Nonlinear smart beam model for energy harvesting

2020 ◽  
pp. 1-35
Author(s):  
Wenguo Zhu ◽  
Marco Morandini
Keyword(s):  
Electromechanical Coupling ◽  
Nonlinear Modeling ◽  
Piezoelectric Transducers ◽  
Constitutive Law ◽  
Beam Model ◽  
Cross Sectional ◽  
Nonlinear Beam ◽  
Mass Properties ◽  
Smart Beam ◽  
Fully Coupled

Abstract In this paper, the nonlinear modeling of beam energy harvester embedded with piezoelectric transducers is presented. Starting from a multibody dynamics perspective, a fully coupled electromechanical nonlinear beam model was derived and a geometrically exact finite volume beam element, including the circuit equation is developed. In this model, the beam resultants-strain constitutive law and mass properties are obtained from a 2D beam cross sectional modeling in which the electromechanical coupling effects are included. The results are verified against numerical and experimental results reported in the literature.

scholarly journals Nonlinear Modeling and Control Design of Active Helicopter Blades

2012 ◽  
Vol 57 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Matthias Althoff ◽  
Mayuresh J. Patil ◽  
Johannes P. Traugott
Keyword(s):  
Structural Model ◽  
Simulation Analysis ◽  
Nonlinear Modeling ◽  
Control Design ◽  
Beam Model ◽  
Linear Quadratic ◽  
Cross Sectional ◽  
Modeling And Control ◽  
Helicopter Blades ◽  
And Control

This paper presents the theoretical basis for the simulation and control of active helicopter blades. The analysis is based on a model that considers the structural dynamics, the aerodynamics, as well as the integrated blade actuation and sensing. The effect of the integral actuation enters the beam model via an active beam cross-sectional analysis. A two-dimensional incompressible, inviscid, quasi-steady aerodynamic model is coupled to the active structural model. For simulation, analysis, and control design, the blade model is discretized in space using a Galerkin approach. The resulting nonlinear model of high order is reduced using the aeroelastic modes of the blade. Finally, the usefulness of a reduced-order model is demonstrated by designing an energy optimal linear-quadratic-Gaussian (LQG) control.

Strain-Rate Effect on the Tensile Behaviour of High Strength Alloys

2011 ◽  
Vol 82 ◽  
pp. 124-129 ◽  
Author(s):  
Ezio Cadoni ◽  
Matteo Dotta ◽  
Daniele Forni ◽  
Stefano Bianchi
Keyword(s):  
Strain Rate ◽  
Rate Sensitivity ◽  
High Strength ◽  
Constitutive Law ◽  
Tensile Behaviour ◽  
Strain Rates ◽  
Cross Sectional ◽  
Split Hopkinson Tensile Bar ◽  
Wide Range ◽  
First Results

In this paper the first results of the mechanical characterization in tension of two high strength alloys in a wide range of strain rates are presented. Different experimental techniques were used for different strain rates: a universal machine, a Hydro-Pneumatic Machine and a JRC-Split Hopkinson Tensile Bar. The experimental research was developed in the DynaMat laboratory of the University of Applied Sciences of Southern Switzerland. An increase of the stress at a given strain increasing the strain-rate from 10-3 to 103 s-1, a moderate strain-rate sensitivity of the uniform and fracture strain, a poor reduction of the cross-sectional area at fracture with increasing the strain-rate were shown. Based on these experimental results the parameters required by the Johnson-Cook constitutive law were determined.

scholarly journals Nonlinear modeling growth body weight of Mangalarga Marchador horses

2017 ◽  
Vol 47 (4) ◽  
Author(s):  
Felipe Amorim Caetano Souza ◽  
Tales Jesus Fernandes ◽  
Raquel Silva de Moura ◽  
Sarah Laguna Conceição Meirelles ◽  
Rafaela Aparecida Ribeiro ◽  
...  
Keyword(s):  
Body Weight ◽  
Linear Models ◽  
Nonlinear Modeling ◽  
Growth Curves ◽  
Live Weight ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Cross Sectional ◽  
Adult Body Weight ◽  
The Cross

ABSTRACT: The analysis of the growth and development of various species has been done using the growth curves of the specific animal based on non-linear models. The objective of the current study was to evaluate the fit of the Brody, Gompertz, Logistic and von Bertalanffy models to the cross-sectional data of the live weight of the MangalargaMarchador horses to identify the best model and make accurate predictions regarding the growth and maturity in the males and females of this breed. The study involved recording the weight of 214 horses, of which 94 were males and 120 were non-pregnant females, between 6 and 153 months of age. The parameters of the model were estimated by employing the method of least squares, using the iteratively regularized Gauss-Newton method and the R software package. Comparison of the models was done based on the following criteria: coefficient of determination (R²); Residual Standard Deviation (RSD); corrected Akaike Information Criterion (AICc). The estimated weight of the adult horses by the models ranged between 431kg and 439kg for males and between 416kg and 420kg for females. The growth curves were studied using the cross-sectional data collection method. For males the von Bertalanffymodel was found to be the most effective in expressing growth, while in females the Brody model was more suitable. The MangalargaMarchador females achieve adult body weight earlier than the males.

