Goranka Štimac Rončević

This paper introduces an enhanced beam formulation for predicting the natural frequencies of thin-walled composite beam-type structures under initial loading. Each wall of the cross-section is idealized as a thin, symmetric, and balanced angle-ply laminate. The formulation is based on Hooke’s law and a geometrically nonlinear framework, taking into account restrained warping and large-rotation effects, respectively. Shear deformation effects are incorporated by applying the Timoshenko–Ehrenfest beam theory for bending and a modified Vlasov theory for nonuniform torsion. Coupling between transverse shear forces and warping-induced torsional moments arising from cross-sectional asymmetry is explicitly included. A consistent mass matrix, accounting for coupling between translational, rotational, and warping degrees of freedom, is derived using a kinetic-energy-based approach for the thin-walled beam element. Within the framework of Hamilton’s variational principle, the governing equations of the structure in global coordinates are formulated, and the associated eigenvalue problem is derived. The proposed formulation is validated through selected benchmark examples, demonstrating its effectiveness in predicting the natural frequencies of geometrically nonlinear, shear-deformable thin-walled beam and frame structures under initial loading.

In this paper, the dynamic response of a Euler–Bernoulli beam subjected to transverse harmonic forces is calculated. The method of separation of variables combined with the mode shape superposition method, which includes the determination of eigenvalues, is used to define the velocity field of the beam surface. The Rayleigh integral was used to calculate the sound radiation and the beam was placed in an infinite baffle. Additional actuators are introduced in order to minimize the sound radiation, or, more specifically, the total sound power level of the vibrating beam, and their optimal position and force amplitude are determined; the conclusions were drawn from the optimization results. This paper proposes a method for faster determination of the optimal actuator parameters in order to achieve the minimum total sound power level. The validity of the obtained results is demonstrated with examples, whose solutions are compared to the results in the published literature.

In this paper a mathematical model of a vehicle with four degrees of freedom i.e. half vehicle model and a procedure for modelling artificial bumps are described. The dimensions of the artificial bumps are prescribed by the Rulebook and depend on speed limits. To show the influence of additional cargo on vehicle movement when driving across artificial bumps, for the selected type of car, required numerical simulations are carried out. All numerical simulations are carried out in the Matlab/Simulink software package. The simulation results are presented in the table form, where the comparison of the maximum values of vehicle and wheel displacements and accelerations for three vehicle speeds (v = 20 km/h, v = 30 km/h and v = 50 km/h) and for two cases, i.e. without and with additional cargo, is given. Vertical and angular displacements and accelerations of the vehicle are also shown in the time domain for speeds 30 and 50 km/h.

This paper presents a comparison between two analytic methods for the determination of natural frequencies and mode shapes of Euler-Bernoulli beams. The subject under scrutiny is the problem of a beam supported by an arbitrary number of translational springs of varying stiffness, which is solved first by the method of Laplace transform and then by the Green’s function method. The two methods are compared on the level of algebraic equivalence of the resulting formulas and these are compared to the results obtained by FEM analysis for the case when the beam is supported with a single spring. It can be shown that both methods result in equivalent algebraic expressions, whose results are to be regarded as accurate for any given set of boundary conditions. This is also verified by means of FEM analysis, whose solutions converged to almost identical values. Hence, the two methods are found to be equally accurate for the calculation of natural frequencies and natural modes. This paper also brings a new formulation for the mode shape equation, obtained by the Laplace transform method, which to the best of the authors’ knowledge has not been reported in existing literature. Additional comments about the advantages and disadvantages of the two employed analytical methods are given from the standpoint of mathematical structure and practicality of implementation, which is also supplemented by a comment on the comparative advantages and disadvantages of FEM analysis.