Mixed Convolved Action Principles for Dynamics of Linear Poroelastic Continua

Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on poroelastic media extends the recent formulation of a mixed convolved action to address a continuum dynamical problem with dissipation through the development of a new variational approach. The action in this proposed approach is formed by replacing the inner product in Hamilton’s principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulations developed here employ temporal impulses of velocity, effective stress, pore pressure and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting mixed convolved action is formulated in both the time and frequency domains to develop two new stationary principles for dynamic poroelasticity. In addition, the first variation of the action provides a temporally well-balanced weak form that leads to a new family of finite element methods in time, as well as space.

Dynamic Analysis of a Cylindrical Roller Bearing With Time-Varying Localized Defects on Raceways

An existing defect on the bearing raceway may evolve with the interactions between the bearing elements, and the evolutions of the defect may be divided into different stages. In this study, a dynamic model for a cylindrical roller bearing with localized defects on raceways is developed to investigate vibration character of the bearing in these stages. The coupling of centrifugal forces, gravity forces and the slipping of the roller are considered. The half sine function and step function are used to construct time-varying models of defects in different stages, which is reflected on the local deflection. The system dynamic equations are solved by the fourth-order Runge-Kutta integration method with variable steps. Time domains and frequency domains are used to analyze dynamic responses of the bearing in every defect stage, which can be used as a reference of fault diagnosis. An experimental comparison in the previous study is carried out to validate the proposed model.

Study on Acoustic Analysis of a Glass Window by BEM and FEM

This research employed acoustic analysis software and established an analytical method for sound transmission loss, which is a sound-insulation performance measure for glass windows. In addition to prediction of transmission loss through vibration of the glass, the research estimated acoustic characteristics that considered transmission loss in the vibration of the frame. Acoustic analysis was conducted with 3D CAD for glass windows of 8 mm plate thickness through preparation of an analysis model under the same conditions as a vibration test. The acoustic analysis also considered both the glass pane and aluminum frame on the side of the sound source. This paper evaluated the results based on analytical values and experimentally observed values.

Modification of Doublet Modes in a Circular Disc Constrained by Cyclic Symmetric Features

From design perspective, structural modification including material modification and geometry modification in a brake system is the most common approach in reducing the brake squeal. Research of this paper will focus on the modification of the largest noise-generating part in motorcycle’s brake system-the circular disc rotor, based on an existing product available in Taiwan. To reach the best geometry design of a circular disc rotor for specific vibration reduction criteria, parametric studies will be carried out in understanding effects of two evenly distributed modifications in the disc — the bolts and ribs. This paper aims to find a criterion in dealing with the design of a pattern on a disk through finite element analyses and experimental modal analyses. From which results, a new criterion for frequency splitting is developed and a mode-veering phenomenon is observed. The outcome has engineering application in reducing specific squeal noise caused by split doublet modes and shifting natural frequencies of a brake disc without creating a new one.

Introducing Entropy for the Statistical Energy Analysis of an Artificially Damped Oscillator

The purpose of this paper is to introduce the concept of entropy for a main resonator attached to a “fuzzy structure”. This structure is described explicitly using the Lagrangian method, and is treated as a layer of discrete resonators. A generic entropy formulation is then developed for the layer of resonators, which is used to determine the individual oscillator entropies. The combined entropy of the linear resonator system is then determined and compared numerically to the sum of the individual oscillator entropies. The entropy behavior of the system is then related to the energy behavior of the system and explained in regards to the the “artificial damping” of the main resonator.

GHz Heterogeneous Phononic Crystal Slab Resonators

In this paper, we present a new design for waveguide-based phononic crystal (PnC) resonators in pillar-based piezoelectric membranes at the GHz frequency range based on mode-gap waveguide termination. The mode confinement in these resonators is achieved by a smooth transition from a phononic waveguide to another phononic waveguide that does not support (and therefore reflects) the guided modes of the first waveguide over a certain frequency range. These resonators can be utilized for applications including wireless communications and sensing [1, 2] where high-Q and high-frequency resonators are highly desirable.

