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Formulas For Natural Frequency And Mode Shape

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New exact solutions for free vibrations of thin orthotropic rectangular plates

Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression

This paper presents a generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates. We exploit a higher-order shear deformation theory in each layer such that the continuity of the displacement and transverse shear stresses at the layer interfaces is ensured. Thanks for enforcing the continuity of the displacement and transverse shear stresses at an inner-laminar layer, the minimum number of variables is retained from the present theory in comparison with other layerwise theories. The method requires only five variables, the same as what obtained from the first- and higher-order shear deformation theories. In comparison with the shear deformation theories based on the equivalent single layer, the present theory is capable of producing a higher accuracy for inner-laminar layer shear stresses. The free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plate are fulfilled without any shear correction factors. The discrete system equations are derived from the Galerkin weak form, and the solution is obtained by isogeometric analysis (IGA). The discrete form requires the C1 continuity of the transverse displacement, and hence NURBS basis functions in IGA naturally ensure this condition. The laminated composite and sandwich plates with various geometries, aspect ratios, stiffness ratios and boundary conditions are studied. The obtained results are compared with the 3D elasticity solution, the analytical as well as numerical solutions based on various plate theories.

A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis

Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration

Axisymmetric vibrations of solid circular and annular membranes with continuously varying density

Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

Formulas for structural dynamics

In the present paper the Differential Quadrature Method, DQM, and the domain decomposition are used to carry out the free transverse vibration analysis of non-uniform multi-span rotating Timoshenko beams with perfect and not perfect boundary conditions. The cross section could vary in a continuous or discontinuous fashion along the beam length. The material of the beam could be different in each beam span. The influence of elastically clamped boundary conditions at hub end are studied and discussed. The effect of an arbitrary hub radius is considered. The governing differential equations of motion for rotating Timoshenko beams come from the derivation of Hamilton’s principle. The first six natural frequencies of vibration are obtained for many particular situations and for some of them the mode shapes are also available. The examples of applications of the method indicated its effectiveness. The results for particular cases are in excellent agreement with published results and results obtained by means of the finite element method.

Transverse free vibration of non uniform rotating Timoshenko beams with elastically clamped boundary conditions

Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications

Diana Virginia Bambill

Papers

Axisymmetric vibrations of solid circular and annular membranes with continuously varying density

Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

Formulas for structural dynamics

Transverse free vibration of non uniform rotating Timoshenko beams with elastically clamped boundary conditions

Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications