Analysis of flat and curved piezo-actuators for vibration control of cylindrical shells

Analytical investigations on flat and curved piezo-actuators are performed in order to design actuator parameters for coupling to lower order cylindrical shell modes. Equivalent forces exerted by different shaped piezo-actuators are studied. It is shown that out-of-phase driven bi-morph piezo-actuators exert line moments along their boundaries regardless of shape. Their wavenumber transforms are presented in order to give a better understanding of the mode coupling characteristics of these piezo-actuators when surface-bonded to structures. It is shown that the out-of-phase configuration couples strongly to higher order modes due to the line moments. Curved bi-morph piezo-actuator models are developed to understand the influence of curvature. The models are developed using static assumptions. Two drive configurations are studied: in-phase and out-of-phase. The in-phase model exerts line forces and uniform pressure load over the patch area. The out-of-phase model exerts line moments. The static assumptions of the curved model are verified using a wave propagation approach. The model developed does reasonably well for actuator thicknesses up to a quarter thickness of the shell at resonances and up to half the shell thickness at off-resonances. Beyond this thickness the dynamic effects of the actuator mass and stiffness cause deviations. Finally, the developed model is used to propose design guidelines using properties like size, location, thickness of the actuator to excite lower order modes in a cylindrical shell. It is shown that in-phase actuation is better for exciting lower order shell modes than out-of-phase actuation. Also, the shell aspect ratio, the actuator size and location are important parameters influencing the shell response. In order to excite lower order cylindrical shell modes and alleviate the spillover problem, large actuators will be required

Wave attenuation in periodic three-layered beams: analytical and FEM study

We study infinite composite beams with periodic simple supports and analyze their vibration attenuation characteristics. In the literature single spans of such beams have been studied for determining their loss factors. Such loss factor information is insufficient for determining attenuation in the periodic or multispan case. Here, we directly derive propagation constants as a function of frequency. Two distinct cases are investigated in detail.The first is a three-layered periodic beam with a continuous central visco-elastic layer.The second is a periodic beam with visco-elastic inserts of finite extent. The former is analytically tractable and yields insight, while the latter has better structural properties for practical applications. The continuous layer case is studied using several different beam theories. The case with inserts is studied for several different configurations using FEM. Dependence of attenuation characteristics on size, location, and number of inserts is presented. This study provides insights that will be useful for designing visco-elastic inserts for vibration attenuation in periodic structures

Dynamics and Control Systems (ME240) Lecture Notes

This is a basic course on classical or s-domain control theory. It will be taught as part of the course with the title "Dynamics and Control Systems (ME 240)". The dynamics portion will be covered during the months of August and September. The controls portion during October and November. There will be two lectures/week (total 3hrs). The relevant lecture notes will be provided in a pdf form. There are in all seven pdf files. This entire material will be covered in the two months. Each pdf file comes with matlab *.m files. The matlab commands for the cases presented in the lectures are given in the *.m files. Separate worksheets will be given for the purpose of practice and study. The solutions will be discussed in a separate classroom session. There will be one midterm for the controls portion around the end of November and then a final exam. This course is meant for students who have no prior background in s-domain control theory. However, since the material is taught within a short span of two months, the teaching pace may be high. These lecture notes draw heavily from the two references mentioned below. The students will benefit by refering to the same

Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell

In this paper, a suitable nondimensional `orthotropy parameter' is defined and asymptotic expansions are found for the wavenumbers in in vacuo and fluid-filled orthotropic circular cylindrical shells modeled by the Donnell-Mushtari theory. Here, the elastic moduli in the two directions are greatly different; the particular case of E-x >> E-theta is studied in detail, i.e., the elastic modulus in the longitudinal direction is much larger than the elastic modulus in the circumferential direction. These results are compared with the corresponding results for a `slightly orthotropic' shell (E-x approximate to E-theta) and an isotropic shell. The novelty of this presentation lies in obtaining closed-form expansions for the in vacuo and coupled wavenumbers in an orthotropic shell using perturbation methods aiding in a better physical understanding of the problem

