The Effects Of Large Vibration Amplitudes On The Mode Shapes And Natural Frequencies Of Thin Elastic Structures, Part III: Fully Clamped Rectangular Isotropic Plates—Measurements Of The Mode Shape Amplitude Dependence And The Spatial Distribution Of Harmonic Distortion

Asymmetric non-linear forced vibrations of free-edge circular plates. Part II: experiments

“…[18] and studied in Ref. [19] the presence of a second harmonic in their measurements, and did not find a theoretical explanation for this. A number of conjectures can be made in attempting to explain this phenomenon.…”

“…The result is that the natural linear modes mix with one to another and give non-linear modes, whose shapes are slightly dependent on the deflection amplitude [23]. This effect seems to be significant only at large deflection amplitude [19], larger than the plate thickness, and does not change the quantitative behaviour of the system.…”

Geometrically Nonlinear Free Axisymmetric Vibrations Analysis of Thin Circular Functionally Graded Plates Using Iterative and Explicit Analytical Solution

“…This method does not require a very good initial estimate of the solution or a step procedure, similar to other methods described for beams and rectangular plates. [20][21][22][23] It was adopted here to ensure rapid convergence when varying the amplitude, which allowed solutions to be obtained with a quite reasonable number of iterations. The fundamental nonlinear mode shape was calculated in the neighborhood of the linear solution corresponding to a small numerical value of the coefficient a r0 (r 0 = 1) of the basic function w * r0 .…”

“…16,20,21,23 For the first nonlinear mode shape, the range of validity of this assumption has been discussed in the light of the experimental and numerical results obtained for the nonlinear frequency-amplitude dependence and the nonlinear bending stress estimates obtained at large vibration amplitude. 20,22 In order to examine the effects of large vibration amplitudes on the membrane stress patterns for clamped circular plates, the contribution of the in-plane displacement U should be taken into account in the membrane strain expression. The assumption introduced above leads to…”

“…Previous studies [20][21][22][23] have shown that the nonlinear mode shapes of beam-and plate-like structures are amplitude dependent. This effect is illustrated in the present case in Fig.…”