  This study presents torsional and transverse vibration analysis of a solar
panel including a rectangular thin plate locally supported by an elastic beam.
The plate is totally free in all boundaries, except for the local part attached
to the beam. The response of the system, which is subjected to a combination of
torsional and transverse vibration, identifies with a couple of PDEs developed
by the Euler-Bernoulli assumption and classical plate theory. To calculate the
system's natural frequencies, the domain of the solution is discretized by
zeroes of the Chebyshev polynomials to apply the Modified Generalized
Differential Quadrature method (MGDQ). Furthermore, governing equations along
with continuity and boundary conditions are discretized. After obtaining
solutions to the eigenvalue problem, several studies are investigated to
validate the accuracy of the proposed method. As can be concluded from the
tables, MGDQ improves the accuracy of results obtained by GDQ. Results for
various case studies reveal that MGDQ is properly devised for the vibration
analysis of systems with local boundary and continuity conditions.
