Energy Harvesting of Piezoelectric Stack Actuator From a Shock Event

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Andrew J. Lee ◽  
Ya Wang ◽  
Daniel J. Inman
Keyword(s):  
Energy Harvesting ◽  
Constitutive Equations ◽  
Equations Of Motion ◽  
The Finite Element Method ◽  
Single Degree Of Freedom ◽  
Coupled Equations ◽  
Model Predictions ◽  
Shock Event ◽  
Sdof Analysis ◽  
Piezoelectric Stack Actuator

The energy harvesting performance of a piezoelectric stack actuator under a shock event is theoretically and experimentally investigated. The first method is derived from the single degree of freedom constitutive equations, and then a correction factor is applied onto the resulting electromechanically coupled equations of motion. The second approach is deriving the coupled equations of motion with Hamilton's principle and the constitutive equations, and then formulating it with the finite element method. Two experimental cases matched well with the model predictions where the percent errors were 3.90% and 3.26% for the SDOF analysis and 1.52% and 1.42% for the FEM.

A Newly Developed Algorithm for Treating the Coupled Dynamic Response of Robotic Fixtureless Assembly

1996 ◽  
Author(s):  
Genady Shagal ◽  
Shaker A. Meguid
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Time Integration ◽  
Integration Scheme ◽  
The Finite Element Method ◽  
Coupled Equations ◽  
Time Integration Scheme ◽  
Implicit Approach ◽  
Cooperating Robots

Abstract The coupled dynamic response of two cooperating robots handling two flexible payloads for the purpose of fixtureless assembly and manufacturing is treated using a new algorithm. In this algorithm, the equations describing the dynamics of the system are obtained using Lagrange’s method for the rigid robot links and the finite element method for the flexible payloads. A new time integration scheme is developed to treat the coupled equations of motion of the rigid links for a given displacement of the flexible payloads. The finite element equations of the flexible payloads are then treated using an implicit approach. The new algorithm was verified using simplified examples and was later used to examine the dynamic response of two cooperating robot arms manipulating flexible payloads which are typical of the automotive industry.

Power Harvesting Prediction of Piezoelectric Stack Actuator From a Shock Event

2013 ◽  
Author(s):  
Andrew J. Lee ◽  
Ya Wang ◽  
Daniel J. Inman
Keyword(s):  
Space Form ◽  
Test Cases ◽  
Governing Equations ◽  
Power Harvesting ◽  
Single Degree Of Freedom ◽  
Percent Error ◽  
First Case ◽  
Impulse Load ◽  
Shock Event ◽  
Piezoelectric Stack Actuator

In this study, the power harvesting performance of a piezoelectric (PZT) ceramic multilayer stack actuator under a shock event is theoretically and experimentally investigated. The model is derived from the constitutive - 33 mode equations under single degree of freedom (SDOF) assumptions, and then a correction factor is applied onto the resulting electromechanically coupled governing equations. These are represented in state space form and solved in the numerical computation software MATLAB. In order to achieve experimental validation, two test cases are compared to the model prediction when impulses of 20.8 mN·s and 1.70 mN·s are loaded on to the PZT stack actuator. The voltage and power output between the model and the test cases matched well. For the first case, the PZT stack actuator harvested 0.3321 μJ from the shock event while the model’s prediction was 0.3358 μJ, which results in a percent error of only 1.1%. In the second case, the PZT stack actuator harvested 34.64 nJ from the shock event while the model’s prediction was 35.80 nJ, which results in a percent error of 3.2%. This paper achieves its objective of deriving a model that can accurately predict the power harvested when an impulse load is applied onto a PZT stack actuator, and then validating this model with testing.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

scholarly journals Nonlinear spectral model for rotating sheared turbulence

2019 ◽  
Vol 866 ◽  
pp. 5-32 ◽  
Author(s):  
Ying Zhu ◽  
C. Cambon ◽  
F. S. Godeferd ◽  
A. Salhi
Keyword(s):  
Turbulent Shear ◽  
Finite Difference Schemes ◽  
Turbulent Shear Flow ◽  
Third Order ◽  
Mean Velocity ◽  
Coupled Equations ◽  
Velocity Gradients ◽  
Model Predictions ◽  
Pseudo Scalar ◽  
High Order Finite Difference

