The influence on coupling vibrations and stability among shaft-torsion, disk-transverse and blade-bending of a rotor system with a mistuned blade's staggle angle was investigated analytically. A shaft-disk-blade system has been found existing two types of coupling vibrations, disk-blade (DB), and blade-blade (BB) modes when the shaft was assumed rigid. If the shaft's torsional flexibility was taken into account, an additional type of coupling modes, shaft-disk-blade (SDB), appeared. When an angle-mistuned blade existed, the blades periodicity was destroyed and it was found to change not only the natural frequencies but also the types of modes. Due to blade's mistune, the shaft torsion had to participate to balance such that DB modes vanished and replaced by SDB modes. A mistuned staggle angle was numerically found to alter the natural frequencies in an almost linear trend. At last, the rotational effects were found to merge frequency loci and eventually reached an instability point. Very interestingly, a mistuned blade diminished the possible instability caused by blade-dominating modes, which existed in a perfect and periodic rotor. In words, the rotor might benefit from a mistuned blade from the stability viewpoint. The shaft-dominating mode, yet, was unaffected by the mistune and retained a possible instability.

Yi-Jui Chiu

Shyh-Chin Huang

The Influence of a Mistuned Blade&#x2019;s Staggle Angle on the Vibration and Stability of a Shaft-Disk-Blade Assembly

The object of this paper is to investigate computationally the possibility of damage prognosis in a structure under the most idealised circumstances. A simple isotropic material &#x2013; Titanium alloy Ti-6Al-4V &#x2013; is assumed. The structure is a simple finite plate under harmonic uniaxial loading and the damage is assumed to be a central mode 1 through crack for which various approximations to the stress intensity factor are known. The damage propagation model is the Paris-Erdogan law. Where the paper departs from complete simplicity is in the assumption that the parameters of the damage propagation law are uncertain. The paper investigates the effect of the parameter uncertainty on the estimated lifetime of the specimen. Two approaches are adopted for the uncertainty propagation, a statistical Monte Carlo scheme and one based on interval arithmetic.

Keith Worden

Graeme Manson

Prognosis under Uncertainty &#x2013; An Idealised Computational Case Study

The presence of a crack in a structure modifies the energy dissipation pattern. As a consequence, damaged structures can present high localized damping. Experimental tests have revealed that crack nucleation and growth increase structural damping which makes this phenomenon useful as a damage locator. This paper examines the energy flow patterns caused by localized damping in rods, beams and plates using the Energy Finite Element Method (EFEM), the Spectral Element Method (SEM) and the Energy Spectral Element Method (ESEM) in order to detect and locate damage. The analyses are performed at high frequencies, where any localized structural change has a strong influence in the structural response. Simulated results for damage detection in rods, beams, and their couplings calculated by each method and using the element loss factor variation to model the damage, are presented and compared. Results for a simple thin plate calculated with EFEM are also discussed.

E.R.O. Santos

V.S. Pereira

J.R.F. Arruda

J.M.C. Dos Santos

Structural Damage Detection Using Energy Flow Models

Vibration-based structural health monitoring of a vehicle crane was studied. The performance of different features to detect damage was investigated after eliminating the normal operational variations using factor analysis. Using eight accelerometers, ten AR parameters from each record were identified for damage detection. Also transmissibilities between sensors were estimated. Damage was introduced with additional masses at different locations of the structure. All damage cases could be detected from either features using control charts, but transmissibilities proved to be more sensitive to damage than the AR coefficients.

J. Kullaa

T. Heine

Feature Comparison in Structural Health Monitoring of a Vehicle Crane

Nuno M.M. Maia

Special issue: International Conference on Engineering Dynamics &#x2013; ICED 2007

