This study is further extended by adding the viscoelastic layers in the core of the smart annular sandwich plate to investigate the performance of the annular PFC actuator in sliding mode in the active constrained layer damping (ACLD) treatment. This study also reveals indicative performance of the shear mode PFC actuator in the ACLD treatment, provided that the viscoelastic layer of suitable thickness is used.
AN ANNULAR PFC ACTUATOR FOR SHEAR MODE PIEZOELECTRIC ACTUATION OF PLANE
ACTIVE CONTROL OF VIBRATION OF ANNULAR PLATES USING A NEW SHEAR MODE PFC
CONCLUSIONS
5.4 (a) Schematic diagram of a typical subvolume and (b) a horizontal plane of the active (2-2 PFC) layer of the subvolume. 6.7 (a) Variations of the maximum displacement amplitude (Wmax) of the annular sandwich plate within a frequency range and (b) the corresponding variations of the maximum stress amplitude within the first radial group (g 1) of the planes p 1 N).
Introduction
Piezoelectric materials
Introduction
- Smart structures
- Analytical developments of smart structures
- Experimental developments of smart structures
- Finite element studies of smart structures
- Optimization studies of piezoelectric sensors/actuators on smart structures
- Static and Dynamic analyses of smart structures
- Thermo-electro-elastic behavior of smart structures
- Piezoelectric fiber composites
- Design of piezoelectric fiber composites (PFCs)
- Analytical and FE evaluation of effective properties of PFCs
- Effective behavior of PFCs using Micromechanical Approaches
- Experimental studies on the effective behavior of PFCs
- Smart structures using PFCs
- Active vibration/ deformation control of smart structures using PFCs
- Experimental active control using PFCs
- Comparative studies on the control capabilities of PFC actuators
- Active constrained layer damping (ACLD)
- Experimental investigations of ACLD
- Analytical and numerical investigations of ACLD
- Research motivation and objectives
- Contributions
- Organization of the thesis
Trindade and Maio (2008) presented a parametric study on the optimal configuration of shear mode piezoelectric actuators for efficient vibration control of a sandwich beam. Robbins and Reddy (1991) investigated the performance of piezoelectric actuators in controlling the static deflections and transverse bending amplitudes of beam oscillations.
CHAPTER
Introduction
For effective use of the SPFC/CPFC as a material of distributed actuator, an arrangement of surface electrodes over the top and bottom surfaces of the smart composite lamina is also presented. Thus, the construction characteristics as well as the effective characteristics of SPFC/CPFC in rectangular coordinates are also presented in parallel with those of the PFCs in cylindrical coordinates.
Constructional features of SPFC
Alternatively, the dimensions (hf,f) of the fiber can be expressed in terms of the similar dimensions (hc,c) of the RVE as, hf hc Ar and f c Ar. The cross-sectional areas of the RVE and the corresponding fiber are denoted by Ac and Af, respectively.
Effective electro-elastic properties of the smart composite
The constitutive relations for the fiber (f) and matrix (m) phases within the RVE can be written in terms of field-averaged volume quantities as, . The electric potential at any point in the RVE volume is denoted by.
FE model of RVE
The electroelastic state at any point within the RVE can be defined by an electroelastic state vector (d ) as,. Using this electroelastic state vector (d), the stress ( ) and electric field (E) vectors at any point within the RVE can be expressed in terms of an operator matrix (L) as,. 2.35a), the form of the operator matrix (L) for the RVE in cylindrical coordinates (Lcylindrical) or for the RVE in rectangular coordinates (Lrectangular) is as follows. 2.32), the first variation of electroelastic internal energy of RVE can be written as (Tiersten, 1969). The electroelastic analysis of the RVE is performed by applying the kinematic boundary conditions (Eq.
Arrangement of electrodes
Across all pairs of electrodes, uniform applied voltage is considered, and this gives uniform magnitude of the electric field within all such pairs. But it facilitates obtaining a significant magnitude of the externally induced electric field by virtue of the small applied voltage across the pairs of surface electrodes. The difficulty may arise in the manufacture of the SPFC actuator due to the small gap in the plane between two consecutive surface electrodes.
- Results and discussions
- Effective coefficients of SPFC/CPFC
- Electric field for present arrangement of surface-electrodes
- Conclusions
For the use of short piezoelectric fibers (Lr = 1), the variations of the same coefficients (e11,e12,e13) with the length ratio (Lr) are illustrated in figure. Also the magnitude of the longitudinal component (Ex) of the volume-averaged electric field (E) is considerably higher than that of its other components (Ey,Ez). 2.14, the variations of the volume-averaged electric field components (Er,E,Ez) for the SPFC/CPFC in cylindrical coordinates are also evaluated.
