1 edition of The attenuation of flexural waves in mass loaded beams found in the catalog.
The attenuation of flexural waves in mass loaded beams
Timothy L. Smith
by Massachusetts Institute of Technology
Written in English
|The Physical Object|
|Number of Pages||185|
Resonance theory for acoustic plane wave transmission through a fluid-loaded layer or plate. Massachusetts A venue, Cambridge Attenuation of flexural waves on a fluid-loaded. Wang, J. Wen and X. Wen, Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method: Application to locally resonant beams with flexural wave band gap, Physical Review B.
To demonstrate the wave-attenuation mechanism, the mode shapes of the adaptive metamaterial beam at 5 and 15 kHz are shown in figure 8(a) and (b), respectively. It can be found that the flexural wave can be efficiently attenuated by the out-of-phase motions in the designed resonators, in which the dominated motion along the z-direction is. effective method of improving the wave attenuation behavior of sandwich beams. The local resonance behavior of the inserted resonators was shown to induce a wave attenuation bandgap which allows for effective attenuation of harmonic flexural waves. In this study, the effectiveness of such a sandwich design under impact loads is considered.
A periodic binary straight beam with different cross sections is constructed and studied. The band structures of flexural waves in the structure are calculated with the plane-wave expansion method and the vibration attenuation spectra of a finite sample of it . Current approaches for manipulating and bending flexural waves depend on either changing the effective refractive index to steer wa23,24, or exploiting frequency bandgaps to guide waves.
For a beam with PCLD, the flexural attenuation performance can be quantified by two flexural-wave propagation constants, which are affected by both Bragg scattering and damping. The overall attenuation level is mainly dominated by Bragg scattering in and near the band-gaps and mainly controlled by damping out of the band-gaps in higher by: 6.
in the beam-type structure to reduce the vibration in extensive studies. Wen  studied the flexural wave propagation of a periodic thin straight beam and discussed the band-gap property caused by Bragg-scattering effect.
Yu  and Xiao  studied the band-gap property of a beam attached with periodic spring-mass systems. Beam cells with same lattice constant but different LRs are illustrated in Fig. the case for N = 3, the mass and stiffness of the local resonator are four times larger than the case for N = The right panel of Fig.
4 implies that larger local resonators result in better wave attenuation. But large resonators mean heavy add-on by: Flexural wave propagation of a metamaterial beam containing membrane-mass structures is investigated. A low-frequency resonant-type bandgap where waves cannot propagate freely is created.
By altering the properties of the membrane-mass Cited by: 9. the attenuation of flexural waves in mass loaded beams by timothy l. smith lt/usn b.s. mech. eng., auburn university () submitted to t department of ocean engineering in partial fulfillment of the requirements for the degrees of master of science in naval architecture and marine engineering and master of science in mechanical engineering Cited by: 1.
Discussion of Time Signals The equation of motion for flexural (bending) waves in a beam is where is the speed of a quasi-longitudinal wave (E is Young's modulus and ρ is the mass density).
This equation of motion is a fourth-order differential equation such that the solutions are not of the form y(x,t) = f(x-ct) + g(x+ct).In addition, the flexural wave speed is dispersive.
ATTENUATION OF PLATE FLEXURAL WAVES BY A LAYER OF DYNAMIC ABSORBERS. Flexural waves on beams or plates are frequently the conduit of unwanted vibratory energy from machines, building structures or ship hulls. They can be attenuated by a distribution of masses resiliently mounted to the structure's surface.
In this section, a low-pass flexural wave filter is designed with the aid of a series of non-uniform Euler-Bernoulli beams with graded quadratic profiles, which is contained in the shadow region in Fig. sub-beams are distributed in series in the region of 0 ≤ x ≤ 2 m, and the thickness in each sub-beam varies in the quadratic form.
In this paper, a beam-piezoelectric structure is introduced to focus on the control of flexural waves in beams with piezo-layers connected to single and multi resonant shunt approaches. The smart structure is modelled using the spectral element method.
Figure 1(a) shows the schematic of the adaptive metamaterial beam with the lattice constant, L, width, w h, and thickness, h, for broadband low-frequency wave metamaterial unit cell is constructed by cutting a 'U' shaped thin slot with the width denoted by w s out of the host beam to form a locally resonant cantilever beam located in the center of the unit cell.
Below Hz, the sample has a strong attenuation on flexural and longitudinal vibration in the first two complete BGs, and absorption of the flexural wave is more significant. In the first complete BG, most of the flexural wave transmissions are lower than −40 dB, and in the second one, the lowest point of the transmission could reach −80 dB.
Liu and Hussein studied wave propagation in flexural beams from both categories and mathematically characterized the condition for transition between Bragg scattering and local resonance band gaps in LR beams.
Most research in the area of LR beams has focused mainly on the effect of discrete resonators. A power‐balance analysis is carried out for the response and sound radiation of a homogeneous fluid‐loaded wave‐bearing structure with many identical supports, when the structure is driven at one support point.
A single second‐order difference equation is found for the response, subject to the hypothesis that the energy flux from any support to its neighbors involves only one wave type.
In this work, designs of vibration neutralizers for the reduction of flexural waves in beams are proposed. The system considered consists of an Euler-Bernoulli beam experiencing a harmonically travelling wave. The neutralizer, which consists of a mass, spring, and damper (viscous or hysteretic), is attached at a point on the beam.
The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators.
Figure 1(a) displays the metamaterial beam proposed in this study, which consists of a host beam containing periodic cavities, a membrane, and a frame mass; figure 1(b) shows one-fourth of the model.
The half-length and thickness of the host beam, membrane, and frame mass are denoted by respectively. The width is same as the length, namely, a square unit cell. The study is conducted through a finite element–based numerical technique and substantiated with a discrete mass-in-mass analytical model.
The band structures and wave dispersion characteristics of the multiresonant pillars erected on a thin elastic plate foundation are analyzed. This paper deals with free flexural wave motion and natural deflection mode shapes of simply supported infinite uniform periodic beams consisting of repeating units that are identical finite beams having equal and unequal span lengths.
Governing equations for the natural frequencies and that for the wave propagation constant have first been set up in terms of the receptances of the individual. Active control of the plate flexural wave transmission through the beam in a semi-infinite beam-reinforced plate is analytically investigated.
The ribbed plate is modeled as a continuous system, using equations of motion to describe the plate in flexure and the beam in both flexure and torsion. The maximum transmission of the plate flexural waves through the reinforcing beam is found to occur.
The flexural-wave attenuation performance of traditional constraint-layer damping in a sandwich beam is improved by using periodic constrained-layer damping (PCLD), where the monolithic viscoelastic core is replaced with two periodically alternating viscoelastic cores.
In this paper, the flexural wave band gaps in metamaterial beams with membrane-type resonators are studied by using finite element method.
Existing publications have shown that the finite element method is an effective and efficient way for the investigation of wave propagation properties of periodic structures [ 15, 26 ].Wang, Michael Y., and Wang, Xiaoming.
"Broadband Wave Attenuation in Locally Resonant Periodic Flexural Beams With Force-Moment Resonators." Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.Recently, the propagation of flexural waves along locally resonant phononic crystal (LRPC) beams has been studied by many researchers.
The local resonance beams are often regarded as infinite.