Young-Hun Lim

Closed loop finite-element modeling of active/passive damping in structural vibration control

A three-dimensional (3D) finite-element closed loop model has been developed to predict the effects of active/passive damping on a vibrating structure. The example used is a cantilever structure containing a viscoelastic material (VEM) layer sandwiched between a piezoelectric actuator and the base structure. This hybrid arrangement is called an active constrained layer damper (ACLD). A piezoelectric sensor is also embedded in the structure. The finite-element analysis includes a control algorithm to close the loop between the sensor and the actuator. The parametric study considers different types of control as well as geometric parameters related to the ACLD. Comparisons are made between active constrained layer and passive constrained layer, and active damping only. The results obtained here reiterate that ACLD is better for vibration suppression than either the purely passive or active system and provides higher structural damping with less control gain when compared to the purely active system. This is the first attempt at a detailed 3D finite-element model that makes no approximations about the piezoelectric devices and includes closed loop modeling.

Finite element simulation of smart structures using an optimal output feedback controller for vibration and noise control

This numerical study presents a detailed optimal control design based on the general finite element approach for the integrated design of a structure and its control system. Linear quadratic (LQ) theory with output feedback is considered on the basis of the state space model of the system. Three-dimensional finite elements are used to model the smart structure containing discrete piezoelectric sensors and actuators by the use of combination of solid, transition and shell elements. Since several discrete piezoelectric patches are spatially distributed in the structure to effectively observe and control the vibration of a structure, the system model is thus utilized to design a multi-input-multi-output (MIMO) controller. A modal analysis is performed to transform the coupled finite element equations of motion into the state space model of the system in the modal coordinates. The output feedback controller is then employed to emulate the optimal controller by solving the Riccati equations from the modal space model. An optimal controller design for the vibration suppression of a clamped plate is presented for both the steady state and the transient case. Numerical simulation is also used to predict the reduction in the sound pressure level inside an enclosure radiated from this optimally controlled plate.

Finite-element modeling of the transient response of MEMS sensors

The finite-element method of analysis is unrestricted by size considerations and is well suited for the study of very small structures such as MEMS devices embedded in structures. This paper presents the numerical approach and results for a silicon-based micro-flow sensor for pulsed-flow sensing. The new approach presented here is the treatment of transient problems. A finite-element formulation is presented for modeling the dynamic response of piezoelectric ceramic sensors embedded in a micro-cantilever subjected to mechanical loading resulting from fluid flow. An unconditionally stable method (called the -method) is used for the direct integration of the equations of motion and implicit - explicit procedures are used for the transient analysis of the linear system of equations. For verification of the code, the device is tested for step, rectangular pulse and sinusoidal loading. For the case of the micro-fluid flow sensor, numerical results are in good agreement with the available experimental data based on a piezoresistive sensor. The numerical approach presented here may be used in CAE models for microsensors under more realistic, transient excitation.

Radiated noise control via structural vibration control

Interior noise control in a cabin enclosure using active vibration control of the walls of the enclosure with discrete piezoelectric actuators and sensors is addressed. A hybrid approach using finite element formulation for the radiating walls of the enclosure. We use an exact 3D formulation without making the usual approximations for the electric field in the piezoelectric devices. The electrical boundary conditions and the charge on the electrodes are treated correctly. Computational time is optimized by using plate elements for the structure and 3D element for the devices with transition elements to connect them. A PD-controlled is used to relate the voltage output of the sensor in an open circuit conditions to the charge input to the actuator via appropriate gains to control vibrations. The acoustic part of the problem is modeled via a modal approach. The modal representation of the pressure is used as a mechanical force term on the structure which can be written in terms of a virtual mass. The driving team for the acoustic field is in turn the displacements on the surface of the radiating walls which is computed from the structural equations. This accounts for the acoustic field-structure interaction and the equations are solved simultaneously. By adjusting the feedback gain, significant noise reduction is achieved globally within the cavity for the dominant vibrational modes of the radiating panel.

Closed-loop finite element modeling of active/passive damping in structural vibration control

A 3D finite element closed loop model is presented for modeling smart structures to predict the effects of both active and active/passive damping on vibrating structures. A comprehensive finite element formulation is presented that includes a control algorithm to relate the sensor voltage to the actuator voltage in a closed lop. Two control approaches based on charge or voltage as the active control force applied to the actuator are studied in the time and frequency domains. Constant velocity and constant displacement feedback control algorithms are subsequently implemented to investigate vibration controllability of structures. A model superposition in conjunction with direct integration is used in the time domain to overcome the numerical difficulties associated with an unsymmetric active damping matrix. A parametric study considers different types of controller as well as feedback gain. Comparisons are made between active constrained layer damping (ACLD) and purely active damping in the frequency domain. Some design studies are presented which examine the performance of ACLD modeling as a function of gain and viscoelastic materials thickness.

