The eigenstructure assignment technique is applied for the vibration control of a clamped/clamped beam to change the eigenfrequencies, damping values and mode shapes so as to agree with prespecified values. Experimental results show that damping can be increased, vibration amplitudes of selected points...
The modal mass for a simply-supported beam is derived by evaluating the square of the mode shape function given in Eq. (1) and is∫0Lψmψndx=L/2form=n,=0form≠n.This integral involving sine functions can be found in most mathematical handbook of integrals. The modal-mass is then ...
Figure1presents a schematic diagram of the micro-force sensor microprinted on the single mode fiber (SMF) end face using TPP. A pair of polymer bases, with lengths of 20 μm, widths of 20 um, and heights of 30 um, were designed to support and connect the clamped beam. The cla...
mode shapesrectangular platesFEMThe 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...
The microbeam deflection can be approximated as follows: Xn wðx; tÞ ¼ ϕiðxÞuiðtÞ i¼1 ð8Þ where ϕi(x) is selected to be the ith undamped, unforced and linear orthonormal clamped–clamped beam mode shape; ui(t) is the ith modal coordinate; and n is ...
where ϕi(x) is selected to be the ith undamped, unforced and linear orthonormal clamped–clamped beam mode shape; ui(t) is the ith modal coordinate; and n is the number of assumed modes. To determine the mode shape functions ϕ(x), we can solve the eigenvalue problem as follows:...
The axial displacements are approximated with the first vibration mode clamped-camped beam functions. The ordinary trigonometric series are employed to represent the displacements in hoop direction. The buckling problem is reduced to the calculation of the minimum eigenvalue for the homogeneous system of...
beam mode shapesExperimental eigenvalues of both square and rectangular clamped flat plates were measured using digital spectrum analysis. Individual mode shapes were recorded experimentally using holographic interferometry. Plate spectra showing the first 35 modes of vibration for each of the square and ...
(3) Double-clamped beam According to §2.2, the displacement function of a double-clamped beam is: (2.95)w(x)=cx2(L−x)2 where L is the length of the beam. By substituting Eq. (2.95) into Eq. (2.87), we find: ω12=4∫0LIE(L2−6Lx+6x2)2dx∫0Lρbhx4(L−x)4dx=504...
2, 2000 Free Vibration Analysis of Angle-Ply Laminated Circular Cylindrical Shells with Clamped Edges length on the natural frequencies and mode shapes of the angle-ply laminated cylindrical shell with clamped edges are investigated numerically and experimentally. A simple approximate frequency equation wi...