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First, the effective properties of the actuator laminate are determined using the Uniform Field Method. Subsequently, the suitability of the current arrangement of displacement actuator lobes and the displacement-based control strategy is substantiated.

A design of shear actuated hybrid damping treatment for annular plates using balanced laminate of PFC

Conclusions and scope of future work

3.10 (a) Variation of the maximum nodal transverse shear amplitude (wmax/h) of the annular sandwich plate with the operating frequency (), (b) the corresponding variations of the maximum control stress (po1.6 N/m2, nr 2, n 8). 6.12 (a) Variations of the resonance displacement amplitude (wmax/h , m0, n1) with the thickness (h1s) of the inner substrate layers in the configurations (PFC-VEM#1 and PFC-VEM#2 ) of the layered annular plate; (b) corresponding variations of the maximum control voltage (Vmax) (po40 N/m2).

List of Tables

List of Symbols

SAFC Shear PFC Fiber Composite BL-PFC Piezoelectric Fiber Composite PFC Balanced Laminate UFM Uniform Field Method.

Chapter 1

Introduction

Piezoelectric materials

As the applied electric field increases from its zero value, the polarization increases linearly (segment AB in Fig. A further decrease in the electric field causes the material to expand to a practical strain limit (F, Fig.

Fig. 1.2 (a) polarization (P)-electric field (E)) hysteresis loop, (b) strain (  )- )-electric field (E)) hysteresis loop (butterfly curve)

Piezoelectric fiber composite (PFC)

They also observed a severe influence of dielectric permittivity of the matrix on the effective properties of the PFC. Sakthivel and Arokiarajan [44, 45] proposed an analytical model to estimate the effective properties of the 1-3-2 piezoelectric assembly.

Smart structures

Aldraihem and Wetherhold [228] demonstrated the active control of laminated beams integrated with distributed 1–3 PFC actuators. They used multi-input-multi-output (MIMO) PPF controller to actuate the MFC actuators and demonstrated the actuation capability of the MFC actuator in active control of the shell.

Hybrid active-passive damping

350] investigated the ACLD treatment of geometric nonlinear vibration of a heated FG plate using 1-3 PFC actuator. Ray and Pradhan [359,360] presented the performance of a vertical/oblique reinforced 1–3 PFC in the partial ACLD treatment of laminated composite cylindrical shells.

Fig. 1.5 Schematic diagram of a substrate structure integrated with a ACLD layer, (a) unreformed and (b) deformed

Motivation and objectives of present research

Moreover, the use of any of the available PFCs or shear mode monolithic piezoelectric actuator for active control of annular/circular plates has not yet been reported in the literature. This derives the requirement of designing microstructure of PFC in the cylindrical material coordinate system for effective active control of annular plates.

Contributions

The performance of BL-PFC in active-passive control of ring plates is presented. The performance of a 0-3 VEC layer in adding active-passive vibration control of annular plates is presented.

Organization of the thesis

Then, BL-PFC is used as a shear actuator patch material in the core of a sandwich beam, and its shear actuation capability is evaluated by evaluating the shear actuated deflection of the sandwich beam. The shear actuation capability of the BL-PFC is also compared with that of traditional monolithic shear-mode piezoelectric actuators.

Chapter 2

Introduction

Design of an extension mode annular PFC actuator

Present annular PFC actuator
Effective properties of the annular PFC actuator

Effective properties of a typical sub-volume

Smart annular plate
Results and discussions
Summary

So, the effective electro-elastic properties of the 2-2 PFC layer vary along the radial direction. 2.2 (b)), (b) the upper surface of the RV with the radial boundaries of the sub-volumes, (c) a typical sub-volume of the RV. Currently, the closed-form expressions for the effective coefficients of the homogeneous subvolume (Fig.

So the electroelastic properties of the RV or PFC ring actuator change along the radial direction. For the second geometric configuration of the PFC actuator (PFC2), the overall radial extent of.

Fig. 2.2 (a) Stacking sequence of different layers within the annular PFC actuator, (b) laminated PFC actuator

Chapter 3

Introduction

Shear actuation capability of obliquely-reinforced 1-3 PFC mechanism and the shear-based active control capability of the obliquely

Present annular sandwich plate with shear actuators

The inner and outer radii of the overall annular plate are denoted by ri and ro, respectively. The thicknesses of the front layers, core and overall plate are denoted by hf , hc and h respectively. The radial and circumferential regions of the uniform spots in the shape of the annular sector are respectively symbolized by  rp and  p, while the corresponding gaps between the spots are indicated by rF and F.