We propose a statistical model for homogeneous turbulence undergoing distortions, which improves and extends the MCS model by Mons, Cambon & Sagaut (J. Fluid Mech., vol. 788, 2016, 147–182). The spectral tensor of two-point second-order velocity correlations is predicted in the presence of arbitrary mean-velocity gradients and in a rotating frame. For this, we numerically solve coupled equations for the angle-dependent energy spectrum${\mathcal{E}}(\boldsymbol{k},t)$that includes directional anisotropy, and for the deviatoric pseudo-scalar $Z(\boldsymbol{k},t)$, that underlies polarization anisotropy ($\boldsymbol{k}$ is the wavevector,$t$the time). These equations include two parts: (i) exact linear terms representing the viscous spectral linear theory (SLT) when considered alone; (ii) generalized transfer terms mediated by two-point third-order correlations. In contrast with MCS, our model retains the complete angular dependence of the linear terms, whereas the nonlinear transfer terms are closed by a reduced anisotropic eddy damped quasi-normal Markovian (EDQNM) technique similar to MCS, based on truncated angular harmonics expansions. And in contrast with most spectral approaches based on characteristic methods to represent mean-velocity gradient terms, we use high-order finite-difference schemes (FDSs). The resulting model is applied to homogeneous rotating turbulent shear flow with several Coriolis parameters and constant mean shear rate. First, we assess the validity of the model in the linear limit. We observe satisfactory agreement with existing numerical SLT results and with theoretical results for flows without rotation. Second, fully nonlinear results are obtained, which compare well to existing direct numerical simulation (DNS) results. In both regimes, the new model improves significantly the MCS model predictions. However, in the non-rotating shear case, the expected exponential growth of turbulent kinetic energy is found only with a hybrid model for nonlinear terms combining the anisotropic EDQNM closure and Weinstock’s return-to-isotropy model.

Finite-element simulation of the photoacoustic–thermal signal generation

1986 ◽  
Vol 64 (9) ◽  
pp. 1030-1036 ◽  
Author(s):  
D. Lévesque ◽  
G. Rousset ◽  
L. Bertrand
Keyword(s):  
Finite Element ◽  
Adiabatic Process ◽  
The Finite Element Method ◽  
Photoacoustic Cell ◽  
Main Interest ◽  
Great Flexibility ◽  
Coupled Equations ◽  
Thermal Signal ◽  
Element Simulation ◽  
Good Agreement

The ability to use the finite-element method to solve numerically the frequency-dependent coupled equations of the photoacoustic–thermal effect is demonstrated. Both solids and fluids are simulated by the same set of equations with temperature and displacement as variables. The main interest of this formulation lies in its great flexibility to deal with mixed fluid–solid systems. As a first application, we consider the influence of thermoacoustic coupling on the pressure in a photoacoustic cell. We show that with increasing frequency, a transition from an isothermal to an adiabatic process occurs. Subsequently, results obtained from a numerical simulation of the photoacoustic cell, which includes the effect of a residual volume, are in good agreement with existing experimental data.

An Approximate Method for the Dynamic Analysis of Elastic Linkages

1977 ◽  
Vol 99 (2) ◽  
pp. 449-455 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Exact Analytical Solution ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Degree Of Freedom ◽  
Suggested Approach ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
System A ◽  
Suggested Technique ◽  
Particular Solution

A new numerical procedure based on an iterative technique is progressively developed in this paper for obtaining an approximate particular solution from the equations of motion of an elastic linkage with small damping and at subresonant speeds. The method is introduced by employing a simple vibrating system, a single degree-of-freedom mass-dashpot-spring model under both harmonic forcing and periodic forcing. A harmonically excited two degree-of-freedom model is also solved by the suggested approach. Error functions are developed for each case to give an estimation of the order of error between the exact analytical solution and the approximate technique. The suggested technique is then extended to solve an elastic linkage problem where the uncoupled equations of motion are treated as a series of single degree-of-freedom problems and solved. These are retransformed into the physical coordinate system to obtain the particular solution. The first and second derivatives of the forcing functions (involving rigid-body inertia) are approximated utilizing the finite difference method.

