Utilizing the Finite Element Method to Analyze the

Utilizing the Finite Element Method to Analyze the

Utilizing the Finite Element Method to Analyze the Active Vibration
Suppression of Structural Systems
Brian P. Baillargeon, Application Engineer
ABAQUS East, LLC, Warwick, Rhode Island, 02886
Tel: 401-739-3637, Fax: 401-739-3302, Email: [email protected]

Finite element model:

Cantilever Beam:

A two dimension plane stress implicit dynamic ABAQUS model is
utilized to characterize the structural response of the cantilever
beam. The model consisted of 2754 CPS8R and CPS8RE
elements (8893 nodes).
The mathematic representation of the compensator is that of a
spring-mass-damper system. A spring-mass-damper system is
included in the model to act as a physical representation of the
The two systems (beam and compensator) are coupled using user
subroutines intrinsic to ABAQUS. In the experiment, the strain at
the root of the beam is used as the sensor input to the control
system. The numerical model is consistent, in that the strain at the
root of the beam applies a force to the compensator. In turn, the
value of the compensator displacement, multiplied by a scalar gain,
is applied as an electric potential to the piezoelectric shear

The use of piezoelectric materials in smart/adaptive structures has
been studied intensely for more than a decade. Engineering
applications using this technology have been proposed and
conceived experimentally, such as for active vibration suppression,
noise cancellation, and shape control.
In this work, a distinctly different piezoelectric transduction mode is
utilized where the electric field is applied perpendicular to the poling
direction. In this case, a piezoelectric rectangular element that is
poled in the longitudinal direction and subjected to an electric field E3
in the thickness direction will undergo shear deformation as shown in
Figure 1(b). This is referred to as the piezoelectric shear actuation
- V +

Steel Block



(Used for repeatable beam excitation)

Figure 3. Cantilever beam configuration


Extension Actuator

- V +
- V +

Rigid Foam

Table 1. Natural frequency comparison


Shear Actuator


Experimental Natural
Frequency (Hz)

Finite Element Natural
Frequency (Hz)

% Diff.

Figure 1. Piezoelectric extension and shear actuators
The finite element method is utilized to replicate experimental results
of the active vibration suppression of a cantilever beam with
embedded piezoelectric shear actuators. The commercial finite
element package ABAQUS is utilized for the numerical modeling.
The feedback control is implemented using FORTRAN subroutines
coupled to the ABAQUS analysis. It is shown that the numerical
model accurately predicts the influence of the feedback control
system on the dynamic response of the beam.

Figure 4. Experimental and finite element comparison of settling time of the
cantilever beam

Table 2. Results of the settling time comparison

Feedback control:
In this study, active vibration suppression is implemented using a
feedback control system. The controller design is that of the
Positive Position Feedback (PPF) algorithm. The structure and the
compensator are coupled using the following relationships:
2 n n 2 g c 2

2 c c c 2 c 2



96.7% reduction in

Figure 5. Cantilever beam tip acceleration with
various feedback control options

The goal of this study was to accurately reproduce the observed experimental response of the vibration suppression of a
cantilever beam using the finite element method. The control algorithm utilized was Positive Position Feedback. It is
shown that the dynamic characteristics of the cantilever beam are accurately represented utilizing the finite element method
with the active vibration suppression active and inactive.

I wish to acknowledge the support of the Maine Space Grant Consortium under the collaborative seed Grant No. EP-02-11.
Figure 2. Experimental implementation of PPF

Recently Viewed Presentations

  • U.S. General Services Administration Easy Ordering with GSA

    U.S. General Services Administration Easy Ordering with GSA

    John BarnicleGSA SmartPay Training ForumJuly 16-18, 2019. U.S. General Services Administration. Training Agenda . GSA Overview . GSA and the National Supply System . The GSA Global Supplyâ„¢ Program. Product Availability. Supply Transformation.
  • Introduction to Cell Division

    Introduction to Cell Division

    The nuclear membrane reforms around each daughter nucleus. Each new cell now contains two sister chromatids that are NOT identical due to crossing over.
  • History and Approaches

    History and Approaches

    Humanist . Humanist theorists, like Abraham Maslow and Carl Rogers, stress the individuals choice and free will. They believe most of our choices are guided by physiological, emotional, or spiritual needs. Hierarchy of needs pyramid . On the other hand,...
  • Chapter 2

    Chapter 2

    Symmetry Is one half of the distribution a mirror image of the other (along a vertical axis)? Three examples of symmetrical distributions: Skew Positive - high frequencies of low values and low frequencies of high values Negative - low frequencies...
  • The Combined Gas Law and Avogadro's Principle

    The Combined Gas Law and Avogadro's Principle

    The Ideal Gas Law Objectives: 7.0 Explain the behavior of ideal gases in terms of pressure, volume, temperature, and number of particles using Charles's law, Boyle's law, Gay-Lussac's law, the combined gas law, and the ideal gas law.
  • Volcanic cones - Welcome to Think Geography

    Volcanic cones - Welcome to Think Geography

    Volcanoes Not just one type Volcanoes Not just one type Composite Cone The volcano is built up of alternate layers of LAVA and ASH. They can explode with great violence.
  • Operational Capabilities As part of Enterprise Productivity Initiatives

    Operational Capabilities As part of Enterprise Productivity Initiatives

    Over 35000+ professionals working across 5 GEOs and successfully handing 100,000+ applications (including large ASM engagements) across a customer base of 100+. HCL's professionals have capability of resolving average 13 000 000 tickets per year and generated ideas worth of...
  • Name of Presentation

    Name of Presentation

    moodle (verb) - process of enjoyable tinkering that often leads to growing knowledge, insight and creativity. It applies both to the way Moodle was developed, and to the way we may use it to teach and learn.