This paper focuses on the nonlinear dynamics modeling and parameter identification of an Aluminum Honeycomb Panel (AHP) with multiple bolted joints. Finite element method using eight-node solid elements is exploited to model the panel and the bolted connection interface as a homogeneous, isotropic plate and as a thin layer of nonlinear elastic-plastic material, respectively. The material properties of a thin layer are defined by a bilinear elastic plastic model, which can describe the energy dissipation and softening phenomena in the bolted joints under nonlinear states. Experimental tests at low and high excitation levels are performed to reveal the dynamic characteristics of the bolted structure. In particular, the linear material parameters of the panel are identified via experimental tests at low excitation levels, whereas the nonlinear material parameters of the thin layer are updated by using the genetic algorithm to minimize the residual error between the measured and the simulation data at a high excitation level. It is demonstrated by comparing the frequency responses of the updated FEM and the experimental system that the thin layer of bilinear elastic-plastic material is very effective for modeling the nonlinear joint interface of the assembled structure with multiple bolts.

In the aeronautical and aerospace fields, a much more attention has been attracted by the assembled mechanical structures which consist of substructures or parts connected to each other through different types of connections [

Among the mechanical connections, bolted joints are applied in assembled mechanical structures very frequently. A number of researchers have paid attention in developing predictive models for bolted joints in different structures. For example, Song et al. [

It is noted that the previous researches mainly focused on the assembled structures consisting of several beams, pipes, or other simple parts connected through a small amount of bolts. Finite Element Models (FEMs) have been developed to describe the dynamic phenomena of assembled structures by treating each connected interface as a thin layer of a nonlinear elastic-plastic material [

It is to be noted here that less attention has been given to model the panel structure with multiple bolted connections although much of the literature focused on modeling of the bolted beams and pipes. The aim of this work is to study the nonlinear dynamics modeling and parameter identification of an AHP with multiple bolted joints. For this purpose, a thin layer of nonlinear elastic-plastic material is used to characterize the nonlinear characteristics of the bolted connection interface. The linear material parameters of the panel are necessarily identified via experimental tests at low excitation levels, whereas the nonlinear material parameters of the thin layer are updated by using the genetic algorithm to minimize the residual error between the measured and the simulation data at a high excitation level. Finally, the efficacy of the proposed scheme is demonstrated via comparisons of the FEM and experimentally obtained results under another exciting level.

As shown in Figure ^{3} and 5.80 kg, respectively. The AHP is fixed at the bottom by using 26 bolts (13 bolts for each side). The pretightening torque of the bolts is set to be about 2 Nm.

(a) The AHP connected to a mounting base via multiple bolts. (b) A graphic illustration of the bolted connections.

The nonlinear characteristics of the bolted joints, such as micro/macroslip, may have a significant effect on the dynamical behavior of assembled structures. Therefore, it is of practical importance to accurately model the nonlinear characteristics of the bolted joints interface. The equation of motion for a nonlinear system with multiple degrees of freedom under harmonic excitation can be expressed as follows [

Quite different from the cases of linear systems, it is well known that the frequency response of such a nonlinear system depends on the levels of the excitation forces due to the presence of the nonlinear internal force. In this study, the finite element method is adopted to model the assembled structure where the connection interface with multiple bolts is treated as a thin layer of bilinear elastic-plastic material so as to characterize the nonlinear behavior of the bolted joints. Figure

The sketch of the thin layer of elastic-plastic material.

The thickness of the thin layer is much less than the geometric sizes in the other two directions. Following [

In the case of the nonlinear material, the constitutive relation has a more complex form. In this study, a bilinear elastic-plastic model under the assumption of isotropic hardening and Von Mises yield criterion is used to describe the stress-strain relationship of a thin layer element [

Bilinear stress-strain behavior for one-dimensional space.

As shown in Figure

The FEM of the AHP with multiple bolts is created in

The FEM of the assembled structure.

In the FEM of the assembled structure, the AHP is treated as a linear plate of homogeneous, isotropic material. The mass density of the plate is determined using the volume and weight of the AHP. The equivalent Young’s modulus and Poisson’s ratio are set to be guessed values and then updated by using the SOL200 procedure in NASTRAN to minimize the error between the first three-order natural frequencies of FEM and real structure. Accordingly, the objective function can be expressed as follows:

Moreover, the nonlinear material parameters of the thin layer, that is, Young’s modulus

Flowchart of the optimization procedure.

Experimental test was conducted to investigate the dynamic characteristics of the AHP with multiple bolts. The testing system setup mainly consists of an electromagnetic vibration exciter (S 51075-M from TIRA GmbH), a power amplifier (B&K2718 from Brüel & Kjær), and a vibration test controller (Spider-81 from Crystal Instruments), as shown in Figure

A schematic view of the experimental setup.

Experimental system for vibration test of the AHP with multiple bolts.

Two different stages of experimental tests were carried out. In the first part, the AHP is excited by using random excitation (RMS

Measured first three natural frequencies.

Order number | 1 | 2 | 3 |

Natural frequency (Hz) | 14.63 | 104.02 | 144.40 |

Measured linear FRF at sensor location A.

The linear material parameters of AHP are updated by minimizing the objective function defined as (

Initial and updated material parameters.

Material parameters | Initial value | Updated value |
---|---|---|

| | |

| 0.33 | 0.29 |

Experimentally measured, initial, and updated natural frequencies.

Natural frequency | Experimental value | Initial value | Updated value |
---|---|---|---|

| 14.63 | 23.6 | 14.63 |

| 104.02 | 149.38 | 102.86 |

| 144.40 | 189.89 | 137.62 |

Variation of Young’s modulus with the design cycles.

Variation of Poisson’s ratio with the design cycles.

Variation of the objective function with the design cycles.

In the second part, the AHP was excited using sinusoidal forces at much larger levels so as to identify the nonlinear characteristics of the system. Two different levels of excitation forces (5 N and 8 N) were considered for the experimental tests with its testing frequency range set to be from 11 Hz to 15 Hz in the Spider-81 software system. Quite different from the case of a linear structure, Figure

Measured nonlinear FRF at sensor location A.

In this part, the parameters of Young’s modulus

Updated parameters of the thin layer.

Parameter | | | |

Updated value | | | |

Measured and updated FRFs with 5 N excitation.

Measured and updated FRFs with 8 N excitation.

The aim of this study is to investigate the nonlinear dynamics modeling and parameter identification of AHP with multiple bolts. It is shown by experimental tests that the dynamic responses of the AHP with multiple bolts under low and high excitation levels are linear and nonlinear, respectively. The equivalent linear material parameters of the panel are identified using the linear response at low excitation level. A thin layer of elastic-plastic material is used to characterize the bolted joints interface since the constitutive relation of such a material can describe the nonlinear behavior of the bolted interface. The parameters of nonlinear material of thin layer are updated by minimizing the error between FEM and experimentally measured results under a high excitation level. It is demonstrated that the frequency responses of the updated FEM model and experimental tests agree well with each other. The updated FEM model can be used to characterize the nonlinear behavior of the assembled structure with multiple bolts subject to higher levels of excitations.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the National Natural Science Foundation of China under Grants 11372130, 11290153, and 11290154 and in part by the Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant 201233.