Vibration of arbitrarily-shaped triangular plates with elastically restrained edges

Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method

Study on flexural vibration of triangular composite plates influenced by fibre orientation

Large amplitude free flexural vibrations of thin plates of arbitrary shape

FREE-VIBRATION ANALYSIS OF RIGHT TRIANGULAR PLATES WITH VARIABLE THICKNESS

Chapter 7 - Vibration Problems of Functionally Graded Triangular Plates

A simplified geometric stiffness in stability analysis of thin-walled structures by the finite element method

Free vibrations are analyzed for isotropic plates in the form of isosceles triangles. We deduce the formula for the evaluation of the frequencies of free vibrations for plates of regular triangular shape with free edges and compute the coefficients of vibration mode and boundary conditions. The frequencies and modes of free vibrations of the isotropic thin isosceles triangular plates with free edges and different apex angles are computed by the finite-element method.

In-plane modal studies of arbitrary laminated triangular plates with elastic boundary constraints by the Chebyshev-Ritz approach

Corner supported isosceles triangular orthotropic plates

This work investigates the effectiveness of a shape-memory alloy (SMA) in controlling the instabilities of triangular composite plates under supersonic flow. Lagoudas’ quadratic polynomial hardening theory models the SMA effect. First-order piston theory was used for the aerodynamic modeling, and the reference-temperature method was used for modeling the thermal heating. The buckling and post-buckling behaviors were studied for different boundary conditions with four different layups. In addition, buckling and post-buckling of the composite plate, with and without shape memory alloy wire, has been studied. The effect of SMA wire on aeroelastic instabilities is accurately studied. The embedded SMA wire significantly increased the stability region (postpone divergence and flutter velocities) and buckling temperature. Also, the time responses of the triangular composite plate are determined at different Mach numbers, showing that by increasing the Mach number, the SMA wire can control or decrease the vibration amplitudes.

In this paper, nonlinear vibration of a triangular shape plate, with several stiffeners, is studied. The governing equation of transversal deflection of the plate, with considering the effects of orthotropic characteristics and external excitation, is analyzed. The ordinary differential equation for the time response of the system, through employing the Galerkin method, is obtained; and the frequency response of the plate-shape structure — using the multiple scale method — is determined. A robust genetic-based multi-objective optimization technique is employed to optimize the system’s response by finding the optimum values of the geometry and locations of the plate’s stiffeners. The influence of various parameters on the optimization results is investigated. According to the results, the optimum design of the stiffeners leads to a better performance of the vibration response.

Free vibration of anti-symmetric angle-ply plates with variable thickness

In this paper, free vibration of Mindlin annular plate with arbitrary boundary conditions is investigated by an accurate solution method. The effects of the restrained stiffness of the springs on modal properties are incorporated in the current framework. The displacement components can be expressed as Fourier cosine series plus auxiliary polynomial functions, which aim to eliminate the discontinuities of displacement and its derivatives at both ends and to enhance the convergence of the results effectively. The current solution method can be used to general boundary conditions without changing the calculate method, which is different from the most existing studies. Numerical examples were presented and discussed for several different geometric and material properties as well as distinct boundary conditions.

Numerical Results and Discussion The numerical applications are carried out for cross-ply spherical shells whose geometrical and material properties are the same for all layers. The transverse deflection presented in the figures is evaluated at (*i,jc2, f) = (0, b/2, ?). Zero initial conditions are assumed. The variations of center deflection with time for antisymmetric cross-ply (0/90) and symmetric cross-ply (0/90/0) laminated spherical caps are shown in Figs. 1 and 2, respectively, for various boundary conditions. It is interesting to note that for SSSS, SSCS, and SSCC boundary conditions the amplitudes are smaller for symmetric cross-ply than for antisymmetric cross-ply laminates, whereas for SSFF, SSFS, and SSFC the amplitudes are higher. Moreover, the first-order (FSDT) and the third-order (HSDT) theories predict almost the same response, whereas the classical theory (CST) differs both in amplitude and phase.

The paper reports an algorithm to analytically solve one of the problems in the mechanics of elastic bodies, which is associated with studying the natural vibrations of a composite two-stage plate whose concave part is smoothly aligned with the part of a constant thickness. We have defined patterns for stating the boundary and transitional conditions, which should be taken into account when considering the natural vibrations of a two-stage plate.The ratios have been obtained, which make it possible to study the distribution of deflections and determine the values of amplitudes of the curved vibrations of the plate. It was noted that the modes of vibrations are based on the symmetry and factorization methods that we had developed and refined earlier. Specifically, it has been found that the deflections can be explored through expressions that are derived through the sum of relevant solutions to two linear second-order differential equations with variable coefficients.Based on the proposed approach, a system consisting of eight homogeneous algebraic equations has been defined, which allowed us to build a frequency equation for the plate rigidly fixed along the inner contour and free along the outer contour. We have determined the values for the plate’s natural frequencies for the first three modes of natural vibrations. Moreover, in order to verify and expand a set of plates of different configurations, the plates with two types of concave in their variable part have been considered. The new approaches and the ratios based on them could be useful for the further advancement of methods for solving similar problems in mathematical physics on natural values. A practical implementation is the problems about the vibrations of plates with variable thickness and of different modes