Bending Vibrations of Beams Coupled by a Double Spring–mass System

Dynamic Responses of Two Beams Connected by a Spring-Mass Device

“…The system parameters are: Lengths L 1 = L 2 = 0.4m, spring connection positions L 1,1 = L 2,1 = 0.2m, cross sections of beams are square with width and height b = h = 0.0095m, tip masses M 1 = M 2 = 0.5658Kg, attached mass M = 0.2829Kg, spring stiffness K 1,1 = K 2,1 = 2.1943 × 10 6 N/m, material density ρ 1 = ρ 2 = 7,840Kg/m 3 and Young's modulus E 1 = E 2 = 2.069 × 10 11 N/m 2 . These parameters match the non-dimensional parameters as in reference [14]: x 1,1 = x 2,1 = 0.5, k 1,1 = k 2,1 = 1000.0, m 1 = m 2 = 2.0, m = 1.0 and K r = 1.0. Table 1 shows the comparisons of the non-dimensional frequency parameters obtained in this article and the reference [14].…”

“…First is the case of two cantilever beams with tip masses coupled with a spring-mass system as in reference [14]. The system parameters are: Lengths L 1 = L 2 = 0.4m, spring connection positions L 1,1 = L 2,1 = 0.2m, cross sections of beams are square with width and height b = h = 0.0095m, tip masses M 1 = M 2 = 0.5658Kg, attached mass M = 0.2829Kg, spring stiffness K 1,1 = K 2,1 = 2.1943 × 10 6 N/m, material density ρ 1 = ρ 2 = 7,840Kg/m 3 and Young's modulus E 1 = E 2 = 2.069 × 10 11 N/m 2 .…”

“…Considering the compatibility requirements across each spring connection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Gurgoze et al [14] solved this system and obtained the solutions from a 13 × 13 determinant matrix. Although it leaded to the exact solution, its scheme was highly numerically intensive, since the dimensional size of the characteristic determinant obtained is relatively high.…”

“…Gurgoze et al [14] treated the bending vibration of beams coupled by a double spring-mass system. Inceoglu and Gurgoze [15] also considered similar problems in beams coupled by several double spring-mass systems.…”

Vibration of two beams connected by nonlinear isolators: analytical and experimental study

“…Vu et al, and Oniszczuk discussed the vibration mode and forced response of two beams with a viscoelastic layer in between separately [7][8][9]. Gurgoze et al, and Inceoglu et al, solved the forced response of two beams coupled by one or several double spring-mass systems [10,11]. Tu and Zheng discussed the new problems and questions associated with the flexible structure vibration isolation in the modal space [12].…”