Fig. 3.2 Schematic diagram of the annular sandwich plate with the embedded shear actuator patches

Shear actuation capability of obliquely-reinforced 1-3 PFC shear actuation force in the xz -plane of the Cartesian material coordinate

The number (number) of patches along the radial direction is taken as 2 (Fig. 3.2), assuming that one of the radial edges of each patch coincides with the inner/outer edge of the overall annular plate, in particular to provide in the external transverse electric field to the actuator runs through the edges of the entire sandwich plate. The value of n is thus currently taken based on the bending modes of vibrations of interest, as illustrated in the later section.

Fig. 3.4 Two bending mode shapes and the corresponding distributions of transverse shear stress (  rz ) at the middle plane of a simply-supported isotropic annular plate; (a), (b) mode: m  1 , n  2 ; (c), (d) mode: m  1 , n 

Shear actuation capability of obliquely-reinforced 1-3 PFC

Properties of constituent materials in the annular sandwich plate
FE model of the annular sandwich plate

So the material properties at any point (r,) of a PFC patch can be obtained in the cylindrical coordinate system (r z) through a transformation of the properties (Eq. With respect to this cylindrical reference coordinate system, the kinematics of deformation of the assembled annular plate is defined according to the layered deformation theory as [390], The state of stress and the state of strain at any point within the kth layer of the assembled annular plate can be written as, .

Shear actuation capability of obliquely-reinforced 1-3 PFC For deriving the FE model of the overall annular plate, the plane of the

Shear-based control strategy

3.2, and the actuator patches are activated according to the sign change of the shear stress (rz). Here the time rate of change of the slope is taken for activating the actuator patches according to the velocity feedback control law. The time rate of change of slope (equation 3.18) for an actuator patch is fed back in the form of the electric field.

Shear actuation capability of obliquely-reinforced 1-3 PFC across the thickness of that patch according to the velocity feedback control law

Shear actuation capability of obliquely-reinforced 1-3 PFC frequency responses of the overall annular plate are analysed to assess the

Shear actuation capability of obliquely-reinforced 1-3 PFC In parallel to this result, similar bending response of the annular sandwich

Thus, driving the annular sandwich plate through the patches of obliquely reinforced 1-3 PFC does not appear in a straight forward manner. In order to make a clear understanding of the corresponding mechanism of actuation, an electroelastic analysis of the overall annular plate is currently carried out in a special way by the transverse electric field over the thickness of the patches of obliquely reinforced 1- 3 to apply. PFC. The geometric properties, material properties and boundary conditions of the overall annular plate are taken as mentioned at the beginning of the section (section 3.6).

Shear actuation capability of obliquely-reinforced 1-3 PFC electric field, the maximum bending deflections of the overall annular plate for

So these coefficients (e36 and e34) have no indicative effect on the bending deformation of the overall annular plate as observed from the curves in Fig. So the shear actuation of the overall ring plate through the coefficient (e33) mainly appears. due to the corresponding shear activation force in the rz plane, and this happens indicatively as shown in figure 3.9, it is clear that the activation of the annular sandwich plate from the parts of the obliquely reinforced PFC 1-3 appears mainly by shear activation forces in the rz plane through coefficients e33 and e35.

Fig. 3.9 Variation of maximum transverse deflection ( w max / h ) of the annular sandwich plate with the fiber orientation angle (  with the z -axis) of the patches of obliquely reinforced 1-3 PFC

Shear actuation capability of obliquely-reinforced 1-3 PFC corresponding variations of the maximum control voltage ( V max ) are also

Shear actuation capability of obliquely-reinforced 1-3 PFC to obtain it, the resonant displacement amplitudes are computed for different

So the application of the obliquely reinforced 1-3 PFC as a material of displacement actuator is mainly limited to a certain value of the load amplitude (po) where the applied control voltage exceeds its allowable value for this 1-3 PFC. It can be seen from Table 3.2 that the resonant displacement amplitude of the annular sandwich plate is indicatively damped by the actuator lobes of the obliquely reinforced 1-3 PFC for any value of the load amplitude (po). Moreover, the decay rate of resonant displacement amplitude or the corresponding increase in control voltage remains almost the same for any load amplitude (po).

Fig. 3.12 Variations of (a) the resonant transverse displacement amplitudes and (b) the corresponding maximum control voltages with the control gain ( k d ) at the first and second bending modes of vibration of the annular sandwich

Shear actuation capability of obliquely-reinforced 1-3 PFC infer an significant shear actuation capability of the obliquely reinforced 1-3

Shear actuation capability of obliquely-reinforced 1-3 PFC Table 3.2 Attenuation of the resonant displacement amplitude and the

Summary

Shear actuation capability of obliquely-reinforced 1-3 PFC control of bending modes of vibration of the annular plate is carried out by

Chapter 4

A balanced laminate of piezoelectric fiber composite for improved shear piezoelectric actuation of beams

Introduction

Present balanced laminate of PFC

A balanced laminate of PFC

Smart sandwich beam
Summary

4.5 (a) Schematic diagram of a balanced PFC laminate beam with two pairs of 2-2 PFC layers, (b) typical cross section of a balanced PFC laminate beam. BL-PFC properties are calculated directly from the current micromechanics formulation (Section 4.2.2). 4.8 (a) Variation of maximum transverse deflection of smart sandwich beam with fiber orientation angle ( with z-axis) of obliquely reinforced 1-3 PFC or balanced laminate of PFC (Ez 50 V/mm).

