Dynamic behavior of a rotating delaminated composite beam including rotary inertia and shear deformation effects

A finite element (FE) model is developed to study the free vibration of a rotating laminated composite beam with a single delamination. The rotary inertia and shear deformation effects, as well as the bending–extension, bending–twist and extension–twist coupling terms are taken into account in the FE model. Comparison between the numerical results of the present model and the results published in the literature verifies the validity of the present model. Furthermore, the effects of various parameters, such as delamination size and location, fiber orientation, hub radius, material anisotropy and rotating speed, on the vibration of the beam are studied in detail. These results provide useful information in the study of the free vibration of rotating delaminated composite beams

Energy harvesting from bridge vibrations with piezoelectric devices - A feasibility study

We present a feasibility study on the use of piezoelectric devices to harvest the energy connected to the vibrations induced on road bridges by travelling vehicles. We have selected an existing urban bridge as case study and collected the available documentation about its original design. Furthermore, the results of a past experimental campaign on the bridge have provided experimental evidence about the natural frequencies and mode shapes of the structure. Next, we have set up a three-dimensional finite element model of the bridge, which is currently being calibrated to match the results of the experimental dynamic analysis. Besides, we have developed a mechanical model of a laminated cantilever beam with a top piezoelectric layer and a concentrated mass on its free end. Our model applies to laminated beams with general (asymmetric) stacking sequences, thus representing an extension of similar models of the literature. The partial differential equation of motion has been determined and solved in the case of free vibrations under both open- and short-circuit electrical boundary conditions. As a numerical example, a piezoelectric cantilever beam has been designed with the same first natural frequency of the case study bridge

Forced Vibration Analysis of Laminated Composite Plates under the Action of a Moving Vehicle

This paper provides a finite element analysis of laminated composite plates under the action of a moving vehicle. The vehicle is modeled as a rigid body with four suspension systems, each consisting of a spring-dashpot. Overall, the vehicle possesses three degrees of freedom: vertical, rolling, and pitching motions. The equations of motion of the plate are deduced based on first-order shear deformation theory. Using the Euler-Lagrange equations, the system of coupled equations of motion is extracted and solved by using the Newmark time discretization scheme. The algorithm is validated through the comparison of both the free and forced vibration results provided by the present model and exact or numerical results reported in the literature. The effects are investigated of several system parameters on the dynamic response. &nbsp

Free vibration analysis of rectangular sandwich plates with compressible core and various boundary conditions

Extended higher-order sandwich plate theory is used to analyze the free vibrations of rectangular sandwich plates with compressible core. Accordingly, first-order shear deformation theory is used to model the laminated face sheets. Besides, the in-plane and transverse displacements of the core are assumed to be cubic and quadratic functions of the thickness coordinate, respectively. To deduce the governing equations, Hamilton’s principle is used. Then, based on the Rayleigh-Ritz method, single series expansions with two-variable orthogonal polynomials – namely, the orthogonal plate functions – are considered to approximate the displacement components. Lastly, a generalized eigenvalue problem is solved to obtain the free vibrational characteristics of sandwich plates with both symmetric and anti-symmetric lay-ups subjected to various boundary conditions. The method is validated against the results obtained by different methods in the literature. Finally, the effects of the plate side-to-thickness ratio, in-plane aspect ratio, and core-to-face sheets thickness ratio on the natural frequencies are discussed

Free Vibration Analysis of Laminated Composite Plates with Arbitrary Shape

In this paper, the undamped free vibration analysis of arbitrary shaped laminated composite plates with general stacking sequences is conducted based on the first-order shear defor-mation theory. The finite element method is used to obtain the plate's vibrational characteris-tics by introducing a six-nodded triangular element, i.e., natural frequencies and the corre-sponding mode shapes. The element considered is a higher-order triangular element. Each node includes five degrees of freedom. Gaussian numerical integration is used to calculate the mass and stiffness matrices. The whole solution method is implemented within the MATLAB. The convergence of the results has been investigated, and results have been com-pared against some available data in the literature and also commercial software ANSYS in which three-dimensional analysis is used. Excellent agreements have been observed. The ef-fects of several parameters – such as boundary conditions, geometry, and lay-ups – on the natural frequencies are studied in detail

Dynamic analysis of generally laminated composite beam with a delamination based on a higher-order shear deformable theory

Abstract In this study, the dynamic response of the laminated composite beam with arbitrary lay-ups has been investigated within the framework of the third-order shear deformation theory using the finite element method. A new three-nodded finite element compliant with the theory is introduced next. To deal with the dynamic contact between the delaminated segments, unilateral contact constraints are employed in conjunction with Lagrange multiplier method. Furthermore, the Poisson's effect is incorporated in the formulation of the beam constitutive equation. Also, the higher-order inertia effects and material couplings (flexure-tensile, flexure-twist and tensile-twist couplings) are considered in the formulation. Results are extracted based on two methods namely the Eigen-value techniques for frequencies and the Newmark method to calculate the transient response. Then, the obtained results have been verified with the other results available in the literature and very good agreements have been observed. Furthermore, the new results have been obtained for the case where the excitation was due to a moving/non-moving force

Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology

Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology

A new solution method for free vibration analysis of rectangular laminated composite plates with general stacking sequences and edge restraints

A method is presented to study the free vibrations of rectangular laminated composite plates with general layups and arbitrary boundary conditions. Based on the first-order shear deformation theory, the governing differential equations and boundary conditions are deduced via Hamilton's principle. Generalised displacements are expanded as series with Legendre polynomials as the base functions. A generalised eigenvalue problem is obtained by following a variational approach, where energy functional is extremised and boundary conditions are introduced by means of Lagrange multipliers. In order to overcome some difficulties in obtaining the natural frequencies and corresponding mode shapes, a new numerical strategy is proposed

Free vibration analysis of a laminated composite sandwich plate with compressible core placed at the bottom of a tank filled with fluid

The paper addresses the free vibration problem of a laminated composite sandwich plate with compressible core, placed at the bottom of a tank filled in with fluid. The analysis is performed based on the extended higher order sandwich plate theory (EHSAPT). First-order shear deformation theory (FSDT) is used for the face sheets. Cubic and quadratic polynomials are used to describe the in-plane and transverse displacements of the core, respectively. The fluid is assumed inviscid, incompressible, and irrotational. To obtain the kinetic energy of the fluid, its velocity potential is expressed by using the compatibility and boundary conditions. The governing differential equations and corresponding boundary conditions are derived from Hamilton’s principle. A single series expansion is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. The natural frequencies of the coupled sandwich plate-fluid system are calculated by using the Rayleigh-Ritz method. Convergence of the adopted strategy is first investigated. Then, comparisons are conducted with previous results reported in the literature. Also, the effects are investigated of several parameters, such as the plate side-to-thickness ratio, the core-to-face sheets thickness ratio, the face sheet-to-core flexural modulus ratio, the height and aspect ratio of the tank