In recent decades, several types of hybrid vehicles have been developed in order to improve the fuel economy and to reduce the pollution. Hybrid electric vehicles (HEV) have shown a significant improvement in fuel efficiency for small and medium-sized passenger vehicles and SUVs. HEV has several limitations when applied to heavy vehicles; one is that larger vehicles demand more power, which requires significantly larger battery capacities. As an alternative solution, hydraulic hybrid technology has been found effective for heavy duty vehicle because of its high power density. The mechanical batteries used in hydraulic hybrid vehicles (HHV) can be charged and discharged remarkably faster than chemical batteries. This feature is essential for heavy vehicle hybridization. One of the main problems that should be solved for the successful commercialization of HHV is the excessive noise and vibration involving with the hydraulic systems. This study focuses on using magnetorheological (MR) technology to reduce the noise and vibration transmissibility from the hydraulic system to the vehicle body. In order to study the noise and vibration of HHV, a hydraulic hybrid subsystem in parallel design is analyzed. This research shows that the MR elements play an important role in reducing the transmitted noise and vibration to the vehicle body. Additionally, locations and orientations of the isolation system also affect the efficiency of the noise and vibration mitigation. In simulations, a skyhook control algorithm is used to achieve the highest possible effectiveness of the MR isolation system.

The M. Nguyen

Mohammad H. Elahinia

Vibration Isolation for Parallel Hydraulic Hybrid Vehicles

The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.

Jiao Sujuan

Li Jun

Hua Hongxing

Shen Rongying

A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory

The problem of dynamic, infinite dimension, modeling of a transmission is considered. An accurate Laplace transfer function matrix of the system that consists of flexible shafts connected by gears that are either rigid or flexible is found. The first step is deriving a set of single input, infinite dimension, transfer functions for a single uniform link. The building blocks of those transfer functions are time delays, representing the wave motion, and low order rational expressions, representing the boundary phenomena. The next step is combining these individual transfer functions into an overall model of the transmission, by means of the link reaction approach that makes use of the geometric relationships and reaction moments between neighboring links. The outcome is a generalized dynamic model with the moments in the gear pairs as the generalized state vector. The explicit and highly structured form of the transfer functions allows physical insight into the system, exact calculation of natural frequencies and the construction of exact simulation schemes built from standard blocks that are available in multi-purpose simulation software.

Irit Peled

Yoram Halevi

Continuous Modeling of a Multi-Link Flexible Transmission

In the finite element method, there are shortcomings using the conventional formulae to calculate the sectional forces, i.e., the bending moment and the shear force, at any cross-section of Bernoulli-Euler beam under dynamic loads. This paper presents some new finite-element formulae overcoming the shortcomings of the conventional ones to calculate the sectional forces at any cross-section of a Bernoulli-Euler beam on continuously viscoelastic foundation subjected to concentrated moving loads. The proposed formulae can easily degenerate into the formulae for calculating the sectional forces of a simply supported or a continuous Bernoulli-Euler beam subjected to concentrated moving loads, and into the formulae for calculating the sectional forces of a Bernoulli-Euler beam on Winkler foundation under static loads. Five numerical examples including static and dynamic analyses are chosen to illustrate the application of the proposed formulae. Numerical results show: (1) compared with the conventional formulae, the proposed formulae can improve the calculation accuracy of the sectional forces of beam; (2) one should use the proposed formulae, not the conventional formulae, to calculate the sectional forces at any cross-section in Bernoulli-Euler beam.

Ping Lou

Finite-Element Formulae for Calculating the Sectional Forces of a Bernoulli-Euler Beam on Continuously Viscoelastic Foundation Subjected to Concentrated Moving Loads

A coupled Euler-Lagrange solution approach is used to model the response of a buried reinforced concrete structure subjected to a close-in detonation of a high explosive charge. The coupling algorithm is discussed along with a set of benchmark calculations involving detonations in clay and sand.

Greg C. Bessette

Modeling Blast Loading on Buried Reinforced Concrete Structures with Zapotec

A physical model of low-velocity probe penetration is developed to characterize soil by type, strength, maximum compaction, and initial density using Newton's second law to describe the processes controlling probe momentum loss. The probe loses momentum by causing soil failure (strength), accelerating and compacting soil around the probe (inertia), and through frictional sliding at the probe/soil interface (friction). Probe geometry, mass, and impact velocity influences are incorporated into the model. Model predictions of probe deceleration history and depth of penetration agree well with experiments, without the need for free variables or complex numerical simulations.

Jerome B. Johnson

James D. Cargile

Donald M. Smith

Soil Properties from Low-Velocity Probe Penetration

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience. 

Shock and Vibration