1,721,034 research outputs found
Forced response of two-dimensional homogeneous media using the wave and finite element method
No full textExperimentally validated model of a membrane strip with multiple actuators
No full textThis paper presents the modeling and experimental validation of a membrane strip actuated in bending and
tension. This investigation is a prelude to the modeling of a circular membrane augmented with smart actuators
around its outer rim. Two macrofiber composite bimorph actuators are attached near the ends of the membrane
strip.Wetreat two configurations. In the first configuration, both bimorph actuators are excited in bending to change
the shape of the membrane strip. In the second configuration, one bimorph acts in bending and the other bimorph
acts in tension. The membrane strip is modeled as a nonuniform, nonhomogenous, Euler–Bernoulli beam under
tension. The finite element method is used to facilitate the handling of the nonuniformities of the combined structure.
Experimental results are used to validate the model developed. The prediction of the finite element model and the
experimental results are in agreemen
Calculating the forced response of two-dimensional homogeneous media using the wave and finite element method
No full textThe forced response of two-dimensional, infinite, homogenous media subjected to time harmonic loading is treated. The approach starts with the wave and the finite element (WFE) method where a small segment of a homogeneous medium is modelled using commercial or in-house finite element (FE) packages. The approach is equally applicable to periodic structures with a periodic cell being modelled. This relatively small model is then used, along with periodicity conditions, to formulate an eigenvalue problem whose solution yields the wave characteristics of the whole medium. The eigenvalue problem involves the excitation frequency and the wavenumbers (or propagation constants) in the two directions. The wave characteristics of the medium are then used to obtain the response of the medium to a convected harmonic pressure (CHP). Since the Fourier transform of a general two-dimensional excitation is a linear combination of CHPs, the response to a general excitation is a linear combination of the responses to CHPs. Thus, the response of a two-dimensional medium to a general excitation can be obtained by evaluating an inverse Fourier transform. This is a double integral, one of which is evaluated analytically using contour integration and the residue theorem. The other integral can be evaluated numerically. Hence, the approach presented herein enables the response of an infinite two-dimensional or periodic medium to an arbitrary load to be computed via (a) modelling a small segment of the medium using standard FE methods and post-processing its model to obtain the wave characteristics, (b) formulating the Fourier transform of the response to a general loading, and (c) computing the inverse of the Fourier transform semi-analytically via contour integration and the residue theorem, followed by a numerical integration to find the response at any point in the medium. Numerical examples are presented to illustrate the approac
An experimentally verified model of a membrane mirror strip actuated using piezoelectric bimorph
No full textThe behavior of a membrane mirror strip actuated using a piezoelectric bimorph is treated. An improved model for the transverse vibration is presented. The model accounts for the changes in physical properties of the membrane strip at the location of the piezoelectric bimorph. The membrane strip is modeled as a pinned-pinned beam under tension and the finite element method (FEM) is used to represent the system mathematically. The beam under tension assumption allows accounting for the traveling wave effect experienced by a membrane strip and the added flexural rigidity induced by the piezoelectric bimorph. Additionally, the structural and air damping effects are included in the model. An experimental setup is built to verify the proposed model. The frequency response obtained from the proposed model is shown to be in agreement with conducted experiments. Furthermore, the importance of including local mass and stiffness effects is demonstrate
Vibration modelling of helical springs with non-uniform ends
No full textHelicalsprings constitute an integral part of many mechanical systems. Usually, a helicalspring is modelled as a massless, frequency independent stiffness element. For a typical suspension spring, these assumptions are only valid in the quasi-static case or at low frequencies. At higher frequencies, the influence of the internal resonances of the spring grows and thus a detailed model is required. In some cases, such as when the spring is uniform, analytical models can be developed. However, in typical springs, only the central turns are uniform; the ends are often not (for example, having a varying helix angle or cross-section). Thus, obtaining analytical models in this case can be very difficult if at all possible. In this paper, the modelling of such non-uniformsprings are considered. The uniform (central) part of helicalsprings is modelled using the wave and finite element (WFE) method since a helicalspring can be regarded as a curved waveguide. The WFE model is obtained by post-processing the finite element (FE) model of a single straight or curved beam element using periodic structure theory. This yields the wave characteristics which can be used to find the dynamic stiffness matrix of the central turns of the spring. As for the non-uniformends, they are modelled using the standard finite element (FE) method. The dynamic stiffness matrices of the ends and the central turns can be assembled as in standard FE yielding a FE/WFE model whose size is much smaller than a full FE model of the spring. This can be used to predict the stiffness of the spring and the force transmissibility. Numerical examples are presente
