Vibration Control of Beams with Negative Capacitive Shunting of Interdigital Electrode Piezoceramics

2005 ◽  
Vol 11 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Chul H. Park ◽  
Amr Baz
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Vibration Control ◽  
Equations Of Motion ◽  
Vibration Modes ◽  
Frequency Range ◽  
Governing Equations ◽  
Interdigital Electrode ◽  
Beam System ◽  
Cantilevered Beam

A pair of interdigital electrode (IDE) piezoceramics is used to simultaneously suppress multimode vibrations of a cantilevered beam. This is achieved by connecting the IDE piezoceramics in parallel to a negative capacitive shunt circuit. The governing equations of motion of an IDE piezo/beam system and associated boundary conditions are derived using the Hamilton principle. The obtained mathematical model is validated experimentally Attenuations ranging between 5 and 20 dB are obtained for all the vibration modes over the frequency range of 0-3000 Hz. The presented theoretical and experimental techniques provide invaluable tools for designing simple and effective passive vibration dampers for structures with closely packed modes.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

Active Vibration Control of Smart Hull Structure Using Piezoelectric Composite Actuators

2008 ◽  
Vol 47-50 ◽  
pp. 137-140 ◽  
Author(s):  
Jung Woo Sohn ◽  
Seung Bok Choi
Keyword(s):  
Vibration Control ◽  
Fiber Composite ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Piezoelectric Composite ◽  
Governing Equations ◽  
Linear Quadratic ◽  
Element Analysis ◽  
Hull Structure ◽  
Active Vibration

In this paper, active vibration control performance of the smart hull structure with Macro-Fiber Composite (MFC) is evaluated. The governing equations of motion of the hull structure with MFC actuators are derived based on the classical Donnell-Mushtari shell theory. Subsequently, modal characteristics are investigated and compared with the results obtained from finite element analysis and experiment. The governing equations of vibration control system are then established and expressed in the state space form. Linear Quadratic Gaussian (LQG) control algorithm is designed in order to effectively and actively control the imposed vibration. The controller is experimentally realized and control performances are evaluated.

scholarly journals The Determination of the Velocities after Impact for the Constrained Bar Problem

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
André Fenili ◽  
Luiz Carlos Gadelha de Souza ◽  
Bernd Schäfer
Keyword(s):  
Mathematical Model ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Simple Mathematical Model ◽  
Governing Equations ◽  
Complex Problems ◽  
Constrained Equation

A simple mathematical model for a constrained robotic manipulator is investigated. Besides the fact that this model is relatively simple, all the features present in more complex problems are similar to the ones analyzed here. The fully plastic impact is considered in this paper. Expressions for the velocities of the colliding bodies after impact are developed. These expressions are important in the numerical integration of the governing equations of motion when one must exchange the set of unconstrained equations for the set of constrained equation. The theory presented in this work can be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment. It can also de applied to problems in which robotic manipulators must handle payloads.

A New Displacement Form for the Nonlinear Equations of Motion of Shells of Revolution

1985 ◽  
Vol 52 (3) ◽  
pp. 507-509 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Shells Of Revolution ◽  
Governing Equations ◽  
Hoop Strain ◽  
Axisymmetric Motion ◽  
Nonlinear Equations Of Motion ◽  
Surface Loads ◽  
Theory Of Shells

In the theory of shells of revolution undergoing torsionless, axisymmetric motion, an extensional and a bending hoop strain are introduced that are linear in the displacements, regardless of the magnitudes of the strains and the meridional rotation. The resulting equations of motion and boundary conditions are derived and some common conservative surface loads are listed along with their potentials. The governing equations appear to be the simplest possible in terms of displacements.

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

2021 ◽  
pp. 107754632110399
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Well Posedness ◽  
Governing Equations ◽  
Two Phase

In this article, the well-posedness of several common nonlocal models for higher-order refined shear deformation beams is studied. Unlike the case of classic beams models, both strain-driven and stress-driven purely nonlocal theories lead to an ill-posed issue (i.e., there are excessive mandatory boundary conditions) when considering higher-order shear deformation assumption. As an effective remedy, the well-posedness of strain-driven and stress-driven two-phase nonlocal (StrainDTPN and StressDTPN) models is pertinently evidenced by studying the free vibration problem of nanobeams. The governing equations of motion and standard boundary conditions are derived from Hamilton’s principle. The integral constitutive relation is transformed equivalently to a differential form equipped with two constitutive boundary conditions. Using the generalized differential quadrature method (GDQM), the governing equations in terms of displacements are solved numerically. Numerical results show that both the StrainDTPN and StressDTPN models can predict consistent size-effects of beams with different boundary conditions.

Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions

2015 ◽  
Vol 32 (3) ◽  
pp. 277-287 ◽  
Author(s):  
D. S. Mashat ◽  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Thermal Buckling ◽  
Governing Equations ◽  
Linear Temperature ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Dynamic Version ◽  
Beam Theories

AbstractAnalyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

Mathematical Model for Gas Bearing With Holes of Tangential Supply

1999 ◽  
Vol 121 (2) ◽  
pp. 301-305 ◽  
Author(s):  
L Q. Liu ◽  
C. Z. Chen
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Inertia Effect ◽  
Governing Equations ◽  
Gas Bearing ◽  
Typical Design

To investigate the dynamic characteristics of gas bearings with holes of tangential supply (TS bearing), drawing on the modified Reynolds equations proposed by Mori, we present new governing equations and their reasonable boundary conditions. Using this mathematical model, the inertia effect of the supplied gas on the aerodynamic film force can be evaluated properly. The governing equations are solved numerically using Finite Element Method (FEM), and the pressure distribution of the gas in the bearing, the critical whirl ratio and so on, are calculated for a typical design. Some results for a cylindrical journal bearing (CJ bearing) and ordinary bearing with holes of radial supply (RS bearing) are also provided for comparison.

On the Free Vibration Analysis of a Sandwich Beam With Tip Mass

2018 ◽  
Author(s):  
E. F. Joubaneh ◽  
O. R. Barry
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Design Parameters ◽  
Governing Equations ◽  
Tip Mass

This paper presents the free vibration analysis of a sandwich beam with a tip mass using higher order sandwich panel theory (HSAPT). The governing equations of motion and boundary conditions are obtained using Hamilton’s principle. General Differential Quadrature (GDQ) is employed to solve the system governing equations of motion. The natural frequencies and mode shapes of the system are presented and Ansys simulation is performed to validate the results. Various boundary conditions are also employed to examine the natural frequencies of the sandwich beam without tip mass and the results are compared with those found in the literature. Parametric studies are conducted to examine the effect of key design parameters on the natural frequencies of the sandwich beam with and without tip mass.

Vibration Analysis of Functionally Graded Graphene Reinforced Porous Nanocomposite Shells

2019 ◽  
Vol 11 (07) ◽  
pp. 1950068 ◽  
Author(s):  
Reza Bahaadini ◽  
Ali Reza Saidi ◽  
Zahra Arabjamaloei ◽  
Asiye Ghanbari-Nejad-Parizi
Keyword(s):  
Boundary Conditions ◽  
Conical Shell ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Weight Fraction ◽  
Effective Elastic Modulus ◽  
Functionally Graded ◽  
Vertex Angle ◽  
Governing Equations

In this study, the vibration of functionally graded porous truncated conical shell reinforced with graphene platelets (GPLs) is investigated. The GPLs nanofillers and pores are considered to be uniform and nonuniform throughout the thickness direction. Using Hamilton’s principle, the governing equations are derived based on Love’s first approximation theory. The generalized differential quadrature method is applied to solve the governing equations of motion and to obtain the natural frequencies of the shells for various boundary conditions. Applying the Halpin–Tsai model and the rule of mixture, the effective elastic modulus, the Poisson’s ratio and the density of nanocomposite shell reinforced with GPLs are computed. The effects of porosity coefficients, distribution patterns of porosity, GPL weight fraction, geometry and size of GPLs, semi-vertex angle as well as boundary conditions on the natural frequency of the system are analyzed. It was observed in the results that the shells with symmetric porosity distribution reinforced by graphene platelet pattern A predict the highest natural frequencies. Furthermore, it was found that the natural frequencies of nanocomposite conical shell can be decreased by increasing the porosity coefficient. Besides, the geometry and size of GPLs as well as weight fraction of GPLs have significant effects on the natural frequencies.

Influence of Symmetrical Boundary Conditions on Free Vibration of Functionally Graded Cylindrical Shells With Ring Support

2009 ◽  
Author(s):  
M. R. Isvandzibaei ◽  
M. M. Najafizadeh ◽  
P. Khazaeinejad
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Third Order ◽  
Graded Materials ◽  
Ring Support

In the present work, the free vibration of thin cylindrical shells with ring support made of functionally graded materials under various symmetrical boundary conditions is presented. Temperature and position dependent material properties are varied linearly through the thickness of the shell. The functionally graded cylindrical shell has ring support which is arbitrarily placed along the shell and imposed a zero lateral deflection. The third order shear deformation theory is employed to formulate the problem. The governing equations of motion are derived using the Hamilton’s principle. Results are presented on the frequency characteristics and influence of the boundary conditions and the locations of the ring support on the natural frequencies. The present analysis is validated by comparing the results with those available in the literature.

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