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Influence of the excitation direction on the dynamics of the laminated beam with symmetrical or anti-
symmetrical layers arrangement Marcin Bochenski, Marek Borowiec, Jaroslaw Gawryluk, Andrzej Teter,
Lublin University of Technology, Faculty of Mechanical Engineering, Department of Applied Mechanics,
Nadbystrzycka 36, PL-20-618 Lublin, Poland; e-mails: m.bochenski@pollub.pl, m.borowiec@pollub.pl,
j.gawryluk@pollub.pl, a.teter@pollub.pl; The research was financed within the framework of the Lublin
University of Technology - Regional Excellence Initiative project, funded by the Polish Ministry of
Science and Higher Education (contract no. 030/RID/2018/19). The cantilever beam made of laminate
with symmetrical or anti-symmetrical layers arrangement was excited in different directions and with
various amplitudes. The couplings of vibration modes in flexible, stiff and torsional directions are
taken place. In this case, it is difficult to predict the dynamic response of the system, especially if
the kinematic excitation can assume any direction and amplitude. Numerical simulations using the
finite element method were performed. The beam was made of unidirectional pre-impregnate with a
matrix of thermosetting epoxy resin reinforced with high-strength R-type glass fibers. The following
layers arrangement was considered: alpha(5)/0/alpha(5) and alpha(5)/0/-alpha(5) called symmetrical
and anti-symmetrical, respectively. A substantially rectangular cross-section of the structure leads to
significant differences in bending stiffness in two perpendicular directions. The continuum shell finite
elements SC8R was used to prepare a numerical model of the beam. The implicit dynamic analysis
using direct integration was used. Experimental verification of the selected numerical results for various
angles (denoted as alpha) of layers arrangement was carried out. The structure was mounted on the
specialized grip on the electromagnetic shaker, which was a source of kinematic excitation. The response
of the system was measured using piezoelectric patches, strain gauges, and contactless laser sensors.
The piezoelectric element type Macro Fiber Composite was included in the numerical model of the
structure. The non-linear characteristics, both types progressive and regressive, for the system response
versus amplitude of excitation were found. The strong influence of layers arrangement on the system
behavior was confirmed. Configurations characterized by low and high values of coupling coefficients
were determined.
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