Topic
Macaulay's method
About: Macaulay's method is a research topic. Over the lifetime, 4 publications have been published within this topic receiving 69 citations.
Papers
TL;DR: A resonant magnetic field microsensor based on Microelectromechanical Systems (MEMS) technology including a piezoresistive detection system has been designed, fabricated, and characterized as mentioned in this paper.
Abstract: A resonant magnetic field microsensor based on Microelectromechanical Systems (MEMS) technology including a piezoresistive detection system has been designed, fabricated, and characterized. The mechanical design for the microsensor includes a symmetrical resonant structure integrated into a seesaw rectangular loop (700 μm × 450 μm) of 5 μm thick silicon beams. An analytical model for estimating the first resonant frequency and deflections of the resonant structure by means of Rayleigh and Macaulay's methods is developed. The microsensor exploits the Lorentz force and presents a linear response in the weak magnetic field range (40–2000 μT). It has a resonant frequency of 22.99 kHz, a sensitivity of 1.94 V T −1 , a quality factor of 96.6 at atmospheric pressure, and a resolution close to 43 nT for a frequency difference of 1 Hz. In addition, the microsensor has a compact structure, requires simple signal processing, has low power consumption (16 mW), as well as an uncomplicated fabrication process. This microsensor could be useful in applications such as the automotive sector, the telecommunications industry, in consumer electronic products, and in some medical applications.
35 citations
TL;DR: In this article, the logical basis of the method is explained, and detailed expressions are derived in a form suitable for immediate application to a wide range of static and pulsating beam problems and to some axially symmetrical plate problems.
Abstract: Some recent references to the use of Macaulay brackets in the analysis of the deflections of beams under discontinuous lateral loads suggest that it is not widely realized that the concept can easily be generalized to apply to a wide range of problems, particularly those occurring in structural mechanics. In this paper the logical basis of the method is explained, and detailed expressions are derived in a form suitable for immediate application to a wide range of static and pulsating beam problems and to some axially symmetrical plate problems.
24 citations
TL;DR: In this paper, the authors extended the Macaulay bracket notation for the deflection analsyis of a Euler-Bernoulli beam subject to multiple or discontinuous loads.
Abstract: The Macaulay bracket notation is familiar to many engineers for the deflection analsyis of a Euler-Bernoulli beam subject to multiple or discontinuous loads. An expression for the internal bending moment, and hence curbature, is valid at all locations along the beam, and the deflection curve can be calculated by integrating twice with respect to the axial coordinate. The notation obviates the need for matching of multiple constants of integration for the various sections of the beam. Here, the method is extended to a Timoshenko beam, which includes the additional deflection due to shear. This requires an additional expression for the shearing force, also valid at all locations along the beam.
21 citations
TL;DR: In this paper, complete non-series solutions for steady-state vibrations of uniform-section beams with all possible combinations of various supports are given, using a generalization of the Macaulay notation commonly used for evaluating static beam deflections.
Abstract: Complete non-series solutions for steady-state vibrations of uniform-section beams with all possible combinations of various supports are given, using a generalization of the Macaulay notation commonly used for evaluating static beam deflections. The presence of flexible restraints and elastic hinges is considered within the same framework. The application of the method is shown by some specific calculations.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2011 | 1 |
| 2007 | 1 |
| 1965 | 1 |
| 1960 | 1 |