Piezoelectric Actuation of von Karman Circular Plates With Thermal Deformation and Nonlinear Oscillation

1995 ◽  
Author(s):  
H. S. Tzou ◽  
Y.-H. Zhou
Keyword(s):  
Circular Plate ◽  
Nonlinear Effects ◽  
Thermal Buckling ◽  
Control Effect ◽  
Control Moment ◽  
Von Karman ◽  
Equivalent Control ◽  
High Control ◽  
Von Kármán ◽  
And Control

Abstract Linear dynamics and distributed control of piezoelectric laminated continua have been intensively studied in recent years. In this study, dynamics, electromechanical couplings, and control of thermal buckling of a piezoelectric laminated circular plate with an initial nonlinear large deformation are investigated. It is assumed that the von Karman type geometrically nonlinear deformation is considered. In addition, the piezoelectric layers are uniformly distributed on the top and bottom surfaces of the circular plate. Accordingly, control effect is introduced via an equivalent control moment on the circumference. Dynamic equations and boundary conditions including elastic and piezoelectric couplings are formulated, and solutions are derived. Active control of plate’s nonlinear deflections, thermal buckling, and natural frequencies using high control voltages are studied, and their nonlinear effects are evaluated.

Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part 2: Control of Nonlinear Deflection, Buckling and Dynamics

1997 ◽  
Vol 119 (3) ◽  
pp. 382-389 ◽  
Author(s):  
H. S. Tzou ◽  
Y. H. Zhou
Keyword(s):  
Circular Plate ◽  
Geometrical Nonlinearity ◽  
Nonlinear Effects ◽  
Thermal Buckling ◽  
Control Effect ◽  
Control Moment ◽  
Piezoelectric Layers ◽  
Equivalent Control ◽  
High Control ◽  
And Control

Linear dynamics and distributed control of piezoelectric laminated continua have been intensively investigated in recent years. In this study, dynamics, electromechanical couplings, and control of thermal buckling of a nonlinear piezoelectric laminated circular plate with an initial large deformation are investigated. It is assumed that the transverse nonlinear component is much more prominent than the other two in-plane components—the von Karman type geometrical nonlinearity. In addition, the piezoelectric layers are uniformly distributed on the top and bottom surfaces of the circular plate. Accordingly, the control effect is introduced via an equivalent control moment on the circumference. Dynamic equations and boundary conditions including the elastic and piezoelectric couplings are formulated, and solutions are derived. Active control of plate’s nonlinear deflections, thermal buckling, and natural frequencies using high control voltages are studied, and their nonlinear effects are evaluated.

ON A NONLOCAL FUNCTIONAL ARISING IN THE STUDY OF THIN-FILM BLISTERING

2010 ◽  
Vol 08 (02) ◽  
pp. 109-123
Author(s):  
N. ANSINI ◽  
V. VALENTE
Keyword(s):  
Thin Film ◽  
Asymptotic Analysis ◽  
Circular Plate ◽  
One Dimensional ◽  
Von Karman ◽  
Nonlocal Functional ◽  
Γ Convergence ◽  
Von Kármán

The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero.

Dynamic Flexoelectric Actuation and Vibration Control of Beams

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Mu Fan ◽  
Bolei Deng ◽  
Hornsen Tzou
Keyword(s):  
Experimental Data ◽  
Dynamic Control ◽  
Longitudinal Direction ◽  
Bottom Surface ◽  
Internal Stresses ◽  
Control Effect ◽  
Flexoelectric Effect ◽  
Control Moment ◽  
Fixed End ◽  
And Control

