https://www.aeromech.usyd.edu.au/wwwcomp/pzferev.pdf

Advances in piezoelectric finite element modeling of adaptive structural elements: a survey

Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Dynamics of viscoelastic structures: a time-domain finite element formulation

The main objective of this article is to present an overview of the modelling that has been proposed by various workers in the field of smart or intelligent structures. Before the main discussion o...

A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures

Since the mid-1960s when the forms of curved shell finite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The first two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell finite elements over the past 15 years. It is hoped that this will be a befitting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell finite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites. Copyright © 2000 John Wiley & Sons, Ltd.

A survey of recent shell finite elements

A finite element for planar beams with active constrained layer (ACL) damping treatments is presented. Features of this non-shear locking element include a time-domain viscoelastic material model, and the ability to readily accommodate segmented (i.e. non-continuous) constraining layers. These features are potentially important in active control applications: the frequency-dependent stiffness and damping of the viscoelastic material directly affects system modal frequencies and damping; the high local damping of the viscoelastic layer can result in complex vibration modes and differences in the relative phase of vibration between points; and segmentation, an effective means of increasing passive damping in long- wavelength vibration modes, affords multiple control inputs and improved performance in an active constrained layer application. The anelastic displacement fields (ADF) method is used to implement the viscoelastic material model, enabling the straightforward development of time-domain finite elements. The performance of the finite element is verified through several sample modal analyses, including proportional-derivative control based on discrete strain sensing. Because of phasing associated with mode shapes, control using a single continuous ACL can be destabilizing. A segmented ACL is more robust than the continuous treatment, in that the damping of modes at least up to the number of independent patches is increased by control action.

https://iopscience.iop.org/article/10.1088/0964-1726/5/5/010/pdf

A finite element for beams having segmented active constrained layers with frequency-dependent viscoelastics

The QUAD4 element found in ASTROS is modified to include piezoelectric layers and a viscoelastic layer. These features are developed and combined to allow for active damping using piezoelectrics, passive damping using constrained layer damping (CLD) and hybrid damping in the form of active constrained layer damping (ACLD). These features are implemented in the QUAD4 element as additional layers in the composite layup definition. The development of these features are presented and the integrity of the implementation is validated by comparing with results found in the literature. A patch placement process is developed which allows the damping treatment to move on the structure and to distort its shape so as to improve the damping characteristics of the design. The structure and damping treatment are simultaneously designed for minimum weight with constraints on the frequency and damping ratio. Both beam and plate structures are used to illustrate this concept. A proportional-derivative controller is used for the active control of the beam and the linear quadratic regulator (LQR) is used to design the active controller for the plates.

http://iopscience.iop.org/article/10.1088/0964-1726/5/5/014/pdf

A comparison of active, passive and hybrid damping in structural design

Two-dimensional finite element modeling of composites with embedded piezoelectrics

The optimum design of structures is obtained for three different types of damping treatments and the resulting designs are compared. The three types of damping treatments considered are constrained layer damping, active constrained layer damping and active damping. Piezoelectric material is used for actuators and sensors in the active damping and active constrained layer damping cases. The constraining layer of the active constrained layer damping case is the piezoelectric actuator. The structure is designed for minimum weight with constraints on the frequency and damping ratio. The problem is modeled using a two dimensional finite element based on the QUAD4 element. The QUAD4 element is modified to include viscoelastic and piezoelectric layers in the composite layup. The damping treatment is also allowed to move on the structure and to distort its shape so as to improve the damping characteristics of the initial design. Both beam and plate structures are considered to illustrate this concept. A proportional-derivative controller is used for the active control of the beam and the linear quadratic regulator (LQR) is used to design the active controller for the plates.

Comparison of active, passive, and hybrid damping treatments in structural design

A piezoelectric element and a constrained layer damping element are combined to allow for an active constrained layer damping treatment. The development of these elements is reviewed and results are compared with the literature to insure that the elements work together. A procedure for placing patches damping treatments or other material anomalies on structures is introduced. The patch placement process uses a grid deformation procedure to realign elements with the patch boundaries. This makes the process of optimally locating the damping treatment one of continuous variables. The patch placement process is used in conjunction with the combined elements and an optimization algorithm to design an active constrained layer damping treatment and the beam to which it is attached.

Optimal design of structures with active constrained-layer damping

A new finite element is developed that reduces the modeling required to define the constrained layer damping treatment. The new element emulates the traditional method of modeling constrained layer damping with plate elements on either side of a thin hex element. Trade studies are performed in the application of constrained layer damping treatments to beams and plates. The effects of the thicknesses of the constraining layer and the viscoelastic layer are studied as well as some studies on the location of the damping treatment.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

S. S. Rao

Papers

A comparison of active, passive and hybrid damping in structural design

Two-dimensional finite element modeling of composites with embedded piezoelectrics

Comparison of active, passive, and hybrid damping treatments in structural design

Optimal design of structures with active constrained-layer damping

Two-dimensional finite element modeling of constrained-layer damping