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The circumferential flexural modes (CFMs) are investigated.
Compatible polynomial variations of the radial and circumferential flexural rigidities are introduced.
When an initial radial breathing mode (RBM) vibration with sufficiently high velocity is imposed to a nanoring, circumferential flexural modes (CFMs) can be excited after a period of RBM-dominated vibration.
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The resulting dynamical model involves two degrees of freedom, representing the vibration amplitudes of two in-plane flexural modes with the same circumferential wavenumber.
Results show that the circumferential modulus provides a major portion of the flexural energy of the vibrating structure while the longitudinal and in-plane shear moduli contribute mostly to the stretching energy.
In the passive periodic shell, two pivotal frequencies (i.e., the cut-off frequency of the periodic shell, and the resonant frequency of flexural vibration of shell ring), which are existed in an arbitrarily high circumferential mode, are found; the frequency range is divided into three regions by these two frequencies.
Using Fourier expansions in the circumferential direction and power series expansions in the radial direction, equations of motion are obtained for longitudinal, torsional, flexural and higher order motion to arbitrary Fourier and power orders.
The problem is treated by first obtaining the exact solution for flexural waves in the annular sector plate by satisfying the flexural equation of motion for the plate with the circumferential edges free.
The lumbar circumferential L3L5 fusion was complete.
They are as follows: the axisymmetric wave motion,n= 0; the flexural or beam-type wave motion,n= 1; the lobar wave motion,n= 2; finally the wave motion with higher circumferential wavenumbers,ngreater than 2. Exact solutions have been found for waves travelling in thick orthotropic shells.
Circumferential pressure from a mug rim unstoppers the device, releasing its contents.
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CEO of Professional Science Editing for Scientists @ prosciediting.com