap zone, and a semi-analytical modeling of nonlinear vibration of bolted thin plate is studied. Specifically, the non-uniform distribution of pressure in the bolted lap zone is simulated by making the storage modulus of virtual material satisfy linear, parabolic and sinusoidal distribution forms, respectively. The storage and loss moduli of the virtual material are set as a high-order polynomial with displacement dependence to simulate the variable stiffness and damping characteristics of the bolted lap zone. By integrating the mechanical properties of the thin plate and the bolted lap zone simulated by virtual material with the energy method, the nonlinear dynamic semi-analytical modeling of the bolted thin plate is completed, and then, the process of using incremental harmonic balance method to iteratively solve the nonlinear vibration response of bolted thin plates is described. Finally, a case study is carried out to verify the rationality of the proposed virtual material simulation model of bolted lap zone, and the created semi-analytical model is used to explain the soft nonlinear vibration of bolted thin plate under different excitation levels. [ABSTRACT FROM AUTHOR]

In this paper, the double-lap bolted plate is used to simulate the fully unfolded state of solar panels, and the method of vibration suppression by attaching constrained layer damping (CLD) is studied. Firstly, based on the principle of interlaminar shear deformation, the semi-analytical dynamic model of the double-lap bolted thin plate with partial CLD is established by using Hamilton's principle. The stress–strain relationship of the CLD is derived. Then, complex spring elements and modified mass are proposed to simulate the interface mechanical behavior and mass effect of the double-lap joint. Moreover, the orthogonal polynomial is introduced as the displacement admissible function. Based on the Evolutionary Structural Optimization (ESO) method, the topology optimization model of the bolted thin plate with CLD is established by taking the maximum sum of the modal loss factors as the optimization objective and the attachment volume as the constraint condition, and processing the optimized results in a convolutional way. After that, a case study is carried out, and the experimental system is established to prove the rationality of the semi-analytical model and attaching CLD to vibration reduction. Finally, the topology optimization is conducted, which verifies that the topology configuration has a better vibration reduction effect. [ABSTRACT FROM AUTHOR]

• Three non-uniformly distributed complex spring elements are proposed. • The displacement dependence of parameters of complex spring elements is proposed. • The nonlinear parameters of complex spring elements are identified by experiments. • The nonlinear vibration mechanism of bolted thin plate is revealed. Due to the existence of bolt influence zone, the interface pressure of bolted joint presents a non-uniform distribution. The nonlinear mechanical behaviors of variable stiffness and variable damping will also occur in bolted joints under varying degrees of forced vibration. In this paper, a nonlinear finite element analysis model of bolted thin plate is established by introducing displacement-dependent nonlinear complex spring elements with non-uniformly distributed parameters. Sinusoidal, parabolic and linearly distributed complex spring elements are used to simulate the non-uniform pressure distribution in the bolt influence zone, respectively. The stiffness and damping displacement-dependent parameters of the complex spring elements are described by higher-order polynomials, and a method to obtain the above parameters by inverse identification is proposed. In the case study, the non-linear finite element model created is used to calculate the resonance frequency and frequency domain response of bolted thin plate under five excitation levels. The maximum differences between the results and the measured values are 2.7% and 0.66%, respectively. The simulation results also reproduce the soft nonlinear vibration phenomenon of the bolted thin plate. Furthermore, by comparing the vibration analysis results of the linear model and nonlinear model for bolted thin plate, the reason for the soft nonlinear phenomenon produced is explained. [Display omitted] [ABSTRACT FROM AUTHOR]