Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

Highly Sensitive Nonlinear Identification To Track Early Fatigue Signs in Flexible Structures

This study describes a physics-based and data-driven nonlinear system identification approach for detecting early fatigue damage due to vibratory loads. The approach also allows for tracking the evolution of damage in real-time. Nonlinear parameters such as geometric stiffness, cubic damping and phase angle shift can be estimated as a function of fatigue cycles, which are demonstrated experimentally using flexible aluminum 7075-T6 structures exposed to vibration. Nonlinear system identification is utilized to create and update nonlinear frequency response functions, backbone curves and phase traces to visualize and estimate the structural health. Findings show that the dynamic phase is more sensitive to the evolution of early fatigue damage than nonlinear parameters such as the geometric stiffness and cubic damping parameters. A modifed Carrella-Ewins method is introduced to calculate the backbone from the nonlinear signal response, which is in good agreement with the numerical and harmonic balance results. The phase tracing method is presented, which appears to detect damage after approximately 40% of fatigue life, while the geometric stiffness and cubic damping parameters are capable of detecting fatigue damage after approximately 50% of the life-cycle.

Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis

In this paper, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoshell (DWPENS) is investigated using nonclassical approach of the Gurtin–Murdoch surface/interface (GMSIT) theory. The piezoelectric nanoshell is simultaneously subjected to visco-Pasternak medium, the nonlinear van der Waals and electrostatic forces. Hamilton’s principles, the assumed mode method combined with Lagrange–Euler’s are used for the governing equations and boundary conditions. Complex averaging method combined with Arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the DWPENS. It is found that the electrostatic and piezoelectric voltages, the length to radius ratio, the nanoshell gap width, van der Waals (vdW) coefficients and other parameters can effectively change the flexural rigidity of the system which in turn affects the nonlinear frequency response. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system’s instability, nonlinear behavior, and bandwidth.

Study of plate vibrating in fluids having part-through crack at random angles and locations

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Topological Optimization of Under-Platform Dampers With Moving Morphable Components and Global Optimization Algorithm for Nonlinear Frequency Response

To limit the risk of high cycle fatigue, underplatform dampers (UDPs) are traditionally used in aircraft engines to control the level of vibration. Many studies demonstrate the impact of the geometry of the damper on its efficiency, thus the consideration of topological optimization (TO) to find the best layout of the damper seems natural. Because of the nonlinear behavior of the structure due to the friction contact interface, classical methods of TO are not usable. This study proposes to optimize the layout of an UDP to reduce the level of nonlinear vibrations computed with the multiharmonic balance method (MHBM). The approach of TO employed is based on the moving morphable components (MMC) framework together with the Kriging and the efficient global optimization algorithm to solve the optimization problem. The results show that the level of vibration of the structure can be reduced to 30% and allow for the identification of different efficient geometries.

A Digital Method of Evaluating Nonlinear Frequency Response Functions Based on Conditioned Spectral Analyses

This paper focuses on the issue of evaluating nonlinear frequency response functions (NOFRFs) of the nonlinear systems with a general input. A new digital approach of evaluating NOFRFs is proposed based on the method of conditioned spectral analysis (CSA). Firstly, a multiple-input/single-output (MISO) linear system with a series of power characterized inputs is obtained by decomposing a nonlinear system according to the NOFRFs theory. Secondly, the correlations among the inputs of various orders are removed by applying CSA method, obtaining an algorithm of identifying the NOFRFs and evaluating the contributions of different order nonlinearities to the output of the system. In the CSA procedure, the different order inputs are conditioned in the sequence from the first order to the highest order. Lastly, two kinds of nonlinear systems with a general input are simulated to verify the effectiveness of the proposed approach on evaluating the frequency response properties of nonlinear systems. It is shown that the results reached by the proposed method are very close to the numerical results obtained by the fourth order Runge-Kutta method, verifying that the proposed method is very effective on the evaluation of NOFRFs.