Introduction
1.6 Motivation and objectives of present research
Chapter 1: Introduction
1-3 PFC actuator is utilized with its different fiber orientation angles, and it is observed that the ACLD patch provides maximum damping when it is in elliptic shape. Vinyas [355] investigated the active-passive damping of skew MEE plates integrated with ACLD patches that are comprised of VEM and 1-3 PFC actuator.
This study reveals feasible vibration suppression of skew plates for the higher skew angles.
1.5.7 ACLD treatment of shells using extension-mode PFC actuator Ray and Reddy [356] analyzed the vibration control of a laminated circular cylindrical shell integrated with the ACLD patches where a horizontally reinforced 1-3 PFC actuator is utilized and the effect of its (PFC) fiber orientation angle on the damping capacity of the treatment is addressed. Ray and Balaji [357] and Ray [358] presented structural-acoustic control of symmetric/anti-symmetric composite panels using two ACLD patches comprised of a 1-3 PFC and the VEM.
Ray and Pradhan [359,360] presented the performance of a vertically/obliquely reinforced 1-3 PFC in the partial ACLD treatment of laminated composite cylindrical shells. Further investigations on the utilization of the same PFC (vertically/obliquely reinforced 1-3 PFC) in the ACLD treatment of shells are available in [361–365]. In [366-368], the theoretical studies on the ACLD treatment of stationary or rotary truncated laminated conical shell are presented using vertically/obliquely reinforced 1-3 PFC. Li and Narita [369] analyzed the attenuation of vibration of a laminated panel using horizontally reinforced 1-3 PFC in the ACLD patch. Shivakumar et al. [370] utilized the same 1-3 PFC for partial ACLD treatment of nonlinear vibration of shallow shells. However, these available studies indicate an extensive utilization of the extension-mode PFC actuators in the ACLD or active-passive damping treatment of structural vibration, whereas an application of the shear-mode PFC actuator in the similar damping treatment is not yet reported in the literature to the best knowledge this author.
Chapter 1: Introduction
shear and extension mode PFC actuators are substantially utilized for active control of deformation/vibration of the thin-walled flexible structures like beams, rectangular plates, plate strips, singly/doubly curved shells, circular cylindrical shells, airfoils, etc. [230-232, 236, 238, 243, 248, 260, 264, 273, 371]. Besides these structures, the plane structures of revolution like annular and circular plates may be treated as the basic structural elements as those are often used in micro-valves, implantable medical devices, micro-switches, micro-pumps, oil storage tanks, brakes in vehicles, airfoil cascades, oceanographic applications, etc. [372-378]. However, it is observed from the available literature that a few studies on the active control of annular/circular plates have been reported in the literature utilizing extension-mode monolithic piezoelectric actuators [151, 160].
Moreover, the utilization 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. So, the primary objective of this research is decided as the design and application of PFC actuators towards the advancement of active, as well as active-passive, vibration control of annular plates.
The existing PFCs are designed in the Cartesian material coordinate system so that these PFCs may not be well-qualified materials for the distributed actuators in active control of annular plates where the mechanically induced stresses/strains usually arise in the cylindrical coordinates. It infers the requirement of the design of microstructure of PFC in the cylindrical material coordinate system for effective active control of annular plates. The research in this concern is not yet addressed in the literature. So, the first objective of this dissertation is decided as the design of a new annular PFC actuator with the cylindrically periodic microstructure in particular to achieve the directional/maximum extensional actuation force along the radial direction in the cylindrical principal material coordinate system. The verification of its (annular PFC actuator) performance in active vibration control of annular plates is also included in the same objective.
The vertically reinforced 1-3 PFC [13] is commonly known as a material of thickness mode piezoelectric actuator, where the extension-mode piezoelectric actuation appears in the thickness/transverse direction for an externally applied transverse electric field. If the vertically oriented fibers in this 1-3 PFC are considered to be obliquely oriented at an angle with the thickness coordinate, then the transverse shear actuation force arises along with the thickness mode
Chapter 1: Introduction
actuation force. This shear actuation force may be utilized for active control of deformation/vibration of flexible structures. However, if it is applied for the shear actuated bending deformation of thin annular plates, then the corresponding effectiveness of the obliquely reinforced 1-3 PFC actuator is in doubt mainly because of the anisotropic properties of this PFC in the reference cylindrical coordinate system for the host annular plate. In this view, the second objective of this dissertation is decided for investigating the shear actuation mechanism and shear-based actuation capability of the obliquely reinforced 1-3 PFC in active control of vibration of annular plates.
The aforesaid obliquely reinforced 1-3 PFC possesses anisotropic material properties so that the transverse shear actuation force within it is coupled with the extensional strain components, and this coupling poses detrimental effect on the shear actuation capability of the PFC. The elimination of this coupling effect through the microstructural change of the PFC may result a new shear mode PFC having superior shear actuation capability. This development of a new shear mode PFC is taken as the third objective of this dissertation. In order to verify the utility of this new shear mode PFC in shear-based vibration control of annular plates, it is required to compare its actuation capability with that of the existing shear- mode piezoelectric actuators namely SAFC and shear-mode monolithic piezoelectric actuators. This comparative study is identified as the fourth objective of the present research.
The passive damping of flexural vibration of annular plates can simply be achieved using the pure viscoelastic materials (VEMs) through UCLD/CLD treatment as the same has been reported in the literature. However, the advanced damping materials like 1-3/0-3 viscoelastic composites (VECs) [325,400] can be used instead of VEM for improved passive damping of the same (annular) plates.
But, the geometry of these plates requires certain changes in the constructional features of the available 1-3/0-3 VECs so that the passive damping may not be augmented in a fruitful manner. The additional issues may arise in implementation of the adaptive control of the annular plates by means of adding a shear-mode PFC or monolithic piezoelectric actuator, where the main difficulty arises in deciding appropriate locations of the VEC layer and the shear actuator since the shear actuation and viscoelastic damping mainly appear through the same field quantity i.e. transverse shear strain. In order to investigate these
Chapter 1: Introduction
issues, another objective of this research is decided as the active-passive control of vibration of annular plates using the shear-mode PFC and VECs.
In order to fulfil the aforesaid objectives in this research, the following theoretical studies have been carried out.
(a) Electromechanical properties and actuation capability of an extension- mode piezoelectric fiber composite actuator with cylindrically periodic microstructure.
(b) Shear actuation mechanism and shear-based actuation capability of an obliquely reinforced PFC in active control of annular plates.
(c) Design of a balanced laminate of piezoelectric fiber composite.
(d) Shear-based vibration control of annular sandwich plates using different piezoelectric fiber composites: a comparative study.
(e) A design of shear actuated hybrid damping treatment for annular plates using balanced laminate of PFC and 0-3 viscoelastic composite.