A unified solution for vibration analysis of laminated functionally graded shallow shells reinforced by graphene with general boundary conditions

The vibration and stability analyses of functionally graded (FG) reinforced porous plates with piezoelectric layers under supersonic flow are investigated. The plate has a FG core reinforced by nanocomposite graphene platelets (GPLs) which surrounded by two piezoelectric layers. The GPLs are distributed thorough the thickness direction both uniformly and non-uniformly. The first-order shear deformation plate theory (FSDT) and first-order piston theory are applied to analyze the stability of FG porous plates. Using Hamilton's principle and Maxwell's equation, the governing equations of motion as well as electrical and mechanical boundary conditions are obtained. Applying the Galerkin approach, the partial differential governing equations are converted to the ordinary differential equations. The numerical results show that the flutter aerodynamic pressure and natural frequencies decrease as the porosity coefficient increases. Besides, the symmetric porosity distribution together with GPL pattern A predicts the highest flutter aerodynamic pressure and natural frequencies. Also, the best efficient way to increase the stability region is considering GPL pattern A, with dispersing more GPLs fillers near the top and bottom surfaces of FG porous plate along with symmetric porosity distribution. Furthermore, FG porous plate enclosed by piezoelectric layers in open circuit condition predicts higher flutter aerodynamic pressure and natural frequencies than similar plate in closed circuit condition.

On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading

This paper studies traveling wave motions of rotating multi-layered functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical shell under general boundary conditions. Theoretical equations are obtained according to Donnell shell theory, and artificial spring technique, where centrifugal and Coriolis effects caused by rotation are considered. By employing general orthogonal polynomials using a Gram-Schmidt process as admissible functions, solutions are achieved via Rayleigh-Ritz approach. Then, the accuracy and convergence of solutions are validated by the comparison of the obtained results with those reported in literature. Finally, free vibrations of FG-GPLRC cylindrical shells in both stationary and rotating states are investigated. The influences of boundary spring stiffness, GPL weigh fraction, total layer number, and geometry parameters on shell vibration characteristics are evaluated. It is revealed that the frequency variation trends along with material and geometric parameters are consistent for different boundary conditions, while variation rates and frequency values are highly dependent on boundary spring stiffness.

Traveling wave analysis of rotating functionally graded graphene platelet reinforced nanocomposite cylindrical shells with general boundary conditions

This paper investigates the thermal vibration and buckling of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral plate using the meshless method. Four distributions of the reinforcements along the thickness direction are considered, which are the uniform distributions (UD), FG-V, FG-O and FG-X. The corresponding effective material properties including Young's modulus, mass density, Poisson's ratio and thermal expansion coefficients are estimated by the rule of mixture with the CNT efficiency parameters accounting for the size-dependence. The first-order shear deformation theory (FSDT) with the consideration of thermal effects is employed. Based on Hamilton's principle and the moving least square (MLS) approximation, the discrete governing equations for the vibration of the FG-CNTRC plate are derived. The free vibration of the regular and irregular plates with and without the temperature effect are considered respectively, and the corresponding natural frequencies and mode shapes are obtained by the eigenvalue problem. The stability analysis of the uniaxial and biaxial mechanical and thermal buckling are also conducted subsequently. The effects of the volume fraction, distribution pattern, geometrical characteristics and temperature on the buckling behaviors of the CNTRC quadrilateral plate are discussed in detail.

Thermal vibration and buckling analysis of functionally graded carbon nanotube reinforced composite quadrilateral plate

Vibration and sound radiation analysis of temperature-dependent porous functionally graded material plates with general boundary conditions

Aero-thermo-elastic flutter analysis of supersonic moderately thick orthotropic plates with general boundary conditions

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equatio...

Closed Form Solutions for Vibration and Sound Radiation of Orthotropic Plates under Thermal Environment

In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified ...

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

In this paper, a modified variational method is developed to study the free and forced vibration of curved beams subjected to different boundary conditions. An arbitrary number of eccentric concentrated elements (ECEs) attached to the beams are taken into account. A modified variational principle and least-square weighted residual method are employed to impose the continuity constraints on the internal interfaces and the boundaries of the curved beam. The shear and inertial (or radial–tangential–rotational coupling) effects are incorporated into the system kinetic and potential functional using the generalized shell theory. To test the efficiency and accuracy of the present method, both free and force vibrations of the curved beams are examined under various boundary conditions including non-classical boundary conditions. Good agreement is observed between the results obtained by the present method and those from finite element program ANSYS. Corresponding curved beams with non-eccentric concentrated elements are also developed to investigate the effects of the ECEs on the vibration behaviors of the curved beams.

A variational formulation for vibration analysis of curved beams with arbitrary eccentric concentrated elements

This paper investigates the free and forced vibration of moderately thick orthotropic plates under thermal environment and resting on elastic supports. Three kinds of elastic supports, namely non-homogeneous elastic foundations, point elastic supports and line elastic supports, are considered in the present study. The first-order shear deformation theory is employed to formulate the strain and kinetic energy functions of the structures, and then the stiffness and mass matrices can be obtained by applying the Hamilton’s principle. The modified Fourier method is adopted to solve the dynamic problems of moderately thick orthotropic plates with different combinations of temperature variations, elastic supports and boundary conditions. The accuracy and reliability of the proposed formulation are validated by comparing the obtained results with the finite element method results. Finally, the effects of some key parameters including temperature variation and stiffness values of the elastic supports on the modal and dynamic characteristics of the plates are analyzed in detail. In views of the versatility of the developed method, it offers an efficient tool for the structural analysis of moderately thick orthotropic plates under thermal environment and resting on elastic supports.

Kai Zhou

Papers

Aero-thermo-elastic flutter analysis of supersonic moderately thick orthotropic plates with general boundary conditions

Closed Form Solutions for Vibration and Sound Radiation of Orthotropic Plates under Thermal Environment

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

A variational formulation for vibration analysis of curved beams with arbitrary eccentric concentrated elements

Free and forced vibration analysis of moderately thick orthotropic plates in thermal environment and resting on elastic supports