Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 63

All structural systems such as beams, columns, and plates are continuous systems with an infinite number of degrees of freedom. Consequently, a continuous system has an infinite number of natural frequencies and corresponding mode shapes. Although easier, modeling a structure using a finite number of degrees of freedom provides just an approximation of the behavior of the system. The analysis of continuous systems requires the solution of partial differential equations. However, analytical solutions to partial differential equations are often difficult to obtain and numerical or approximate methods are usually employed to analyze continuous systems in particular at high frequencies. However, flexural vibration of some common structural elements can be analytically studied. Sound radiation can be produced by the vibration of these structural elements. Such is the case of the vibration of thin beams, thin plates and thin cylindrical shells that will be discussed in the following sections.