Study on the multi-mode response of continuous systems

Nonlinear forced oscillations of continuous systems such as strings, membranes and beams are considered. These systems have an infinite number of natural frequencies and an infinite number of corresponding natural modes. Under some conditions, some of these modes may interact with each other, and so-called multimode responses may occur. To see whether any particular types of multi-mode responses in fact occur and what their characteristics are, the oscillations induced by a periodic excitation near primary resonance points are discussed. The first system discussed is a string. Its natural frequencies are in a ratio of prime integers. Due to this, oscillations containing several subharmonic or super-harmonic components occur. Thus it is shown that a type of multi-mode response occurs. The second system is a circular membrane. In this system, two modes exist in pairs with the same natural frequency and the same modal shape but are shifted circumferentially. Due to this, oscillations of rotary type occur. The third system is a square membrane. As in the circular membrane, oscillations of rotary type occur. Thus, in circular and square membranes another type of multi-mode response occurs.