Vibration analysis of a tyre model using the wave finite element method

The vibration of a tyre is predicted using the wave finite element (WFE) method. The material properties are considered to be frequency dependent. The WFE method starts from a conventional finite element (FE) model of only a short section of a structure, which is uniform in one direction. Existing element libraries can be fully utilised and the size of the FE model can be very small. Free wave propagation characteristics are extracted from the dynamic stiffness matrix of the FE model. The forced response is calculated using the wave approach. An approach for determining the amplitudes of the directly excited wave is proposed to reduce numerical difficulties. The method is applied to a tyre FE model formed using ANSYS. The material properties of rubber are considered to be frequency dependent. The free wave propagation is shown including nearfield waves. The predicted forced response is compared with experimental data. Good agreement can be seen on the whole

Emissions testing of two recreational marine engines with water contact in the exhaust stream

Recreational marine engine operation effects water quality as well as air quality. Significant quantities of hydrocarbons are discharged into the rivers, lakes, and estuaries used as recreational boating waters. In order to investigate the impact of recreational marine engine operation on water quality, a MerCruiser 3.0LX four-cylinder four-stroke inboard engine and a Mercury 650 two-cylinder two-stroke outboard engine were tested using EPA required certification procedures. Both engines were tested with exhaust gas/cooling water mixing (scrubbing) in the exhaust stream using both freshwater and saltwater. Additionally, the inboard engine was tested without exhaust scrubbing. Gaseous emissions (HC, NOx, CO, and CO2) from the engines were continuously measured using a constant volume sampling system. Both exhaust gas and cooling water samples were collected and speciated for hydrocarbon species present. In addition, carbonyl compounds were collected by diverting a portion of the exhaust stream through 2,4-dinitrophenylhydrazine (DNPH) charged cartridges. Chromatography methods were used for species identification. Detailed descriptions of the testing apparatus, equipment, and analysis procedures used are included. Results for gaseous emissions, carbonyl compounds, and aqueous samples are reported. The mass ratios of hydrocarbons to carbon dioxide gaseous emission for the MerCruiser and Mercury engines were approximately 0.0046 and 0.55 respectively. These results show that concerns over gaseous hydrocarbon emissions from these sources are warranted. Additionally, high levels of acetone were detected in gaseous emissions from the MerCruiser engine while operated with exhaust scrubbing

Reactions of cyclomanganated complexes with carbon disulfide: routes to η²-aryldithiocarboxylate-Mn(CO)₄ complexes and to the trithiocarbonate complex (μ₃-CS₃)₂Mn₄(CO)₁₆

Reaction of cyclomanganated aryl ketones with CS₂ proceeds with insertion into the Mn–C bond to give η²-dithiocarboxylato–Mn(CO)₄ compounds. With other cyclomanganated substrates such as that from Ph₃P=S and also with Mn₂(CO)₁₀, CS₂ gives (μ₃-CS₃)₂Mn₄(CO)₁₆ with bridging trithiocarbonate ligands

Manganese carbonyl-mediated reactions of azabutadienes with phenylacetylene, methyl acrylate and other unsaturated molecules

Reaction of PhCH₂Mn(CO)₅ with l,4-di-aryl-1-aza-1,3-butadienes gave substituted pyrrolinonyl rings which were η⁴-coordinated to a Mn(CO)₃ group. These are formed by intramolecular CO insertion into a (non-isolated) cyclomanganated intermediate, followed by cyclisation. Other unsaturated reagents (PhC≡CH, CH2=CHCOOMe, PhNCO) gave products arising from insertion of these, including a structurally characterised tri-aryl-η⁵-azacyclohexadienyl-Mn(CO)₃ complex from the reaction with the alkyne. PhCH₂Mn(CO)₅ reacts with l,4-di-aryl-1-aza-1,3-butadienes in the presence of unsaturated substrates to give products based on a cyclomanganated intermediate

Flexural wave propagation in slowly varying random waveguides using a finite element approach