Fig. 4.2 (a) Vertically reinforced 2-2 PFC lamina and (b) the corresponding representative volume element (denoted by RVE1)

Chapter 5

Shear-based vibration control of annular sandwich plates using different piezoelectric fiber composites: a

Introduction

Comparative study on shear-mode piezoelectric actuators poled ( P ) along the x -direction and the externally applied external electric field (

Shear actuator laminate and effective properties

The top and bottom surfaces of each actuator (active) layer are fully electrode surfaces, and the active layers within the laminate are considered to be activated by the uniform external electric field/voltage. According to the aforementioned arrangement of electrodes in the laminate/RVE, the active (piezoelectric) layer is subjected to a dominant electric field (Ez) in the transverse (z) direction. Thus, the inverse piezoelectric constitutive relationship for the active (piezoelectric) layer and the similar constitutive relationship for the epoxy layer can be written as,

Comparative study on shear-mode piezoelectric actuators

According to the mixture rule, the average field quantities (U and U) over the RVE volume can be assumed in terms of similar average field quantities of the phase volume, so that the following expression can be obtained. Equation (5.5) can be arranged in a form similar to Eq. 5.1a) or (5.1b) to obtain an effective inverse piezoelectric constitutive relationship for the RVE/laminate as,.

Comparative study on shear-mode piezoelectric actuators where, C and e are the effective stiffness and the vector of piezoelectric

Smart annular sandwich plate
Properties of constituent materials in the annular sandwich plate
FE model of the annular sandwich plate

3.3, and the core layer in the laminate's sandwich corresponding to that in fig. of the mechanically induced transverse shear stress (rz) in the rz plane of the annular sandwich plate. However, for using the patches as actuators, the electric field in actuator patches is always specified.

Comparative study on shear-mode piezoelectric actuators Table 5.1 Effective properties of the PZT5H, BL-PFC and SAFC laminates

Comparative study on shear-mode piezoelectric actuators densities of these actuator laminates are also computed using the rule of

Comparative study on shear-mode piezoelectric actuators 5.6.3 Analysis of shear-based active control of the annular sandwich

Thus, the resonant displacement amplitude can be attenuated to the desired mark by increasing the control gain without additional control voltage overhead. These results infer the suitability of actuator patch deployment and the associated shear-feedback control strategy. It may be noted here that this type of actuator patch arrangement and associated shear-based feedback loop control strategy was proposed in Chapter 3 when using a bias-gained 1-3 PFC for active shear-based control of an annular plate.

Fig. 5.4 Variations of (a) the maximum transverse displacement-amplitude (

Comparative study on shear-mode piezoelectric actuators shear-based feedback control strategy, can fruitfully be used for the present

Comparative study on shear-mode piezoelectric actuators needs more number of velocity sensors according to the present shear-based

Comparative study on shear-mode piezoelectric actuators procedure is followed for every mode, and the corresponding optimal values of

However, for different values of control gain (kd) and load amplitude (po), the corresponding variations of resonance displacement amplitude and peak control voltage are illustrated in Figs. However, for an increase in the control gain (kd) at different load amplitudes (po), the corresponding decrease in the resonant displacement amplitude and the increase in the maximum control voltage are measured by determining the parameters W(%) and V. (%) as given in Eqs. It also infers that all shear actuator laminations act uniformly for an increase in control gain at any load amplitude.

Fig. 5.7 Variations of the resonant displacement-amplitude ( w max / h ) and the corresponding maximum control voltage ( V max ) with the control-gain ( k d );

Summary

Comparative study on shear-mode piezoelectric actuators actuator laminate are determined through a micromechanics formulation based

Chapter 6

A design of shear actuated hybrid damping treatment for annular plates using balanced laminate of PFC and 0-3

Introduction

A design of shear actuated hybrid damping treatment

Annular piezo-foam composite disc using BL-PFC patches
Design of an annular disc of 0-3 VEC
Design of a layered annular plate for shear actuated hybrid damping treatment
Properties of the constituent materials in the layered annular plate
FE model of the overall annular plate
Shear-based active control strategy

6.3(b) to follow their (viscoelastic layer) locations against the top and bottom faces of the assembled plate. This comparison confirms the present FE formulation for handling the vibration of the annular plate. These two configurations of the layered annular plate are currently designated PFC-VEM#1 (Fig.