Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

Natural vibration analysis of rectangular bottom plate structures in contact with fluid

“…are non-dimensional stiffness at x ¼ 0, x ¼ a, y ¼ 0 and y ¼ b, respectively, and correspond to the translational spring constants per unit length k Tx1 , k Tx2 , k Ty1 and k Ty2 ;as explained in Cho et al (2013Cho et al ( , 2014 and Kim et al (2012). In the same manner,…”

“…By taking into account above mentioned the non-dimensional parameters ξ and η, and introducing α ¼ a=b and S ¼ kGh=D, the following expressions are valid for the potential and kinetic energy of plate with length a and width b, having arbitrary edge constraints (Cho et al, 2013(Cho et al, , 2014Kim et al, 2012): …”

“…Mathematical models for dry natural vibration analyses of different plate systems based on the assumed mode method are considered in Cho et al (2013Cho et al ( , 2014 and Kim et al (2012). However, in order to present a self-contained paper, an outline of the procedure with some necessary adjustments is given here.…”

“…The assumed mode method is applied to analyse the natural response of bottom plates and stiffened panels in contact with fluid. Lateral displacement and angles of rotations can be expressed by superposing the products of the orthogonal polynomials (Cho et al, 2013(Cho et al, , 2014Kim et al, 2012) …”

“…Up to now, the assumed mode method using the characteristic polynomials of the Timoshenko beam (Chung et al, 1993) is successfully applied to the dry vibration analysis of rectangular plates and stiffened panels with arbitrary boundary conditions (Kim et al, 2012;Cho et al, 2013Cho et al, , 2014Cho et al, , 2015. This concept very similar the Rayleigh-Ritz method (Liew et al, 1995), but instead of minimizing the energy functional, it opts to apply Lagrange's equation of motion.…”