This work investigates structural wave propagation in waveguides with randomly varying properties along the axis of propagation, specifically when the properties vary slowly enough such that there is negligible backscattering. Wave-based methods are typically applied to homogeneous waveguides but the WKB (after Wentzel, Kramers and Brillouin) approximation can be used to find a suitable generalisation of the wave solution in terms of the change of phase and amplitude, but is restricted to analytical solutions. A wave and finite element (WFE) approach is proposed to extend the applicability of the WKB method to cases where no analytical solution is available. The wavenumber is expressed as a function of the position along the waveguide and a Gauss-Legendre quadrature scheme is used to obtain the phase change while the wave amplitude is calculated using conservation of power. The WFE method is used to evaluate the wavenumbers at each integration point. The flexural vibration example is considered with random field proprieties being expressed by a Karhunen-Loeve expansion. Results are compared to a standard FE approach and to the WKB analytical solution. They show good agreement and require only a few WFE evaluations, providing a suitable framework for spatially correlated randomness in waveguides

Vibration control of beams and plates with hybrid active-passive constrained layer damping treatments

The concept of hybrid active-passive constrained layer damping treatments, which consists of viscoelastic materials, piezoelectric materials and elastic constraining materials, was proposed in the 1990s in order to ameliorate problems of instability in traditional active control systems in the higher frequency range. In this paper, the performances of four types of hybrid active-passive constrained layer damping treatments are investigated for beam and plate applications. These types are Active Constrained Layer Damping (ACLD), Active-Passive Constrained Layer Damping (APCLD), Active Control/Passive Constrained Layer Damping (AC/PCLD) and Active Control/Passive Stand-Off Layer Damping (AC/PSOLD). The performances of each treatment are compared through simulation with numerical models using the Finite Element Method. Finally, control performances of all configurations for curved plates are discussed with measured Frequency Response Functions of each case

Adaptive control of radiated sound power based on time-domain estimates of acoustic radiation modes

In active structural acoustic control, broadband control of the radiated sound power from a structure can be achieved by minimizing the amplitudes of the acoustic radiation modes (ARMs). The shape of these ARMs is frequency dependent and only a few might radiate significant power in a given frequency range. In this paper a method is described by which the ARMs are estimated in real-time from a number of point response measurements taken on a vibrating structure. These estimates can be used to calculate the radiated power or, here, in a feedforward adaptive control system. Estimates of the ARM amplitudes in the time domain are produced by digitally filtering the outputs of an array of sensors mounted on the radiator. These filters are designed by FIR filters in the frequency domain based on the frequency-dependent ARMs and implemented in the time domain. These estimates are then used as the cost function in a feedforward, adaptive, filtered-X LMS controller. The theory is described with reference to a 2-dimensional vibrating structure. Finally numerical results of real-time simulations are presented

Time-domain estimation of acoustic radiation modes and active structural acoustic control

This paper presents a method of calculating the radiated sound power of vibrating structures based on the time domain estimation of acoustic radiation modes (ARMs). Each ARM is frequency-dependent, radiates power independent of the other ARMs and can be estimated in the time domain from measurements made at discrete sensor locations on the surface of the radiating structure. The individual ARM components are estimated digitally in the time domain using finite impulse response filters, which are designed to provide a best weighted fit to the ARMs in the frequency domain. The ARM amplitudes are estimated by filtering the vectors of measured velocities at points on the radiating surface with these ARM filters, before summing the product of the square of these amplitudes with the relevant eigenvalues to estimate the radiated sound power. The method is described with reference to a simply supported beam model. The results show that the sound power calculated from the proposed approach and from a frequency domain approach are comparable. Finally, a time domain feedforward active structural acoustic control system developed using the proposed method is presented and time domain simulations demonstrate the performance of the system

A framework for the analysis of vibrations of structures with uncertain attachments

Attachments affect the dynamic response of an assembled structure. When engineers are modelling structures, small attachments will often not be included in the “bare” model, especially in the initial design stages. The location of these attachments might be poorly known, yet they affect the response of the structure. This paper considers how attachments jointed to the structure at uncertain points, can be included in the dynamic model of a structure. Two approaches are proposed. In the time domain, a combination of component mode synthesis, characteristic constraint modes and modal analysis gives a computationally efficient basis for subsequent analysis using, for example, Monte Carlo simulation. The frequency domain approach is based on assembly of frequency response functions of bare structure and attachment. Numerical examples of a beam and a plate with a point mass added at an uncertain location are considered and predictions compared with experiment results