Introduction
- Variational formulation for smart beam
- Numerical results for the analysis of smart beam
In this section, the variational formulation for the bending analysis of the smart beam is first verified. Thus, an insignificant change in the magnitude of the actuation, corresponding to an increase in the applied voltage (V), can be observed at a higher mechanical load (Q). From this figure it can be seen that the magnitude of actuation increases linearly with increasing applied voltage (V) for both the linear and nonlinear deformations of the total beam.
- FE model of smart annular plate
- Smart damping
- Numerical results for the analysis of vibration of the smart annular plate
According to the displacement field (Equation 3.18)), the strain-displacement relations at any point of the entire annular plate can be written as. The governing equations of motion of the smart annular plate are derived using Hamilton's principle as: The smart damping in the overall plate can also be increased by increasing the value of the control gain (kd).
Conclusions
Then, the driving ability of the SPFC/CPFC in cylindrical coordinates is investigated by using it to control transverse vibration of an annular substrate plate. The SPFC/CPFC actuator is used in the form of patches attached to the top surface of the simply supported annular plate. For efficient control of both vibration modes of the entire plate, the actuator patches are activated through the feedback of their local transverse velocities.
A comparative study on the smart damping capabilities of cylindrically orthotropic
Introduction
Then, the geometrical and material properties of PFC actuators are described (Figs. 4.1 and 4.2) to treat all these actuators in a uniform way, especially for a comparative study on their control capabilities. These relationships are then used in deriving an FE model of the smart annular plate. Based on these optimal configurations of the smart ring plate, the modal damping capabilities of the PFC actuators are evaluated.
Configuration of smart annular plate
Using this FE model, a new numerical method is presented to determine the optimal configuration of actuator patches corresponding to a vibration mode of the smart annular plate. Through this numerical methodology, the optimal configurations of the smart annular plate for different PFC actuators are determined for each of its (plate) fundamental symmetric and asymmetric vibration modes. These evaluated results for each of the basic symmetric and asymmetric vibration modes are then analyzed to investigate their (PFC actuators) relative damping capabilities.
Electric field vs. applied voltage for the PFC actuators
So, the same gradient value (G) for the linear relationship (E G V ) between the electric field (E) and the applied voltage (V ) is considered in the use of the LCC actuator. A common issue in the use of these actuators is that the induced electric field within a PFC actuator appears due to the applied electric potential/electric field as well as the mechanical stress of the overall structure. So the electric field induced in a PFC can be assumed to be the result of the applied electric field only especially in its use (PFC) as an actuator.
FE model of smart annular plate
The shapes of the stiffness matrices (Cbk, Csk) of the substrate plate (k1) are given in Eq. For the PFC actuator patches (k 2), the forms of different property matrices can be written as,. 4.5) For radially/circumferentially/transversely poled fibers, the corresponding forms of the matrices (ebk,esk) in Eq. The transverse velocity (wq) at this center point is measured and fed back in the form of voltage (Vq) across the pairs of surface electrodes of the corresponding (. qth) actuator patch according to the negative velocity feedback control strategy given in Eq.
Estimation of active damping within the smart plate
Present strategy for optimal configuration of actuator-patches
- Initial configuration of the smart annular plate
- Optimal configuration of a typical/representative sector
Basically, the sectors of half sine waves are created according to the nodes of the mode shape. Thus, the volume of the PFC sector layer does not change when the test point is located at different points. These heights form a surface with a modal loss factor over the r plane of the sector layer.
Numerical results and discussions
- Symmetric mode
- Asymmetric mode
- Active damping-capabilities of PFC actuators
4.6(a)) indicates to consider one initial PFC sector layer over the top surface of the annular host plate. 4.7(a) and 4.7(c)) for the important location of LCR material can be verified by the distribution of radial stress on the upper surface of the host plate. In the case of the LCR actuator, the area of the modal loss factor () over the area of the representative sector layer is plotted in Figure 2.
Conclusions
A comparative study is presented on the smart damping capabilities of actuators taking into account the basic symmetric and asymmetric oscillation modes of the annular plate. These optimal smart ring plate configurations for various PFC actuators are then used to evaluate their (PFC) modal damping performance. The modal damping capabilities of PFC actuators are evaluated based on the modal loss factor.