Wave transmission through two-dimensional structures by the hybrid FE/WFE approach
No full textThe knowledge of the wave transmission and reflection characteristics in connected two-dimensional structures provides the necessary background for many engineering prediction methodologies. Extensive efforts have previously been exerted to investigate the propagation of waves in two-dimensional periodic structures. This work focuses on the analysis of the wave propagation and the scattering properties of joined structures comprising of two or more plates. The joint is modelled using the finite element (FE) method whereas each (of the joined) plate(s) is modelled using the wave and finite element (WFE) method. This latter approach is based on post-processing a standard FE model of a small segment of the plate using periodic structure theory; the FE model of the segment can be obtained using any commercial/in-house FE package. Stating the equilibrium and continuity conditions at the interfaces and expressing the motion in the plates in terms of the waves in each plate yield the reflection and transmission matrices of the joint. These can then be used to obtain the response of the whole structure, as well as investigating the frequency andincidence dependence for the flow of power in the system
Inverse dynamics based tuning of a fuzzy logic controller for a single-link flexible manipulator
No full textSince its introduction to engineering applications, fuzzy logic has attracted many researchers because of its simplicity and robustness. Experience with a system is translated into heuristic rules which can be used to control that system. This article proposes a novel method for a generalized inverse dynamics based fuzzy logic controller (FLC) of a single-link flexible manipulator. The deflection of the flexible link was modeled using the assumed modes method. The control action is distributed between two FLCs: A joint angle controller and a tip controller. Each controller produces a torque value. The torque values are summed, and the resulting control action is used to drive the manipulator. A novel method for varying the ranges of the variables of the two controllers as a function of the motion parameters and the inverse dynamics of the system is presented. The relative shapes and distribution of the fuzzy membership sets (with respect to each other) are kept fixed. Simulation results show that joint trajectory tracking is accomplished, and that the residual vibration of the flexible link is suppressed
Modeling and control of membrane mirror strip using single piezoelectric bimorph
No full textThis paper presents an improved finite-element model of a membrane strip actuated by a single piezoelectric bimorph. The paper also treats the static shape control problem of the structure under study. The membrane strip is modeled as an Euler—Bernoulli beam under tension, with non-uniform physical properties. The finite-element method allows the development of a model that accounts for the actuator dynamics. The static shape control problem is formulated as a disturbance rejection problem and solved using a proportional-integral (PI) controller. The PI control gains are obtained using the linear quadratic regulator theory. The proposed model is verified experimentally, and the closed loop system is simulated to demonstrate the effectiveness of the control law
On the optimal energy harvesting from a vibration source
No full textThe optimization of power acquired from a piezoelectric vibration-based energy harvester which utilizes a harvesting circuit employing an inductor and a resistive load is described. The optimization problem is formulated as a nonlinear program wherein the Karush–Kuhn–Tucker (KKT) conditions are stated and the resulting cases are treated. In the first part of the manuscript, the case of a purely resistive circuit is analyzed. While this configuration has received considerable attention in the literature, previous efforts have neglected the effect of damping on the optimal parameters. Here, we explore the impact of damping on power optimality and illustrate its quantitative and qualitative effects. Further, we analyze the effect of electromechanical coupling demonstrating that the harvested power decreases beyond an optimal coupling coefficient. This result challenges previous literature suggesting that higher coupling coefficients always culminate in more efficient energy harvesters. In the second part of this work, the effect of adding an inductor to the circuit is examined. It is demonstrated that the addition of the inductor provides substantial improvement to the performance of the energy harvesting device. It is also shown that within realistic values of the coupling coefficient, the optimal harvested power is independent of the coupling coefficient; a result that supports previous findings for the purely resistive circuit
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