On Hurty/Craig-Bampton Substructuring With Interface Reduction on Contacting Surfaces

Structural dynamics models with localized nonlinearities can be reduced using Hurty/Craig-Bampton component mode synthesis methods. The interior degrees-of-freedom of the linear subcomponents are reduced with a set of dynamic fixed-interface modes while the static constraint modes preserve the physical coordinates at which the nonlinear restoring forces are applied. For finite element models with a highly refined mesh at the boundary, a secondary modal analysis can be performed to reduce the interface down to a truncated set of local-level characteristic constraint modes. In this research, the cost savings and accuracy of the interface reduction technique are evaluated on a simple example problem involving two elastic blocks coming into contact.

A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning

In this work the effect of the inhomogeneous material properties are investigated in regenerative turning processes by introducing white noise in the cutting coefficient. The model is a one degree of freedom linear delayed oscillator with stochastic parameters. A full discretization method is used to calculate the time evolution of the second moment to determine the moment stability of the turning process. The resultant stability chart is compared with the deterministic turning model.

Nonlinear Oscillations of Hyperelastic Annular Membranes With Varying Density

This research presents the mathematical modeling for the nonlinear oscillations analysis of a pre-stretched hyperelastic annular membrane with varying density under finite deformations. The membrane material is assumed to be homogeneous, isotropic, and neo-Hookean and the variation of the membrane density in the radial direction is investigated. The membrane is first subjected to a uniform radial traction along its outer circumference and the stretched membrane is fixed along the outer boundary. Then the equations of motion of the pre-stretched membrane are derived. From the linearized equations of motion, the natural frequencies and mode shapes of the membrane are obtained analytically. The vibration modes are described by hypergeometric functions, which are used to approximate the nonlinear deformation field using the Galerkin method. The results are compared with the results evaluated for the same membrane using a nonlinear finite element formulation. The results show the influence of the stretching ratio and varying density on the linear and nonlinear oscillations of the membrane.

Structural Shape Reconstruction of FBG Flexible Plate Using Modal Superposition Method

Structural shape reconstruction is a critical issue for real-time structural health monitoring in the fields of engineering application. This paper shows how to implement structural shape reconstruction using a small number of strain data measured by fiber Bragg grating (FBG) sensors. First, the basic theory of structural shape reconstruction is introduced using modal superposition method. A transformation is derived from the measured discrete strain data to global displacement field through modal coordinate, which is the same for strain mode shape superposition and displacement mode shape superposition. Then, optimization of the sensor layout is investigated to achieve the effective reconstruction effect. Finally, structural shape reconstruction algorithm using modal superposition method is applied in experiments. The experiment results show that the reconstructed displacements match well with those measured by a laser displacement sensor and the proposed approach is a promising method for structural shape reconstruction.

A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems

Flexible multistage rotor systems have a variety of engineering applications. Vibration optimization is important to the improvement of performance and reliability for this type of rotor systems. Filling a technical gap in the literature, this paper presents a virtual bearing method for optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. In the development, a distributed transfer function formulation is used to define the optimization problem. Solution of the optimization problem by a real-coded genetic algorithm yields the locations and dynamic coefficients of bearings, by which the prescribed operational requirements for the rotor system are satisfied. A numerical example shows that the proposed optimization method is efficient and accurate, and is useful in preliminary design of a new rotor system with the number of bearings unforeknown.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

On Improvement of Operation Bandwidth of Duffing-Like Vibration-Based Harvesters Using a Mechanical Motion Rectifier

A novel vibration-based energy harvester which consists of a monostable Duffing oscillator connected to an electromagnetic generator with a mechanical motion rectifier (MMR-Duffing) is studied. The mechanical motion rectifier converts the bi-directional vibratory motion from ambient environments into uni-directional rotation to the generator and causes the harvester to periodically switch between a larger- and small-inertia system, resulting in nonlinearity in inertia. By means of the method of averaging, it is analytically shown that the proposed Duffing-MMR harvester outperforms traditional monostable Duffing oscillator energy harvesters in twofold. First of all, it increases the bandwidth of energy harvesting, given identical nonlinear stiffness. Second of all, it mitigates the jump phenomenon due to nonlinear stiffness and thus exploits more potential bandwidth of energy harvesting without inducing any jump phenomenon. Finally, the analytical analyses are verified via numerical simulations of a prototype of the proposed Duffing-MMR harvester.

Analysis of the Periodic Damping Coefficient Equation Based on Floquet Theory

In this paper, we study the response of a linear differential equation, for which the damping coefficient varies periodically in time. We use Floquet theory combined with the harmonic balance method to find the approximate solution and capture the stability criteria. Based on Floquet theory the approximate solution includes the exponential part having an unknown exponent, and a periodic part, which is expressed using a truncated series of harmonics. After substituting the assumed response in the equation, the harmonic balance method is applied. We use the characteristic equation of the truncated harmonic series to obtain the Floquet exponents. The free response and stability characteristics of the damped system for a set of parameters are shown.

Some Dynamic Properties of Contact Patches in Bolted Joints

The dynamics of structures built-up from components connected by bolted joints are not well understood. Experiments were conducted with bolted joints in a shear configuration in which instantaneous vibration frequencies and damping could be measured. A system with bolted joints was excited and the free vibration decay measured. As the vibration decays, the damping decreases and the frequencies increase. This suggests a new interpretation for the contact patch in a bolted joint, involving bound, slipping and alternating regions. The changing size of the bound region controls the instantaneous frequencies and the relative displacement inside the slipping region and the alternating region controls the damping behaviour. Shims of different lengths enabled the behaviour of the contact patch to be investigated. A clear trend exists between the length of the shims and the non-linear dynamic behaviour. The introduction of multiple shims did not increase the damping or alter the dynamic nonlinear behaviour. The introduction of grease into the bolted joint increased the damping but oil did not. The vibration measurements enable the size of the contact patch to be estimated.

An Improved Re-Scaling Frequency Stochastic Resonance and its Application to Weak Fault Signal Detection

Weak fault detection is crucial to incipient mechanical fault diagnosis. In order to extract weak fault signals, a method named improved Re-scaling Frequency Stochastic Resonance (IRFSR) is proposed in this paper. The method consists of four steps: (i) Frequency Information Exchange (FIE); (ii) Amplitude Coefficient Adjustment; (iii) Re-scaling Frequency Stochastic Resonance (RFSR); and (iv) Frequency Information Recovery. By means of the exchange of frequency information, the high-frequency information of the target signal is accordingly transferred to the low frequency band which can be rescaled to satisfy the small-parameter limits of classical stochastic resonance. Then IRFSR is able to overcome the limitation of RFSR, which is that the sampling frequency of RFSR is at least 50 times greater than the frequency of the target signal. Numerical results are reported to evaluate the effectiveness of IRFSR to detect the target signal with higher frequency at a low sampling frequency as compared with RFSR. And the feasibility of the IRFSR in incipient fault detection is demonstrated using case history data obtained from a sliding bearing test rig.