... development of A-GPSFs followed in the middle plane of thin-walled beams and plates to study the free vibrations of the same components [ 17 , 18 ]. The adoption of A-GPSFs within the middle plane of a structural element needed a variant for using these bases. Indeed, thin-walled beams and plates when used...

...Lisha Yuan; Romesh C. Batra We numerically analyze, with the finite element method, free vibrations of incompressible rectangular plates under different boundary conditions with a third-order shear and normal deformable theory (TSNDT) derived by Batra. The displacements are taken as unknowns...

... is equivalent to an arbitrary value of the acceleration Eq. ( 4.15 ). The examples in Sec. 4 show that the critically damped free vibration response to displacement and velocity initial value problems can be significantly influenced by the initial internal state of the damper spring. The analysis...