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Thin cylindrical shells are susceptible to cracking under long-term load and external impact, and it is of considerable scientific and technical value to investigate the nonlinear vibration response characteristics and monitor the health condition of the shell structure. Based on the Flügge shell theory, the nonlinear dynamic model for the thin cylindrical shell is established. By the partial Fourier transform combined with the residue theorem, the forced vibration generation and propagation mechanism of the thin cylindrical shell are investigated, and the analytical solution of forced vibration displacement in the space domain is obtained. Then, the local flexibility matrix is derived from the perspective of fracture mechanics, and the continuous coordination condition on both sides of the straight crack is constructed using the linear spring model. Combined with the wave superposition principle, the analytical approach for nonlinear vibration response is proposed to reveal the evolution law of vibration characteristics of the thin cylindrical shell with a straight crack, and then, a straight crack identification method based on natural frequency isolines and amplitude maximization methods is presented. Finally, the effect of various morphological information of the straight crack on the nonlinear vibration response characteristics of the thin cylindrical shell is studied in detail, and a numerical case is conducted to verify the effectiveness of the proposed straight crack identification method.

The free vibration responses are divergent based on a complex time-domain damping model. The traditional step by step integration method cannot be used to calculate the time-domain responses. Based on the theoretic solution that eliminates the divergent term for the complex damping model, the equivalent viscous damping model is proposed and the corresponding average acceleration method is realized in this paper. The numerical cases show that the calculated results of the equivalent viscous damped system are convergent, which are equal to the ones of the deleted divergent term based on the complex damping model. The correctness of the proposed method is verified, and the computational efficiency is high.

Studying the wind-induced vibration model and response characteristics of lightning rods is crucial for achieving their rational design and wind stability. To address the current shortcomings in considering on-site wind load characteristics and the lack of differentiated considerations in the design phase of lightning rods, it is essential to establish an effective simulation model that accurately reproduces the wind induced vibration response of lightning rods and extracts key parameters for analysis. In this study, a 330kV independent lightning rod in Ningxia province, China, was identified as the subject of analysis. Building upon the structural vibration model, the response of the lightning rod to wind induced vibrations was calculated, and the simulation results were systematically validated through on-site measurements. The results indicate that the simulation model developed in this study can effectively replicate the vibration process of the lightning rod under wind load, providing comprehensive mechanical data. The research findings contribute to a deeper understanding of the wind induced characteristics of on-site lightning rods, facilitating the simulation analysis of lightning rod wind induced responses. Furthermore, the vibration law and characteristic parameters of the lightning rod structure hold great significance for the differentiated design and structural health monitoring of independent lightning rods.

The effect of structure on the vibration response was explored for four piano soundboards with different but commonly adopted structures. The vibration response was obtained using the free-vibration method, and the values of the dynamic modulus of elasticity and dynamic shear modulus obtained using the free-vibration frequency method (EF and GF) were compared with the dynamic modulus of elasticity obtained using the Euler beam method (EE) and dynamic shear modulus obtained using the free-plate torsional vibration method (GT), respectively. It was found that the soundboards with different structures had different vibration modes and that excitation at different locations highlighted different vibration modes. For all the soundboards analyzed, the EE and GT were higher than EF and GF by 2.2% and 24.3%, respectively. However, the trends of the results of these methods were the same. The four piano soundboards with different structures possessed varying dynamic moduli of elasticity and dynamic shear moduli. These rules are consistent with the grain directions of the soundboards and the anisotropy of the wood (the direction of the units of the soundboards). The results show that the vibration mode of the piano soundboard is complex. The dynamic elastic modulus of the soundboard can be calculated using the Euler beam method. The results provide a reference for studies on the vibration response, material selection, production technology, and testing of piano soundboards.

An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J Sound Vib, 337:301–320, 2015 ; J Sound Vib 357:168–194, 2015 ). In the proposed model, the shaft is discretized using a finite element method and the effects of the swing of the rigid disk and stagger angles of the blades are considered. Furthermore, the mode shapes of rotor-blade systems can be obtained based on the proposed model. The proposed model is more accurate than our previous model, and it is also verified by comparing the natural frequencies obtained from the proposed model with those from the finite element model and published literature. By simplifying the casing as a two degrees of freedom model, the single- and four-blade rubbings are studied using numerical simulation and experiment. Results show that for both the single- and four-blade rubbings, amplitude amplification phenomena can be observed when the multiple frequencies of the rotational frequency ( f r ) coincide with the conical and torsional natural frequencies of the rotor-blade system, natural frequencies of the casing and the bending natural frequencies of the blades. In addition, for the four-blade rubbing, the blade passing frequency (BPF, 4 f r ) and its multiple frequency components also have larger amplitudes, especially, when they coincide with the natural frequencies of the rotor-blade system or casing; the four-blade rubbing levels are related to the rotor whirl, and the most severe rubbing happens on the blade located at the right end of the whirl orbit.

