M.Sc Thesis

M.Sc StudentFridman Yulia
SubjectAn Investigation of the Stability of Axially Loaded Beams
in the Presence of Piezoelectric Patches
DepartmentDepartment of Aerospace Engineering
Supervisor ASSOCIATE PROF. Haim Abramovich


The aim of the present study is to analytically and numerically investigate the stability of laminated composite columns under axial compression using piezoelectric patches.

In the present study we use piezoelectric materials because of their electro-deformation capability. An active actuation mechanism was developed to enhance the axial loading capability of a composite laminated beam. It will induce a counteractive bending moment to the mechanical one. The following criterion forms the basis for the active mechanism: the voltage induced on the sensor due to the bending of the beam is amplified by constant gain and supplied to the actuators.

A mathematical model of a piezo-laminated composite beam was developed formulated and applied in the present study. It is based on a first order shear deformation theory (FSDT) which includes shear deformations and linear piezoelectric constitutive relations.

Firstly the case of a composite beam with continuous piezoelectric layers bonded on the top and bottom of beam’s surfaces. For the case of continuous piezoelectric layers, closed form solutions for the bending angle, axial and lateral displacements for symmetric and non-symmetric beams with various boundary conditions were derivate. In the second phase, the cases of a composite beam with piezoelectric patches were examined

A parametric investigation was carried out to study the stability of a beam and the influence of the piezoelectric sensing-actuation mechanism. Numerical results were obtained for composite beams made of graphite-epoxy and piezoelectric sensors/actuators made from PZT-5H. Buckling loads, natural frequencies, lateral displacements and mode shapes of vibrations for beams with and without piezoelectric layers and patches of symmetric and anti -symmetric lay-ups, having various boundary conditions simply-simply, clamped-clamped, clamped-free, clamped-simply, were computed. The main conclusion is that the buckling load and natural frequencies of a beam can be increased by using the sensing-actuation mechanism developed in the present study.                     

For a composite beam with piezoelectric patches the level of improvement of the buckling load and the natural frequencies depends on the gain value (namely the power of the actuation), on the PZT patches size and location on the beam, on the lay-up type and of course on the beam's boundary conditions

An experimental investigation of PZT patches, acting as sensors, under cyclic mechanical loads was also performed throughout the present study. The voltage measured on the PZT sensors was found to be consistent throughout the tests.