Dynamic stiffness elements for free vibration analysis of rectangular Mindlin plate assemblies

Slobodne Vibracije Pravougaonih Izotropnih Višeslojnih Ploča Primenom Metode Dinamičke Krutosti

“…The amplitudes of the transverse displacement, the boundary layer function, as well as the rotations of a rectangular plate element can be presented as a sum of four symmetry contributions: symmetric-symmetric (SS), symmetric -anti-symmetric (SA), antisymmetric -symmetric (AS) and anti-symmetric -anti-symmetric (AA) [26]. Following the procedure given in [22,23], the deflections ˆ( , , ) w x y  , the rotations ˆ( , , ) y xy  andˆ( , , ) x xy  , the forces and moments in all symmetry contributions can be obtained. Then, the corresponding displacement and the force vectors (q and Q ) that contain displacements and forces on the boundaries x=a and y=b are obtained for all symmetry contributions.…”

“…Then, the corresponding displacement and the force vectors (q and Q ) that contain displacements and forces on the boundaries x=a and y=b are obtained for all symmetry contributions. Using the Projection method [27,28] as shown in [21][22][23] (9) where IJ D K is the dynamic stiffness matrix for considered symmetry contribution. The details regarding the SS case are givein in [22,23] .…”

“…However, the main lack of the proposed methods is the inapplicability to the plates having arbitrary combinations of boundary conditions. This has been overcome in the authors' investigations [21][22][23], where the dynamic stiffness matrices for a completely free rectangular isotropic plate based on the Mindlin-Reissner's first-order shear deformation theory (FSDT) and the Reddy's higher-order shear deformation theory (HSDT) were developed. These solutions are free of restrictions regarding the boundary conditions.…”

Dynamic stiffness method in the vibration analysis of circular cylindrical shell

“…Ovaj metod se naziva metod superpozicije i korišćen je, uz metod projekcije kojim su diskretizovani granični uslovi, za izvođenje dinamičke matrice krutosti pravougaone ploče po Kirchhoff-oj teoriji [8]. Primenom metoda superpozicije i metoda projekcije formulisana je i dinamička matrica krutosti pravougaone ploče za naprezanje u ravni [9], za poprečne vibracije po Mindlinovoj teoriji [10], kao i za poprečne vibracije slojevite ploče primenom smičuće teorije višeg reda [11].…”

“…Casimir [8] used the method of superposition, along with the method of projection for discretization of boundary conditions, and derived dynamic stiffness matrix of a rectangular Kirchhoff plate [8]. In the same manner, continuous rectangular plate elements for the in-plane vibration [9], transverse vibration according to the Mindlin plate theory [10] and transverse vibration of a laminated plate using the higher-order shear deformation theory [11] have been formulated, as well.…”