In this paper there is presented an experimental procedure used to determine the flexural rigidity for composite sandwich bars with polypropylene honeycomb core with various thickness values: 1, 1,5 and 2 cm. The composite bars will be reinforced with one layer of carbon fiber. The width value of the composite bars will be of 6 cm. In order to obtain the flexural rigidity the composite bars will be clamped at one end and left free at the other. An accelerometer will be placed at the free end used to record the free vibrations of these bars. The simplifying assumption of “bar” will be used in this research, so I have chosen several free lengths for the bars: 29, 32 and 35 cm. The eigenfrequency of the first eigenmode will be used to determine the flexural rigidity of the bars.
Tiago Silva, Maria Loja, Nuno Maia and Joaquim Barbosa
Elishakoff, I. and Pentaras, D. (2006). Apparently the first closed-form solution of inhomogeneous elastically restrained vibrating beams, Journal of Sound and Vibration 298(1-2): 439-445.
Grossi, R. and Albarracín, C. (2003). Eigenfrequencies of generally restrained beams, Journal of Applied Mathematics 2003(10): 503-516.
Kitayama, S., Arakawa, M. and Yamazaki, K. (2011). Differential evolution as the global optimization technique and its application to structural optimization, Applied Soft Computing 11(4): 3792-3803.
Cornel Haţiegan, Gilbert Rainer Gillich, Gheorghe Popovici and Luminita Haţiegan
The alysis of free vibrations on rectangular plates with mixed conditions of buckling in the thermal environment is carried out by means of the 3D elasticity theory. In this paper there has been analyzed by the finite element method (FEM), the mode shape and the eigen-frequencies for a rectangular plate clamped on the contour for different temperatures. In this analysis successive heat degrees have been used, this fact helping to find the critical values in which the frequencies were at zero and to correlate these temperatures with the values obtained from the static analysis The temperature rise, the material graded index and the geometrical parameters on the eigen-frequencies were studied.
Pavel Akishin, Andrejs Kovalovs and Evgeny Barkanov
An inverse technique, based on the planning of experiments and response surface methodology have been applied to determine elastic properties of unidirectional carbon fiber composite plate and carbon nanotubes reinforced aluminium plate.
The nuances of application of investigated technique for orthotropic material properties determination are considered on the example of a composite plate. In turn, possibility of using of this technique on specimens with small dimensions (80x60x2 mm) is checked up and estimated on an example of an isotropic nanocomposite plate.
The results obtained were verified by comparing the experimentally measured eigenfrequencies with numerical ones obtained by FEM using determinated elastic material properties.
The classical non-conservative Beck’s beam, loaded by follower compressive force, is generalized by allowing an arbitrary angle of action of the follower force as well as allowing for excentric positioning of the applied force. For the corresponding boundary eigenvalue problem, the frequency equation is derived. Results of parametric studies are presented with an emphasis laid on the lowest eigenfrequencies. The characteristic shape of the computed curves indicates whether stability loss by divergence or by flutter occurs. A map of stability is presented in terms of parameters describing the excentricity and the angle under which the follower force acts on the beam.
 Mikota, J. Compensators for the Attenuation of Fluid Flow Pulsations in Hy- draulic Systems, In: Selected Topics in Structronics and Mechatronic Systems, 2003, Eds. Belyaev A., Guran A., 49-81.
 Brun, M., G. F. Giaccu, A. B. Movchan, N. V. Movchan. Asymptotics of Eigenfrequencies in the Dynamic Response of Elongated Multi-structures. Proc. R. Soc. A, 468 (2012), No. 2138, 378-394. DOI: 10.1098/rspa.2011.0415.
 Dimarogonas, A. D., S. A. Paipetis, T. G. Chondros. Analytical Methods in
The main aim of this paper is to present a Stochastic Finite Element Method analysis with reference to principal design parameters of bridges for pedestrians: eigenfrequency and deflection of bridge span. They are considered with respect to random thickness of plates in boxed-section bridge platform, Young modulus of structural steel and static load resulting from crowd of pedestrians. The influence of the quality of the numerical model in the context of traditional FEM is shown also on the example of a simple steel shield. Steel structures with random parameters are discretized in exactly the same way as for the needs of traditional Finite Element Method. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable the determination of the structural response and, thanks to the Least Squares Method, its final probabilistic moments.
The main aim of this work is to verify an influence of the response function type in direct symbolic derivation of the probabilistic moments and coefficients of the structural state variables of axisymmetric spherical steel dome structures. The second purpose is to compare four various types of domes (ribbed, Schwedler, geodesic as well as diamatic) in the context of time-independent reliability assessment in the presence of an uncertainty in the structural steel Young modulus. We have considered various analytical response functions to approximate fundamental eigenfrequencies, critical load multiplier, global extreme vertical and horizontal displacements as well as local deformations. Particular values of the reliability indices calculated here can be of further assistance in the reliability assessment by comparing the minimal one with its counterpart given in the Eurocode depending upon the durability class, reference period and the given limit state type.
The paper deals with free and forced vibrations of a horizontal thin elastic plate submerged in an infinite layer of fluid of constant depth. In free vibrations, the pressure load on the plate results from assumed displacements of the plate. In forced vibrations, the fluid pressure is mainly induced by water waves arriving at the plate. In both cases, we have a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surface. At the same time, the pressure load on the plate depends on the gap between the plate and the fluid bottom. The motion of the plate is accompanied by the fluid motion. This leads to the so-called co-vibrating mass of fluid, which strongly changes the eigenfrequencies of the plate. In formulation of this problem, a linear theory of small deflections of the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation is constructed in the doubly connected infinite fluid domain. To this end, this infinite domain is divided into sub-domains of simple geometry, and the solution of the problem equation is constructed separately for each of these domains. Numerical experiments are conducted to illustrate the formulation developed in this paper.
The paper deals with free vibrations of a horizontal thin elastic circular plate submerged in an infinite layer of fluid of constant depth. The motion of the plate is accompanied by the fluid motion, and thus, the pressure load on this plate results from displacements of the plate in time. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the gap between the plate and the fluid bottom. In theoretical description of this phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. This coupling leads to the so-called co-vibrating (added) mass of fluid, which significantly changes the fundamental frequencies (eigenfrequencies) of the plate. In formulation of the problem, a linear theory of small deflections of the plate is employed. At the same time, one assumes the potential fluid motion with the potential function satisfying Laplace’s equation within the fluid domain and appropriate boundary conditions at fluid boundaries. In order to solve the problem, the infinite fluid domain is divided into sub-domains of simple geometry, and the solution of problem equations is constructed separately for each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.