The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

Assessment of locations along the proposed HS2 Routes that are likely to experience ground vibration boom from high-speed trains

Ground vibration boom is a physical phenomenon associated with a dramatic increase in railway-generated ground vibrations that can occur when train speeds exceed the velocity of Rayleigh waves in the supporting ground. The present paper describes the results of the preliminary assessment of the proposed HS2 routes from the point of view of possible occurrence of ground vibration boom. The analysis is based on the available geological information about the soil composition along the proposed HS2 routes and on the expected train speeds, including areas of train acceleration and deceleration between railway terminals. Rayleigh wave velocities have been calculated for all sites along the routes using the geological data and compared with the expected train speeds at the relevant locations. Using this method, several sensitive locations have been identified where ground vibration boom is likely to occur. The expected levels of ground vibration boom for some sites have been estimated

Structural-acoustic properties of flexible rectangular boxes

Rectangular box-like structures are used widely in a large number of engineering applications, e.g. as elements of railway carriages, heavy goods vehicles, buildings, civil engineering constructions, etc. Although flexible rectangular boxes represent one of the geometrically simple types of engineering structures, their structural-acoustic properties cannot be described by closed-form analytical solutions. In the present study, a comprehensive numerical investigation of typical all-flexible rectangular box structures has been carried out to elucidate the physics of structural-acoustic interaction in them and to explore the possibilities of reduction of the associated structure-borne interior noise. Finite element method has been used to compute the resonant frequencies, the mode shapes and the structural-acoustic frequency response functions of different rectangular box models. The obtained results could assist in better understanding of structural-acoustic properties of flexible rectangular boxes as well as of numerous more complex structures using rectangular boxes as their building elements

Finite element study of the effect of structural modifications on structure-borne vehicle interior noise

This paper presents the results of the numerical investigation of structure-borne vehicle interior noise in a simplified model of vehicle compartment. The aim of the paper is to analyze the effects of different variations of certain geometrical and material parameters of vehicle structure on structural-acoustic frequency response functions. It has been found that geometrical modifications have little influence on the structural natural frequencies. However, they strongly affect the acoustic natural frequencies and normal modes as well as the resulting sound pressure responses. The increase in thickness of the bottom plate suppresses the sound pressure responses very efficiently. However, variations of material characteristics of wind- and back-screen do not have much influence on the interior noise

New approach to investigation of resonant vibrations of noncircular shells based on the theory of coupled waveguides

In the present paper a new simple method of analytical description of resonant vibrations of finite noncircular cylindrical shells is developed. The method is based on the theory of coupled waveguides formed by quasiflat areas of the same noncircular shells having an infinite length (depth). The physical reason for guided wave propagation along quasiflat areas of such shells is the difference between flexural wave velocities in their quasiflat and curved areas, respectively. Using asymptotic expressions for flexural wave velocities in circular shells with different radii of curvature, approximate dispersion equations are derived for waves propagating in such waveguides and their corresponding coupling coefficients. After that, considering shells of finite length, the transition is made from the coupled guided modes to the coupled resonant vibrations of the shell. The obtained resonant frequencies and spatial distributions of the resulting vibration modes are in good agreement with the results of finite element calculations

Finite element and experimental modelling of structure-borne vehicle interior noise

The present paper describes the results of the combined finite element and experimental approach to studying structure-borne vehicle interior noise using a simplified reduced-scale model of a car. The numerical investigation included finite element calculations of structural and acoustic modes as well as frequency response functions for interior acoustic pressure. Experimental tests included measurements of frequency response functions at driver‟s and passenger‟s ear positions, when an electromagnetic shaker exciting structural vibrations was located at different places. The effects of engine mass and of boot load on structure-borne interior noise have been investigated as well. Some of the obtained numerical results have been compared with the experimental ones. The obtained reasonably good agreement between them indicates that structure-borne interior noise in the vehicle model under consideration can be predicted and understood rather well. This implies that the proposed combined numerical and experimental approach to studying vehicle interior noise based on using reduced-scale structural models is simple and reliable, and it can be used successfully by noise and vibration engineers for prediction and mitigation of vehicle interior noise on a design stage

Numerical and experimental modelling of structure-borne aircraft interior noise

In the present paper, the problem of structure-borne interior noise generated in an aircraft cabin has been considered using a simplified reduced-scale model of a passenger aircraft. Experimental investigations included measurements of frequency response functions at several positions of a microphone inside the aircraft, when an electromagnetic shaker exciting structural vibrations was located at different places. Numerical investigations have been carried out as well, and they included finite element calculations of structural and acoustic modes as well as frequency response functions for interior acoustic pressure. Some of the obtained numerical results have been compared with the experimental ones. The observed reasonably good agreement between them indicates that structure-borne interior noise in the described reduced-scale aircraft model can be predicted and understood rather well. This demonstrates that the proposed approach employing simplified reduced-scale structural models can be used successfully for prediction and mitigation of aircraft interior noise

Simplified modelling of vehicle interior noise: comparison of analytical, numerical and experimental approaches

The present paper describes the results of the investigation of low and medium frequency vehicle interior noise carried out using simplified structural-acoustic models. Analytical, finite element (FE) and experimental studies are presented and compared. In particular, the analytical approach is based on the formula representing the interior acoustic pressure in terms of structural and acoustic normal modes. This procedure does not take into account the effect of the enclosed air on structural vibrations. The FE analysis considers structural vibration modes, interior acoustic modes, full structural-acoustic interaction and the resulting structure-borne noise. The above-mentioned analytical and numerical results are compared with each other, and both of them are compared with the experimental results obtained for the simplified reduced-scale vehicle model “QUASICAR” developed in Loughborough University. The comparisons demonstrate some specific features of the analytical and numerical approaches and outline the acceptable limits of simplification in modelling vehicle interior noise. Although this study is concerned with structure-borne vehicle interior noise, its results and conclusions could be of interest for a wider range of engineering problems, such as building acoustics and dynamics of thin shell structures

Finite element calculations of structural-acoustic modes of vehicle interior for simplified models of motorcars

The present paper describes the results of finite element analysis of structural vibration modes, interior acoustic modes, and structural-acoustic modes in some simplified models of road vehicles having different levels of complexity, in particular in the QUArter-Scale Interior Cavity Acoustic Rig (QUASICAR) developed in Loughborough University. All the analysis has been carried out using the original code that had been developed in Patran Command Language (PCL) specifically for the purpose of this research. Resonant frequencies and spatial distributions of structural and acoustic modes have been calculated initially separately and then taking into account structuralacoustic interaction. The results have been compared with the experimental data obtained for QUASICAR. The comparison has demonstrated good agreement between numerical calculations and experimental results. The developed approach is reliable and efficient, and it can be extended to more complex vehicle models, thus assisting in better understanding of vehicle interior noise

Recent progress in reduced-scale modelling of vehicle interior noise

The paper gives a review of the recent research into simplified reduced-scale models of structure-borne vehicle interior noise carried out in Loughborough University. The models under consideration evolve from the simplest ones to more sophisticated developments that take into consideration some important structural dynamic and acoustic features of real vehicles. Analytical and numerical approaches to the theoretical description of such models are discussed. The results of theoretical calculations are compared with the measurements on some reduced-scale models. The comparison of the theory with the measurements demonstrates that simplified reduced-scale models can be used successfully for studying interior noise in real road vehicles. One of the most important issues in this approach is to find a compromise between the minimum degree of complexity of a model and the required accuracy of description of frequency contents and noise levels in a real vehicle