| Abstrakt: |
The velocity amplitude of a thin, sperical shell can be rigorously described by a two-mesh electrical circuit, and a considerable amount of information can be obtained from this circuit without computations. The exact solutions for the radial and tangential velocity components for point excitation of the shell are represented by two oscillator terms with frequency-independent coefficients and are interpreted physically. It is proved that by confining the computations to resonance vibration (using only one generalized coordinate to represent the ''two-resonance-frequencies'' modes) the coefficients of the exact solution can be derived with the aid of the Hamilton principle. The resonance frequencies can be approximated with relatively high accuracy by a simple expression, and the mean-value solution and the envelopes through the resonance peaks and the anti-resonance minima are easily derived. The shell turns out to be very stiff at low frequencies; resonances occur only at relatively high frequencies, i.e., near and above the ring resonance frequency. As the frequency enters the resonance range, the shell becomes very soft but, with increasing frequency, it stiffens up again, and its impedance approaches that of an infinite plate of the same thickness. [ABSTRACT FROM AUTHOR] |