Resonance and beating phenomenon in a nonlinear rigid cylindrical acoustic waveguide: The axisymmetric mode

A rigid-walled semi-infinite circular cylindrical waveguide enclosing a weakly nonlinear fluid is considered. A quadratic nonlinear interaction is assumed as a model. A flat rigid piston generates an axisymmetric harmonic pressure that is prescribed as the input at the finite end of the waveguide. The objective is to study the modal interactions of waves. A regular perturbation method is used to separate the linear (primary) and the quasilinear (second harmonic) equations. First, linear solutions are established. Their quasilinear interactions then lead to modal interactions. Typically, the linear wavenumbers at the quasilinear order generate homogenous wavenumbers. Intersections of both these wavenumbers in the wavenumber-frequency plane are considered as resonances since the resulting pressure grows in amplitude in the axial propagating direction. The conditions under which the solutions become resonant or non-resonant are presented. In this last case, a beating phenomenon occurs with distance. It is found that the resonances are rare, except for the plane wave. Generally, the forced linear wavenumbers and the quasilinear generated wavenumbers acquire numerical values close to each other and create the beating phenomenon. (C) 2019 Elsevier Ltd. All rights reserved

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode

An asymptotic analysis for the coupled dispersion characteristics of a structural acoustic waveguide

Analytical expressions are derived, using asymptotics, for the fluid-structure coupled wavenumbers in a one-dimensional (1-D) structural acoustic waveguide. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation with an added term due to the fluid-structure coupling. As a result of this coupling, the prior uncoupled structural and acoustic wavenumbers, now become coupled structural and acoustic wavenumbers. A fluid-loading parameter e, defined as the ratio of mass of fluid to mass of the structure per unit area, is introduced which when set to zero yields the uncoupled dispersion equation. The coupled wavenumber is then expressed in terms of an asymptotic series in e. Analytical expressions are found as e is varied from small to large values. Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. This systematic derivation helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Though the asymptotic expansion used is limited to the first-order correction factor, the results are close to the numerical results. A general trend is that a given wavenumber branch transits from a rigid-walled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an-intersection in the coupled case, but a gap is created at that frequency. (c) 2007 Elsevier Ltd. All rights reserved

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc

Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell

In this paper, a suitable nondimensional `orthotropy parameter' is defined and asymptotic expansions are found for the wavenumbers in in vacuo and fluid-filled orthotropic circular cylindrical shells modeled by the Donnell-Mushtari theory. Here, the elastic moduli in the two directions are greatly different; the particular case of E-x >> E-theta is studied in detail, i.e., the elastic modulus in the longitudinal direction is much larger than the elastic modulus in the circumferential direction. These results are compared with the corresponding results for a `slightly orthotropic' shell (E-x approximate to E-theta) and an isotropic shell. The novelty of this presentation lies in obtaining closed-form expansions for the in vacuo and coupled wavenumbers in an orthotropic shell using perturbation methods aiding in a better physical understanding of the problem

Asymptotic expansions for wavenumbers in orthotropic fluid-filled circular cylindrical shells for intermediate fluid loading

Coupled wavenumbers in infinite fluid-filled isotropic and orthotropic cylindrical shells are considered. Using the Donnell-Mushtari (DM) theory for thin shells, compact and elegant asymptotic expansions for the wavenumbers are found at an intermediate fluid loading for both the coupled rigid-duct modes (''fluid-originated'') and the coupled structural wavenumbers (''structure-originated modes'') over the entire frequency range where DM theory is valid. The coupled rigid-duct expansions are found to be valid for O(1) orthotropy and for all circumferential orders, whereas the coupled structural wavenumber expansions are valid for small orthotropy and for low circumferential orders. These two above results are then used to derive the expansions for a set of multiple complex roots that display a locking behavior at this intermediate fluid-loading. The expansions are matched with the numerical solutions of the coupled dispersion relation and the match is found to be good over most of the frequency range. (C) 2014 Acoustical Society of America