Tham khảo tài liệu 'wave propagation 2011 part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A Multiplicative Method and A Correlation Method for Acoustic Testing of Large-Size Compact Concrete Building Constructions 315 u 1 i u2 e 3 where u1 wmax cos and 2 u . sm . Similarly the force vector can be represented as u F1 ifr 4 Substituting 3 and 4 into 1 we obtain K - Q2 M iQ C u i 2 F1 i F2 5 Note that for forced vibrations this equation does not include the time t only stationary vibrations are considered in the modal analysis . The solution of Eq. 5 allows calculation of the displacement amplitude of each element of the model at the current frequency of the driving force. Multiple solution of this equation for each frequency in the range of interest makes it possible to construct the spectral characteristic of forced vibrations of the model in this frequency range for the element of interest. To date several software packages allowing FEM-based computer calculations have become widespread. In this study the FEM calculations were performed according to the ANSYS program with the Multiphysics package Chigarev . Kravchuk . Smalyuk . 2o04 Kaplun . Morozov . Olfer eva . 2003 Basov . 2002 . The ANSYS graphical environment facilitates constructing a 3D model specifying the material properties and the boundary conditions and visualizing the calculation results. In this study the ANSYS package was used to calculate the spectra of free and forced vibrations in concrete articles with different shapes. The calculation of the spectra of free and forced vibrations for a thin rod similar to that considered above is presented below and is intended for primary verification of the simulation results. The simulation procedure consists of several stages. A geometrical model of the rod is created a cylinder with a diameter d m and a length l m Fig. 8a . The elastic properties of the material are specified the density p 2400 kg m3 the Young modulus E N m2 and the Poisson ratio Ơ . A grid is imposed on the geometrical model. In this .