A flexoelectric cantilever beam actuated by the converse flexoelectric effect is evaluated and its analytical and experimental data are compared in this study. A line-electrode on the top beam surface and a bottom surface electrode are used to generate an electric field gradient in the beam, so that internal stresses can be induced and applied to distributed actuations. The dynamic control effectiveness of the beam is investigated with a mathematical model and is validated by laboratory experiments. Analyses show that the actuation stress induced by the converse flexoelectric effect is in the longitudinal direction and results in a bending control moment to the flexoelectric beam since the stress in the thickness is inhomogeneous. It is found that thinner line-electrode radius and thinner flexoelectric beam lead to larger control effects on the beam. The position of the line-electrode on the top surface of the beam also influences the control effect. When the line-electrode is close to the fixed end, it induces a larger tip displacement than that is close to the free end. Analytical results agree well with laboratory experimental data. This study of flexoelectric actuation and control provides a fundamental understanding of flexoelectric actuation mechanisms.

Actuator Placement and Micro-Actuation Efficiency of Adaptive Paraboloidal Shells

2003 ◽  
Vol 125 (4) ◽  
pp. 577-584 ◽  
Author(s):  
H. S. Tzou ◽  
J. H. Ding
Keyword(s):  
Communication Systems ◽  
Design Parameters ◽  
Shells Of Revolution ◽  
Control Effect ◽  
Control Effectiveness ◽  
Membrane Bending ◽  
High Control ◽  
Control Forces ◽  
And Control ◽  
Actuator Placement

Paraboloidal shells of revolution are commonly used in communication systems, precision opto-mechanical systems and aerospace structures. This study is to investigate the precision distributed control effectiveness of adaptive paraboloidal shells laminated with segmented actuator patches. Mathematical models of the paraboloidal shells laminated with distributed actuator layers subjected to mechanical, temperature, and control forces are presented first. Then, formulations of distributed actuating forces with their contributing micro-meridional/circumferential membrane and bending components are derived using an assumed mode shape function. Studies of actuator placements, actuator induced control forces, micro-contributing components, and normalized actuation authorities of paraboloidal shells are carried out. These forces and membrane/bending components basically exhibit distinct modal characteristics influenced by shell geometries and other design parameters. Analyses suggest that the membrane-contributed components dominate the overall control effect. Locations with larger normalized forces indicate the areas with high control efficiencies, i.e., larger induced actuation force per unit actuator area. With limited actuators, placing actuators at those locations would lead to the maximal control effects of paraboloidal shells.

Nonlinear Vibration of Rotating Thin Disks

2000 ◽  
Vol 122 (4) ◽  
pp. 376-383 ◽  
Author(s):  
Albert C. J. Luo ◽  
C. D. Mote,
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlinear Effects ◽  
Linear Vibration ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Von Karman ◽  
Thin Disks ◽  
Von Kármán

The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

Actuator Placement and Control Efficiency of Paraboloidal Shell Structures

2001 ◽  
Author(s):  
H. S. Tzou ◽  
J. H. Ding
Keyword(s):  
Distributed Control ◽  
Communication Systems ◽  
Design Parameters ◽  
Control Force ◽  
Shells Of Revolution ◽  
Control Effect ◽  
Membrane Bending ◽  
High Control ◽  
Control Forces ◽  
And Control

Abstract Paraboloidal shells of revolution are commonly used in communication systems, precision opto-mechanical systems and aerospace structures. This study is to investigate the precision distributed control effectiveness of paraboloidal shells laminated with segmented actuator patches. Mathematical models of the paraboloidal shells laminated with distributed actuator layers subjected to mechanical, temperature, and control forces are presented first, followed by formulations of distributed control forces with their contributing meridional/circumferential membrane and bending control components using an assumed mode shape function. Studies of actuator placements, control forces, contributing components, and normalized control authorities of paraboloidal shells are carried out. These forces and membrane/bending components basically exhibit distinct modal characteristics influenced by shell geometries and other design parameters. Analyses suggest that the membrane contributed components dominate the overall control effect. Locations with larger normalized forces indicate the areas with high control efficiencies, i.e., larger induced control force per unit actuator area. With limited actuators, placing actuators at those locations would lead to the maximal control effects.

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