scholarly journals MODAL ANALYSIS OF REINFORCED CONCRETE AND FIBER CONCRETE BEAMS

2021 ◽  
Vol 3 (1) ◽  
pp. 95-105
Author(s):  
T. Makovkina ◽  
◽  
M. Surianinov ◽  
O. Chuchmai ◽  
◽  
...  

Analytical, experimental and numerical results of determination of natural frequencies and forms of oscillations of reinforced concrete and fiber concrete beams are given. Modern analytical, numerical and experimental methods of studying the dynamics of reinforced concrete and fiber concrete beams are analyzed. The problem of determining the natural frequencies and forms of oscillations of reinforced concrete and fiber concrete beams at the initial modulus of elasticity and taking into account the nonlinear diagram of deformation of materials is solved analytically. Computer modeling of the considered constructions in four software complexes is done and the technique of their modal analysis on the basis of the finite element method is developed. Experimental researches of free oscillations of the considered designs and the comparative analysis of all received results are carried out. It is established that all involved complexes determine the imaginary frequency and imaginary form of oscillations. The frequency spectrum calculated by the finite element method is approximately 4% lower than that calculated analytically; the results of the calculation in SOFiSTiK differ by 2% from the results obtained in the PC LIRA; the discrepancy with the experimental data reaches 20%, and all frequencies calculated experimentally, greater than the frequencies calculated analytically or by the finite element method. This rather significant discrepancy is explained, according to the authors, by the incorrectness of the used dynamic model of the reinforced beam. The classical dynamics of structures is known to be based on the theory of linear differential equations, and the oscillations of structures are considered in relation to the unstressed initial state. It is obvious that in the study of free and forced oscillations of reinforced concrete building structures such an approach is unsuitable because they are physically nonlinear systems. The concept of determining the nonlinear terms of these equations is practically not studied. Numerous experimental researches and computer modeling for the purpose of qualitative and quantitative detection of all factors influencing a spectrum of natural frequencies of fluctuations are necessary here.

Author(s):  
J. Poirier ◽  
P. Radziszewski

The natural frequencies of circular saws limit the operating speeds of the saws. Current industry methods of increasing natural frequency include pretensioning, where plastic deformation is induced into the saw. To better model the saw, the finite element model is compared to current software for steel saws; C-SAW, a software program that calculates frequencies for stiffened circular saws. Using C-SAW and the finite element method the results are compared and the finite element method is validated for steel saws.


1995 ◽  
Vol 1 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Jamal A. Masad

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.


1966 ◽  
Vol 1 (3) ◽  
pp. 223-230 ◽  
Author(s):  
D. J. Dawe

The finite element method is applied to the calculation of the deflection under a uniformly distributed load and the natural frequencies of the rhombic cantilever plate. This has required the derivation of stiffness and inertia matrices for a plate element of parallelogrammic planform. Although, in common with the work of past investigators, the accuracy of the results decreases with increase in skew angle it is shown that the method is adequate for angles up to about 45°.


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