This article presents an analysis of forced vibrations of a homogeneous cantilever beam using a vision method. Based on measurements, displacements of defined beam points have been determined as a function of time in directions perpendicular to and along the beam axis together with the trajectory of these points in the plane of the beam transverse vibrations. A model describing the displacement of the beam with a moving holder (kinematic excitation) is presented along with formulas defining motion of points in the plane of the beam transverse vibrations, which have been verified experimentally by recording beam vibrations using a specialised vision system.
The study investigates the behaviour of three-layered cantilever sandwich beams filled with magnetorheological fluids (MRFs) differing in the iron particle content by volume. Outer layers are made of aluminium, the space between them is sealed with silicone rubber. Two types of beams are considered: fully filled beams and partially filled beams, subjected to the magnetic field. The aim of the study is to determine stiffness and damping characteristics in relation to the magnetic field strength and the actual location where the magnetic field acts upon the beam. For this purpose, measurements have been taken of the beam free vibration response for various magnetic field strength levels and for various positions of the electromagnet located along the beam axis. Basing on the developed measurement data processing algorithm, the influence of the vibration amplitude on the natural frequency and a dimensionless damping coefficient have been determined. Finally, the equivalent natural frequency and the dimensionless damping coefficient have been derived accordingly, and the stiffness and damping ratio have been determined in function of the magnetic field strength, the electromagnet position and the MRF iron particle content by volume.
The paper presents the procedure of identification of a complex shear modulus which describes properties of MR fluid in the pre-yield regime as a function of magnetic field. Data necessary for identification were collected basing on measurements of free vibrations of a three-layered cantilever beam at a special laboratory stand. Magnetic field exerting on MR fluid placed in the beam was generated by electromagnet. In the next step, complex modes of beam vibrations for various places of applying the magnetic field and its strength were calculated.
The paper presents the finite element, which can be used to analyse the vibration of a three–layer beam with magnetorheological (MR) fluid layer. The MR fluid layer was sealed with silicone rubber. On the basis of the analysis of displacements, deformations of each layer has been established. Next, potential and kinetic energy of the three–layer beam were calculated. Because of the complexity of the beam with MR fluid, efficient solutions can be obtained only after discretization of the system. The finite element method was used in the study. For this purpose the mass and stiffness matrices were determined for the proposed linear finite element of two nodes and four degrees of freedom in each node.
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