An annular PFC actuator for shear mode piezoelectric actuation of plane structures of
Introduction
So the flexibility and adaptability of the 2-2 PFC laminate can be significantly reduced especially for a large radial span of interest. According to this fiber arrangement, the PFC laminate is expected to have sufficient flexibility and conformability. In the following sections, the design features of the current PFC crop actuator are first presented.
Constructional features of the present shear mode PFC actuator
Now, for a given value of this external electric field, the required voltage increases as the thickness of the PFC 2-2 layer increases. Then, the various effective electro-elastic properties of the PFC actuator are evaluated using the Uniform Field Model (UFM) (Bent and Hagood, 1997). Next, a FE procedure is developed for the numerical homogenization of the shear mode PFC actuator.
Effective properties of the shear mode PFC actuator
- Effective properties of a typical sub-volume
- Effective coefficients of the sub-volume using FE formulation According to the present arrangement of the electrodes and the corresponding
In this section, the closed-form expressions for the effective subvolume coefficients (Fig. 5.5(a)) and the closed-form expressions for the effective subvolume coefficients are derived. 5.5(a)), the stress components (zr, z and z) are assumed to be uniformly distributed over the domain of the subvolume.
Results and discussions
- Verification of the present homogenisation procedures
- Effective properties of the shear mode PFC actuator
This comparison verifies the current FE procedure for estimating the effective coefficients of the 2-2 PFC layer. 5.5(b)) in the cylindrical coordinate system, the magnitudes of the effective coefficients are calculated using the current FE procedure. These results are illustrated in Table 5.3 (Cutting mode 2-2 PFC in the cylindrical coordinate system) for a FVF (vf ) and other geometric properties of the RVE (Fig.
Conclusions
Active vibration control of annular plates using a novel cylindrical shear mode PFC actuator.
Active control of vibration of annular plates using a new shear mode PFC actuator with cylindrically
Introduction
Present smart annular sandwich plate
The inner/outer radius and thickness of the overall annular plate is denoted by , . At present, a strategy is proposed for the arrangement of the patches by taking the identical patches in the form of an annular sector. The patches are made by dividing the plane of this ring-shaped PFC actuator, and the material of the patches is denoted by PFC#1.
FE model of the smart annular sandwich plate
- Implementation of control strategy
For each bending mode of deformation of the entire plate, the transverse shear stress (rz/z) appears with an indicative magnitude in the center plane of the plate. For the corresponding vibration of the entire annular plate, the first variations of the total potential energy (Tpe) and the total kinetic energy (Tke) of a typical element at a given time (t) can be written as,. Each patch of the sliding mode PFC actuator is activated by taking the feedback of the local transverse velocity.
Results and discussions
6.3(a)) appears following the nature of variation of the piezoelectric shear coefficient (e35( )r , line 1 in Fig. 5.7) for the first geometric configuration of the annular PFC actuator. For his (PFC actuator) design with the second geometrical configuration, similar distribution of the electrically induced shear strain (rz) over the center plane of the overall annular plate is illustrated in . In order to investigate the effect of the control gain (kd) on the controlled frequency response of the overall plate, the value of the control gain (kd) is varied with a constant value of the load amplitude (p).
Conclusions
Then, feasible control gain values corresponding to a load amplitude lie within the left sub-domain. 6.9(c) or 6.9(d) is a graphical representation of the relationship between control gain, load-amplitude, and voltage-amplitude. These results demonstrate the control capability of the current shear mode PFC ring actuator for active ring plate vibration control.
Active-passive damping characteristics of a smart annular sandwich plate using a new shear mode
Introduction
The FE model of the entire annular sandwich plate is developed based on the theory of layered shear deformation, and its (whole plate) active-passive damping characteristics are studied according to the above objectives.
Smart annular sandwich plate
In the second, one layer of piezofoam is compressed between two identical viscoelastic layers, as the corresponding cross-section of the entire annular plate is shown in the figure. The thicknesses of the entire plate and front layers are indicated by h and hf, respectively. Similarly, the thickness (hp/2) of the piezo foam layer in CONFIG#1 is half the thickness (hp) of the similar layer in CONFIG#2.
FE formulation for the annular sandwich plate
For the second geometric configuration of the PFC ring actuator (row 3/4 in Figure 5.7), it is made into four parts by dividing the radial space (ro-ri) of application into four equal divisions. Patches within a radial gap are made by dividing the radial and circular spaces of the corresponding part of the ring actuator of the PFC, and the material of the patches is denoted by PFC#2. As the PFC ring actuator parts are embedded within the foam layer, two different element stacking sequences appear in the FE mesh of the overall ring plate for each of its configurations (CONFIG#1 (Fig.
