In order to realize the accurate prediction of the vibration fatigue life of the beam in service, a loose coupling analysis method is proposed to carry out vibration fatigue analysis of a beam with an initial crack. In modal analysis, the initial crack segment is replaced with a torsion spring, and the damping loss factor is introduced by the complex modulus of elasticity; for the simply supported beam, the inherent vibration characteristic equation of the cracked beam is derived. In vibration fatigue analysis, the interaction between the crack’s growth and vibration analysis is considered, and a loose coupling analysis method is proposed to conduct modal dynamic response and vibration fatigue analysis simultaneously. Results indicate that the crack’s relative location and depth determine the modal of the cracked beam, and crack parameters, damping loss factor and external excitation frequency are important factors for the vibration fatigue life of the beam.

An analytical method is proposed to calculate the natural frequency of a cantilever beam with a breathing oblique crack. A double-linear-springs-model is developed in the modal analysis process to describe the breathing oblique crack, and the breathing behaviour of the oblique crack is objectively simulated. The finite element method (FEM) analysis software ABAQUS is used to calculate the geometric correction factors when the cracked plate is subjected to a pure bending moment at different oblique crack angles and relative depths. The Galerkin method is applied to simplify the cracked beam to a single degree of freedom system, allowing the natural frequency of the beam with the breathing oblique crack to be calculated. Compared with the natural frequencies of the breathing oblique cracked beam obtained using the ABAQUS FEM method, the proposed analytical method exhibits a high computational accuracy, with a maximum error of only 4.65%.

In this paper, a new method is developed to investigate the anti-penetration performance of the steel/nylon sandwich plate, which incorporates experimental method with numerical simulation. Constitutive parameters of the steel/nylon sandwich plate are measured by the Hopkinson Pressure Bar, and LS-DYNA is applied to simulate the penetration process of projectiles into the sandwich plate. The dynamic response, failure modes and energy absorption coefficients are obtained, and the penetration tests are conducted to verify the numerical method. Results show: results obtained by experimental and numerical methods have very high agreement, which demonstrates that the method proposed can be applicable for predicting the anti-penetration performance of the sandwich plate.