Finite element modeling of the dynamic response of a MEMS sensor

A finite element formulation is presented for modeling microelectromechanical systems (MEMS) to predict the behavior of dynamic response of piezoelectric ceramics subjected to both mechanical and electrical loadings. The FEM formulation presented is based on variational principle using the concept of virtual work. An unconditionally stable method for direct integration of the equations of piezoelectric material is introduced and can be put in the form of 3-step linear multistep method of second order equations. A thin cantilever plate with PZT sensor mounted on it, is investigated to show the feasibility of analysis using 20 node isoparametric 3D piezoelectric elements, flat-shell elements, transition elements which are implemented for the numerical analysis. Under a given initial loading, a structure would deform accordingly, and the distributed sensor outputs could be calculated at each time step. Such calculation can be used as design tool for MEMS structures containing sensors and actuators.

Dynamical finite element models for MEMS and smart structures

Advances in application of MEMS to smart structures can be accelerated by implementation of CAD tools, optimization and parametric studies which will result in rapid prototyping and virtual design. Dynamical finite element models are ideally suited to capture the complexity of active sensor and actuator devices that make up a smart structure. MEMS are miniature electro-mechanical devices that can also be modeled by FE analysis. Recent advances in FE analysis allows us to zoom in and magnify the mesh at desired locations while maintaining the larger structural model. Thus we can achieve economy in computational time without sacrificing accuracy. In designing a smart structure, the active devices whether they be MEMS or larger devices must be modeled in detail, with special attention to the coupled fields present in these devices (electric, magnetic, elastic, thermal, etc.) and the accompanying additional boundary conditions. Lumped parameter approximations are usually insufficient to describe the observed behavior of these devices. During optimization procedures, one must have the ability to move these devices on the structure and hence one needs automatic remeshing procedures. This paper will review finite element models for smart structures as they have evolved over the last decade and summarize some of the more recent advances for dynamical modeling of MEMS and smart structures including closed loop modeling and design optimization. Practical examples as well as comparisons and code validation with experimental results will be provided wherever possible.

Finite element modeling of the transient response of smart structures

A finite element (FE) formulation is presented for modeling the dynamical response of smart structures with embedded piezoelectric ceramic devices subjected to transient loading. The FEM formulation presented is based on a variational principle using the concept of virtual work. An unconditionally stable method ((alpha) -method) is utilized for the direct integration of the equations of motion and can be put in the form of a 3-step linear multistep method of second order equations. A thin cantilever plate with piezoelectric devices is investigated to show the feasibility of the analysis and numerical simulation. The code employs 20 node isoparametric 3D piezoelectric elements, flat-shell elements and transition elements at the interface of the piezoelectric devices and the plate. Under a given external loading, the structure and the embedded sensors deform and the voltage response of the sensor can be calculated as a function of time. Such calculations can be useful as a design tool for smart structures.

Closed‐loop finite‐element modeling of smart structures—An overview

Smart structures incorporate sensors, actuators, and control electronics that permit the structure to tailor its response to changes in the environment in an optimal fashion. The sensors and actuators are constructed using functional materials such as piezoelectric materials. Finite‐element modeling has been successfully used to model these complex structures. More recently, closed‐loop numerical simulation of the tailored response of a smart structure has become possible by combining the finite‐element equations of the sensor response to applied dynamical loads to the input voltage or current to the actuators via a control algorithm. Optimization of sensor/actuator placement as well as optimization of the control gains will be discussed. Applications to control of cabin noise are studied. Constrained layer damping, incorporating active passive damping, can also be simulated. The talk will present an overview of the approach in relation to others in the extant literature.

Closed‐loop finite‐element modeling of active/passive structural vibration damping in the time domain

Finite‐element modeling is used for the study of structures with piezoelectric actuators and sensors augmented by viscoelastic passive dampers. The structure is excited by a transient force; the response of the structure as determined by the computed voltage response of the sensor is used to construct a feedback loop that excites the actuator. A constant gain P–D (proportional and derivative) controller is used. The controller changes the effective stiffness of the structure and the derivative feedback also introduces the desired damping. The increased stiffness also lowers the vibration amplitude. Active vibration damping is compared and contrasted with passive damping provided by a viscoelastic dampers. A BMG model is used for the viscoelastic phase. A hybrid approach using modal superposition in conjunction with time integration is used for solving the matrix equations in space and time in an efficient manner. A parametric set of results is presented showing the contribution of active and passive damping for the transient response of a clamped plate structure.