Nomenclature loaded distance between the inner and outer raceway A j groove curvature centre, mm radial component of , mm Ar j A j axial component of , mm Aa j A j B total curvature factor, dimensionless Bd unloaded distance between the inner and outer raceway groove curvature centre, mm c speed of sound, m/s C damping matrix, Ns/m d rolling element diameter, mm F load vector, N force on the spring which represents the gear meshF m stiffness, N mass moment of inertia with respect to direction i, kg m 2 Im i k wave number, m -1 gear mesh stiffness, N/m k g stiffness constant elements of the bearing stiffness k ij matrix, N/m K stiffness matrix, N/m load-deflection constant, N/m K cd gear mesh coupling stiffness matrix, N/m K e bearing stiffness matrix, N/m K m finite element matrix, N/m n K Mi gear mass, kg m i M mass matrix, kg resultant moment in the i direction, Nm M i p pressure, N/m 2 q displacement vector, m velocity vector, m/s . q acceleration vector, m/s 2 .. q r curvature radius of the internal ring (for ball roller) or primitive radius (for cylindrical roller), m curvature radius of the external ring of the ball bearing, m r e curvature radius of the internal ring of the ball bearing, m r i radial gap, m r L base circle radius of the i-th gear, m R bi driven gear pitch radius, m R bc driver gear pitch radius, m R bp resultant force in the i direction, N R i X main axis in the x-direction Y main axis in the y-direction Z main axis in the z-direction, or number of rolling elements Greek Symbols angular displacement in the i-direction, degrees i contact angle without load, degrees 0 resultant elastic deformation of the j-th ball or roller j element, mm axial displacement of the j-th roller element, mm a j translational displacement in the i-direction, mm i resultant elastic deformation of the j-th ball element, mm E radial displacement of the j-th roller element, mm r j resultant elastic deformation of the j-th roller ele-R ment, mmIn this article, a global vibro-acoustic method to model gearboxes, which is based on the finite element and boundary element methods, is presented. The final aim of the method is to investigate the vibration and noise transmitted to the gearbox structure casing, which originate from the excitation caused by the gear train, in order to predict the vibro-acoustic parameters. Thus, the mathematical formulae that allow the determination of generalised stiffness matrices are presented in terms of the bearing and gear elements. A numerical model of the geared axle system that allows the estimation of the bearing reactions due to the gear forces transmitted is developed. This model takes into account the influence of modifying the gears teeth profile. The finite elements and boundary meshes were devised and generated in order to represent the gearbox. These meshes were used for the estimation of the acoustic parameters and for vibro-acoustic predictions. † Member of the International Institute of Acoustics and Vibration (IIAV) (pp 61-72)
This paper presents the procedures and results of an experimental, numerical simulation and analytical model of sound reduction index of solid brick wall. The solid brick used has the following dimensions: 22×10×5 cm and density of 1850 kg/m3. The physic-mechanical characteristics: density, resistance, and elasticity modulus were measured using a set of small walls (0.60×0.63 m). One wall of 4.10×3.20×0.10 m (length/height/thickness) was built between two reverberant rooms, with 60 and 63 cubic meters in volume, respectively. Two kinds of junctions were used between the wall and the concrete walls of the reverberant rooms: elastic junction (with a thin layer of rubber, sealed with silicon rubber on both sides and the top of the wall) and rigid junction (using the normal mortar). The sound reduction index was measured according to ISO 140-3 using airborne transmission. The brick characteristics were used as input data for the statistical energy analysis (SEA) model. The results from SEA, analytical, and measured models are compared.
The governing equation iS Both ends fixed 20 Mass and spring at the left end-right end fixed 22 Mass and spring support between ends while ends are fixed Cable with support and mass-spring attached at each end CHAPTER 4. DAMPED CABLE AND DAMPED SUPPORT SYS TEM The excitation load iii A damped taut string with both ends fixed 59 Damped cable with support and both ends fixed 68 Reduction in cable response due to the support damping 72 Transient response when left span is excited by a point load at the midpoint 76 Damped cable with damped support and damped mass-spring attachment at the ends 83 Transient response at selected points when exciting left span with a point load at its midpoint 86
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