Dynamic Modeling of Robotic Fish Caudal Fin With Electrorheological Fluid-Enabled Tunable Stiffness

2015 ◽  
Author(s):  
Sanaz Bazaz Behbahani ◽  
Xiaobo Tan
Keyword(s):  
Equations Of Motion ◽  
Electrorheological Fluid ◽  
Robotic Fish ◽  
Dynamic Equations ◽  
The Finite Element Method ◽  
Modeling Framework ◽  
Caudal Fin ◽  
Body Theory ◽  
Tunable Stiffness ◽  
Er Fluid

In this study, we investigate the modeling framework for a robotic fish actuated by a flexible caudal fin, which is filled with electrorheological (ER) fluid and thus enables tunable stiffness. This feature can be used in optimizing the robotic fish speed or maneuverability in different operating regimes. The robotic fish is assumed to be anchored and the flexible tail undergoes undulation activated by a servomotor at the base. Lighthill’s large-amplitude elongated-body theory is used to calculate the hydrodynamic force on the caudal fin, and Hamilton’s principle is used to derive the dynamic equations of motion of the caudal fin. The dynamic equations are then discritized using the finite element method, to obtain an approximate numerical solution. In particular, simulation is conducted to understand the influence of the applied electric field on the stiffness and thrust performance of the caudal fin.

Study of Sand Particle Trajectories and Erosion Into the First Compression Stage of a Turbofan

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Adel Ghenaiet
Keyword(s):  
Equations Of Motion ◽  
Leading Edge ◽  
Sand Particle ◽  
The Finite Element Method ◽  
Particle Trajectories ◽  
Compression Stage ◽  
Trailing Edges ◽  
Blade Tip ◽  
Lagrangian Tracking ◽  
Aero Engines

Aero-engines operating in dusty environments are subject to ingestion of erodent particles leading to erosion damage of blades and a permanent drop in performance. This work concerns the study of particle dynamics and erosion of the front compression stage of a commercial turbofan. Particle trajectories simulations used a stochastic Lagrangian tracking code that solves the equations of motion separately from the airflow in a stepwise manner, while the tracking of particles in different cells is based on the finite element method. As the locations of impacts and rates of erosion were predicted, the subsequent geometry deteriorations were assessed. The number of particles, sizes, and initial positions were specified conformed to sand particle distribution (MIL-E5007E, 0-1000 micrometers) and concentrations 50–700 mg/m3. The results show that the IGV blade is mainly eroded over the leading edge and near hub and shroud; also the rotor blade has a noticeable erosion of the leading and trailing edges and a rounding of the blade tip corners, whereas in the diffuser, erosion is shown to spread over the blade surfaces in addition to the leading edge and trailing edge.

scholarly journals Investigation on the Dynamics of an On-Board Rotor-Bearing System

2012 ◽  
Author(s):  
Mzaki Dakel ◽  
Sébastien Baguet ◽  
Régis Dufour
Keyword(s):  
Dynamic Behavior ◽  
Fourier Transforms ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Beam Theory ◽  
Rigid Base ◽  
The Finite Element Method ◽  
Mass Unbalance ◽  
Motion Display

In ship and aircraft turbine rotors, the rotating mass unbalance and the different movements of the rotor base are among the main causes of vibrations in bending. The goal of this paper is to investigate the dynamic behavior of an on-board rotor under rigid base excitations. The modeling takes into consideration six types of base deterministic motions (rotations and translations) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are computed. The finite element method is used in the rotor modeling by employing the Timoshenko beam theory. The proposed on-board rotor model takes into account the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk. The Lagrange’s equations are applied to establish the differential equations of the rotor in bending with respect to the rigid base which represents a noninertial reference frame. The linear equations of motion display periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the base rotational motions. In the proposed applications, the rotor mounted on rigid/elastic bearings is excited by a rotating mass unbalance associated with sinusoidal vibrations of the rigid base. The dynamic behavior of the rotor is analyzed by means of orbits of the rotor as well as fast Fourier transforms (FFTs).

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