The contact states including stick, slip, and separation can occur at the bolted joint interface of bolted flange joint structures, which significantly affects and complicates the vibration characteristics of connected structures. However, the mechanism of the influence of these three contact states on structural vibration is still not well understood. This paper establishes a universal theoretical model of bolted flange joint plate systems considering the stick, slip, and separation states simultaneously, which can be extended to a structure with an arbitrary number of bolts and plates. The bi-linear hysteretic model is adopted to model the three contact states. The contact pressure between the bolts and flanges is considered as two-dimensional distribution form, which is closer to real contact situation. Based on the Kirchhoff plate theory, the energy functions of plate and flange are obtained. Further, the nonlinear dynamic equation is derived using Lagrange equations, and solved by the Newmark-beta method. The experimental studies are performed on a plate system connected with bolted flange joint to illustrate the effectiveness of the theoretical model. The results highlight the influence of separation state and friction coefficient on the vibration response. It is found that as the tightening torque decreases, the resonance amplitude increases due to the occurrence of interface separation. The slip state can cause the nonlinear softening property, but this property will weaken when the separation occurs at bolted joint interfaces.

Traditional rigid photovoltaic (PV) support structures exhibit several limitations during operational deployment. Therefore, flexible PV mounting systems have been developed. These flexible PV supports, characterized by their heightened sensitivity to wind loading, necessitate a thorough analysis of their static and dynamic responses. This study involves the development of a MATLAB code to simulate the fluctuating wind load time series and the subsequent structural modeling in SAP2000 to evaluate the safety performance of flexible PV supports under extreme wind conditions. The research explores the critical wind speeds relative to varying spans and prestress levels within the system. Modal analysis reveals that the flexible PV support structures do not experience resonant frequencies that could amplify oscillations. The analysis also provides insights into the mode shapes of these structures. An analysis of the wind-induced vibration responses of the flexible PV support structures was conducted. The results indicated that the mid-span displacements and the axial forces in the wind-resistant cables are greater under wind-pressure conditions compared to wind-suction conditions. Conversely, for mid-span accelerations, the wind-suction conditions resulted in higher values than the wind-pressure conditions. Furthermore, the wind-induced vibration coefficients were computed, with findings suggesting a recommended coefficient range of 1.5 to 2.52. To mitigate wind-induced vibrations, structural reinforcement strategies were assessed. The results indicate that the introduction of support beams at the mid-span is the most effective measure to attenuate wind-induced vibrational responses. Conversely, increasing the diameter of the tensioned cables exhibited a negligible effect in reducing these responses. On the other hand, implementing stabilizing cables at the mid-span demonstrated a substantial reduction in wind-induced vibrational responses under suction wind-load conditions.

The vibration and response of multi-contact interface micro-motion time-varying stiffness wheel are analyzed, and the nonlinear vibration response characteristics caused by the unbalance force of multi-contact interface contrate gear face of a gas turbine rotor are studied. Firstly, the local sliding model of dry friction-damped contact is extended to establish a holistic and local unified sliding model. The equivalent stiffness and damping of the damping device are calculated by means of the equivalent linearization method and the first harmonic balance method. Finally, the finite element model of multi-contact contrate gear rotor wheel is established to analyze the influence of different unbalanced masses on vibration response under nonlinear frictional contact. The results show that the response caused by the unbalance mass of multi-contact interface wheel with contrate gear is mainly radial response, and the peak value of resonance response increases with the increase of unbalance force.

PurposeThis paper aims to propose a two-stage vibration isolation system for large airborne equipment to isolate aircraft vibration load.Design/methodology/approachFirst, the vibration isolation law of the discrete model of large airborne equipment under different damping ratios, stiffness ratios and mass ratios is analyzed, which guides the establishment of a three-dimensional solid model of large airborne equipment. Subsequently, the vibration isolation transfer efficiency is analyzed based on the three-dimensional model of the airborne equipment, and the angular and linear vibration responses of the two-stage vibration isolation system under different frequencies are studied.FindingsFinally, studies have shown that the steady-state angular vibration at the non-resonant frequency changes little. In contrast, the maximum angular vibration at the resonance peak reaches 0.0033 rad, at least 20 times the response at the non-resonant frequency. The linear vibration at the resonant frequency is at least 2.14 times the response at the non-resonant frequency. Obviously, the amplification factor of linear vibration is less than that of angular vibration, and angular vibration has the most significant effect on the internal vibration of airborne equipment.Originality/valueThe two-stage vibration isolation equipment designed in this paper has a positive guiding significance for the vibration isolation design of large airborne equipment.

ABSTRACT This study investigates GNSS (Global Navigation Satellite System) dynamic monitoring for assessing structural seismic damage. Initially, vibration table experiments were designed to simulate structural seismic response, in which structural response signals were collected by GNSS. The FFT+NTFT (Fast Fourier Transform and Normal Time-Frequency Transform) method was utilised to extract the signal’s time-frequency features and the maximum relative errors of calculation results are 4.90%, verifying the GNSS dynamic monitoring accuracy. Subsequently, the study utilised the GNSS dynamic monitoring data from the Su-Tong Bridge during the Hengchun earthquake. The response of the structural vibration with an amplitude of approximately 5 mm was extracted by comparing the spectral variation characteristics of the monitoring data before and after two consecutive earthquake excitations. The vibration response signal frequencies for the two earthquake excitations were found to be 0.1564 Hz and 0.1553 Hz, respectively. The structural vibration response time was found to be 8.0 minutes and 9.5 minutes, respectively. The research results demonstrate that leveraging the advantages of GNSS dynamic monitoring for rapid acquisition of structural seismic response signals, combined with time-frequency characteristic analysis of the signals, enables prompt assessment of structural damage and determination of remaining load-bearing capacity, thereby providing crucial reference bases for emergency decision-making.