The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamilton's principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those obtained using the finite element method, with values of particular cases of the model available in the literature, and with measurements in an experimental device. 1. Introduction The study of the dynamic properties of beam systems is very important in structural design as they are the cornerstone for many resistant structures. The issue is relevant virtually in all fields of engineering: structures composed of beams can resist by virtue of its geometry. Such structures can be found from large scale, such as bridges and buildings located in seismically active regions to microbeam systems used in modern electronic equipment which is subject to vibration environment. As Laura and his coworkers pointed out [1], many excellent books and technical papers deal with vibrating beam systems, including [2–6]. Many researchers have analyzed the vibration of beam systems. Reference [1] dealt with the determination of the fundamental frequency of vibration of a frame elastically restrained against translation and rotation at the ends, carrying concentrated masses. Reference [7] proposed a hybrid analytical/numerical method to do dynamic analysis of planar serial-frame structures. Reference [8] presented an elastic- and rigid-combined beam element to determine the dynamic characteristics of a two-dimensional frame composed of any number of beam segments. In his paper, Mei [6] considered the vibration in multistory planar beam structures from the wave vibration standpoint. Reference [9] analyzed in-plane vibrations of portal frames with elastically restrained ends. An approximate solution is
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