Vibration of Rectangular Plates Using Plate Characteristic Functions as Shape Functions in the Rayleigh–ritz Method

Modal Vibration Damping of Anisotropic FRP Laminates Using the Rayleigh–ritz Energy Minimization Scheme

“…Bernoulli-Euler-type beam functions [16] have been a popular choice for these functions, although improvement in the results have been reported by using Timoshenko beam equations (for Mindlin plates) [17,18], orthogonal polynomials [19] and plate functions [20]. Minimizing the total energy of the system with respect to the coefficients would form the eigenvalue problem, the solution of which would yield the frequencies and the unknown coefficients.…”

Ritz Vector Approach for Static and Dynamic Analysis of Plates With Edge Beams

“…Several mathematical functions have been proposed as Ritz vectors by various researchers for idealized boundary conditions [11][12][13][14][15]. In this paper, we use simple and easy-to-use mathematical functions given by Blevins [11].…”

Simplified analytical methods for the crashworthiness and the seismic design of lock gates

“…A brief literature review shows that a classical approach to overcome this problem is to express Δ !W, X" as a linear combination of admissible predefined functions. For example, this procedure was followed by Rajalingham et al [132] to get the vibration modes of a dry rectangular plate with clamped edges 11 . Another application was made by Liew and Wang [101], who studied the vibrations of plates with curved boundaries or reentrant corners.…”

“…!W, X, S", developing (7.43) leads to the following classical expression: which is widely used in the literature (see references [90], [100], [101] and [132], amongst others). For the particular case of modal displacements, since Δ !W, X" is an eigenfunction minimizing the Rayleigh quotient and .…”