LAUSR

Abstract A semi-analytical approach to understand the manifestation of plate modeshapes associated with twin frequencies has been presented. Square Mindlin’s plate, clamped on all sides, has been considered here. It highlights the importance of efficacy of the beam-wise trial functions in an energy-based plate vibration analysis method, in terms of (a) accuracy, (b) orthogonality, (c) sense (plus/minus) and (d) interference. The inconsistency in the modeshapes of repeated frequencies, seen extensively in literature, has been attempted to be removed, through superior closed-form orthogonal set of Timoshenko admissible functions into the Rayleigh-Ritz method. The constructive/destructive interferences of the admissible functions, which are the products of the beam-wise modeshapes, give the final nodal patterns and the prominence of the anti-nodes. Also, the pairs of ‘very close’ but distinct frequencies, which were often considered as ‘numerical errors’, have been counter-intuitively justified through their Eigenvectors, which are either symmetric or skew-symmetric in the matrix form. Nodal patterns for CCCC plate modeshapes are accurately investigated; i.e. chess-board and diagonal nodal patterns.