A new type of solution for plate vibrations at low frequencies

✍ Scribed by S. Ljunggren

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 584 KB
• Volume: 116
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(87)81324-x

✦ Synopsis

A new analytical solution is derived for the out-of-plane motion of an infinite plate. The plate is of uniform thickness and consists of a material that is isotropic, homogeneous and linearly elastic. The excitation is harmonic in time and space. The new solution is obtained as an asymptotic expression of a general solution and is valid for low frequencies down to the static case. However, in contrast to the corresponding solutions of the classical plate equations, it is valid only for relatively large wave numbers. It is shown that the new solution describes the stiffness of the plate in a transitional region. In the case of comparatively small wave numbers, the new solution turns into the solutions of the classical plate equations and in the case of large wave numbers into Lamb's solution for forced Rayleigh waves. The new solution also shows that two sets of free waves exist beside the usual bending and quasi-longitudinal waves. The practical significance is demonstrated by some examples from the field of building acoustics.