scholarly journals Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
W. Gafsi ◽  
F. Najar ◽  
S. Choura ◽  
S. El-Borgi
Keyword(s):  
Passive Control ◽  
Inverse Eigenvalue Problem ◽  
Beam Dynamics ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Beam Model ◽  
Nonlinear Frequency ◽  
Nonlinear Beam

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

scholarly journals Fast Attitude Maneuver of a Flexible Spacecraft with Passive Vibration Control Using Shunted Piezoelectric Transducers

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Bassam A. Albassam
Keyword(s):  
Differential Equations ◽  
Electromechanical Coupling ◽  
Design Method ◽  
Equations Of Motion ◽  
Control Design ◽  
Piezoelectric Transducers ◽  
Control Input ◽  
Attitude Maneuver ◽  
Shunt Circuit ◽  
Flexible Appendages

This paper is concerned with designing a bang-bang control input to perform a quick rotational maneuver of a rigid spacecraft hub connected with flexible appendages. The control design is based on only the rigid body mode making it very simple to design and at the same time achieve the quickest maneuver possible. The induced vibrations are suppressed using piezoelectric transducers bonded to the appendages and connected to an electric circuit with the objective of converting the vibrational energy to electrical energy and then dissipating it using passive electric elements, such as a resistance and an inductor. The proposed control design method is applied to a spacecraft containing a rigid hub and flexible appendages. The attitude control torque is produced using either the reaction wheels contained inside the rigid hub or jet thrusters mounted outside it. The control design process starts with deriving the nonlinear partial differential equations of motion for the spacecraft using Hamilton’s principle which accounts for the electromechanical coupling and the presence of resistive or resistive-inductive circuits. To simplify the analysis, the nonlinear ordinary differential equations of motion are then obtained using the assumed mode method. The effectiveness of the control design method is numerically tested on a spacecraft that is required to perform a quick attitude maneuver and, simultaneously, suppress the induced vibrations. The simulations show a quick and accurate maneuver has been achieved combined with very low levels of vibrations resulting from the reduced coupling between flexible and rigid motions as well as the damping added as a result of the passive shunt circuit. Furthermore, the resistance-inductance shunt circuit is shown to be more effective in damping the vibrations than the resistance shunt circuit.

An Analytical Shape Memory Polymer Composite Beam Model for Space Applications

2016 ◽  
Vol 16 (02) ◽  
pp. 1450093 ◽  
Author(s):  
D. Bergman ◽  
B. Yang
Keyword(s):  
Shape Memory ◽  
Polymer Composite ◽  
Geometric Model ◽  
Shape Memory Polymer ◽  
Constitutive Law ◽  
Finite Difference Approximation ◽  
Dynamic Equations ◽  
Difference Approximation ◽  
Beam Model ◽  
Space Applications

Shape memory polymer composite (SMPC) structures, due to their ability to be formed into a small compact volume and then transform back to their original shape, are considered as a solution in the design of light-weight large deployable space structures. There is a wide array of constitutive and qualitative work being done on SMPC’s but little or no development of dynamic equations. This paper documents a macroscopic model for the shape fixation and shape recovery processes of a SMPC cantilever beam. In particular the focus is on the shape fixation process, whereby a quasi-static equilibrium model can be used instead of a full equation of motion. Numerical results are obtained in this regard by use of finite difference approximation with Newton’s method. This formulation combines a nonlinear geometric model with a temperature dependent constitutive law. Additionally, the dynamic equations of the SMPC cantilever are derived. Future work will include a dynamic numerical model, and a finite element model of the SMPC structure.

Flexible Riser Top Connection Analysis With I-Tube Interface and Bending Hysteresis Effect

2019 ◽  
Author(s):  
Yangye He ◽  
Hailong Lu ◽  
Murilo Augusto Vaz ◽  
Marcelo Caire
Keyword(s):  
Kinematic Hardening ◽  
Bending Moment ◽  
Element Model ◽  
Beam Model ◽  
Flexible Riser ◽  
Nonlinear Bending ◽  
Cross Sectional ◽  
Irregular Wave ◽  
Global Dynamic ◽  
Curvature Distribution

Abstract The flexible riser top connection to the floating production platform is a critical region for fatigue lifetime (re)assessment. The interface with the I-tube and its curved sleeve combined with the gap between the riser and bend stiffener may lead to different curvature distribution when compared to the traditional modeling approach that considers the bend stiffener attached to the pipe. For a more accurate top connection assessment, the flexible riser bending hysteresis can also be directly incorporated in the global dynamic analysis helping to reduce curvature amplitude and lifetime prediction conservatism. This work investigates a 7” flexible riser-bend stiffener top connection with I-tube interface by performing irregular wave global dynamic analyses with the OrcaFlex package and considering a nonlinear bending moment vs curvature riser behavior obtained from a detailed cross sectional model developed in Abaqus. OrcaFlex curvature distribution results are also compared with a quasi-static finite element model that uses an elasto-plastic formulation with kinematic hardening to represent riser hysteresis through an equivalent beam model. A good curvature distribution correlation is observed for both top connection models (OrcaFlex x Abaqus) in the bend stiffener area with reduced amplitudes when riser bending hysteresis is considered.

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