Profiling a Cylindrical Roller Bearing Oil-Film Thickness Distribution With Ultrasound

The rollers and raceways in cylindrical roller bearings are separated by an extremely thin lubricant film over a narrow region, which is critical to performance. The ultrasound method has been applied successfully to a range of bearings including journal and ball bearings. But the actual maximum speed that can be measured is limited by the repetition frequency of the ultrasonic pulse. Otherwise, a single measurement point cannot image the thickness distribution of the cylindrical roller bearing. This paper describes the measurement of lubricant-film thickness distribution in a roller bearing by moving the ultrasound transducer. A new ultrasonic pulser-receiver is used to get enough effective measurement points. For a range of loads and speeds, the oil-film thicknesses of four positions along the roller are measured. The influences of the rotating speed and radial load on the film thickness measurement are consistent with the theoretical predictions. The limits of the PRR used in measurements are discussed and the averaging effect of the transducer focal zone size is observed.

‘Acoustic Fiber’ Aluminum-Clad Copper Cable for Communication and Power Transmission

An ‘acoustic fiber’, analogous to optical fiber, is presented as a means of long-distance data and energy transfer. Low-loss axial guided waves are produced along a cable-like waveguide, which is composed of a solid core and a cladding layer, where the cladding’s acoustic speeds of sound, both longitudinal and transverse, exceed those of the core. A similar condition exists in glass fiber optic cables consisting of a core surrounded by a cladding of lower index of refraction. This results in total internal reflection of light at the core-cladding interface and effective confinement of light to the core. A specific acoustic waveguide construction is analyzed, composed of an aluminum cladding with longitudinal wave speed of 6.198 km/s and shear wave of 3.122 km/s and copper core with longitudinal speed of 4.505 km/s, and shear speed of 2.164 km/s. Finite element simulations show that a guided wave mode that is confined largely to the core exists and is capable of propagating long distances with very little loss to the surroundings. A 6 mm diameter aluminum-cladded copper core (2 mm diameter) fiber was found to have a propagation loss of 0.023 dB/m when operating at 2 MHz predict (neglecting material attenuation). When including material attenuation, the same waveguide produced a propagation loss of 0.24 dB/m. Similarly, a 12 mm cladding with 4.8 mm core at 1 MHz had losses of 0.10 dB/m, and a 22 mm diameter cladding with 9 mm core at 500 kHz had losses of 0.062 dB/m. Relationships were found between frequency, total diameter and core diameter yielding the highest efficiencies. The minimum total dimension of an aluminum-clad-copper acoustic fiber was found to have an inverse relationship with frequency. The optimum ratio of core to total diameter was about 0.45 but between values of 0.35 and 0.5, attenuation was relatively constant (insensitive to frequency). Outside of that range, attenuation climbed rapidly. Due to this property, attenuation in properly designed fibers should always be dominated by, and roughly equivalent to, the material attenuation rather than attenuation due to leakage.

Wideband Acoustic Luneburg Lens Based on Graded Index Phononic Crystal

The present study proposes a wideband two-dimensional Luneburg lens using graded phononic crystals (GPCs). We present a method to broaden the range of operation frequency of the Luneburg lens based on GPCs. The GPCs is composed of circular cylindrical rods with triangular lattice air background. In long wavelength limit assumption, periodic structure behaves like a homogeneous medium since dispersion relations is almost linear. The effective refractive index can be tuned by adjusting the filling ratio. The plan wave expansion method is utilized to calculate the band structures of the locally GPCs and the effective refractive index of the locally GPCs with different filling ratio. Finite element simulations was employed to confirm the acoustic properties of designed device. Our numerical simulations demonstrate that the operation frequency range of GPCs of circular cylindrical rods arranged as triangular array is much wider than those of square array. A wideband acoustic Luneburg lens can be achieved by using graded phononic crystals of triangular array.

Aeroacoustics of Open Cavities With Modified Geometry for Low Mach Number Flow

A numerical study using our source code to acquire the acoustic properties of subsonic flow past an open cavity with different modified geometries will be presented in this paper. A Modified Curle’s analogy will be applied to solve the far field acoustics of the flow. Several cases with different leading edge of cavity fillet radii will be analysed and the effects will be investigated. It is important to find a way to attenuate the sound generation by the cavity, as it is an undesired situation for most applications. In this work a passive system, fillet modification to the leading edge of the cavity, is suggested and the effects of it on the sound generation is investigated.