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Engineering Analysis with Ansys Software Episode 1 Part 9

Tham khảo tài liệu 'engineering analysis with ansys software episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 144 Chapter 4 Mode analysis Figure 4.1 FEM element types a beam element b shell element and c solid element. 4.2 mode ana lysis of a straight bar 4.2.1 Problem description MO.A H . Obtain the lowest three vibration modes and resonant frequencies in the y direction ofthestraight steel bar shownin Figure 4.2. t 5 mm Cross section 10 mm 100 . I X mm Figure 4.2 Cantilever beam for mode analysis. Thickness of the bar is 0.005 m width is 0.01 m and the length is 0.09 m. Material of the bar is steel with Young s modulus E 206 GPa and Poisson s ratio 1 0.3. Density p 7.8xl03kg m3. Boundary condition All froedomsare gonstrainedattSle77end. 4.2.2 Analytical solution Before mode analysis is attempted using ANSYS program an analytical solution for resonrntfrnauenciee wiUWeebtained to confirm the validity of ANSYS solution. The analytical solution of resonant frequencies for a cantilever beam in y direction is given by st Ẽ0 . t Ág t7 ơ i 2 n . . 4.ir 2.V - V M where length of the cantilever beam L 0.09 m cross-section area of the cantilever beam A 5 X IQ-5 m2 and Young s modulus E 206 GPa. 4.2 Mode analysis of a straight bar 145 The area moment of inertia of the cross-section of the beam is I bt3 i2 0.01 X 0.0053 12 1.042 X 10-1 m4 Mass per unis width M sML L sM 7.8xio3 - s kg m Ấ1 1.875 Ấ2 4.694 À3 7.855. For that sea ofdaSa the following m a -- are a ained 5125 H5fd 3222 mz and f3 8994 Hz. Figure 4.3 shows the vibration modeaand tire jwsitions 0 nodes obtained by Equation 4.1 . Í 1 i 2 i 3 0.868 L Figure 4.3 Analytical vibration mode and the node position. 4q Q __ _ _ .Z.J Model for finite-element analysis 4.2.3.1 Element type selection In FEM analysis it is very important to select a proper element type which influences the accuracyof solution woolóng time foomodel construction and CPU time. In this example the two-dimensional elastic beam as shown in Figure 4.4 is selected for the following reaorn a Vibrati.n models constrained in thetwofoimonsiooal .