Free vibration analysis of sandwich plates with compressible core in contact with fluid

In this paper, the extended higher-order sandwich plate's theory (EHSAPT) is used to analyze the free vibration of the sandwich plate with compressible core and different boundary conditions in contact with fluid. First-order shear deformation theory is adopted for the top and bottom face sheets, while the in-plane and transverse displacements of the core are considered to be cubic and quadratic functions of the transverse coordinate, respectively. A single series is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. Besides, the fluid is considered to be irrotational, inviscid and incompressible. By taking into account the boundary conditions and compatibility conditions, the fluid velocity potential is acquired. The natural frequencies of the system are calculated by the Rayleigh-Ritz method. An excellent accuracy is obtained between the results in the available literature and the present method. Finally, the effects of various parameters including boundary conditions, side-to-thickness ratio, thickness of the core to thickness of the face sheets ratio, face sheet to core flexural modulus ratio, dimensions of the container, and aspect ratios on the natural frequencies of the sandwich plate are presented and discussed in detail

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 springdashpot. 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 EulerLagrange 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

Design and analysis of porous functionally graded femoral prostheses with improved stress shielding

One of the most important problems of total hip replacement is aseptic loosening of the femoral component, which is related to the changes of the stress distribution pattern after implantation of the prosthesis. Stress shielding of the femur is recognized as a primary factor in aseptic loosening of hip replacements. Utilizing different materials is one of the ordinary solutions for that problem, but using functionally graded materials (FGMs) could be better than the conventional solutions. This research work aims at investigating different porous FGM implants and a real femoral bone by a 3D finite element method. The results show that a neutral functionally graded prosthesis cannot extraordinarily make changes in the stress pattern of bone and prosthesis, but an increasing functionally graded prosthesis leads a lower level of stress in the prosthesis, and a decreasing functionally graded prosthesis can properly reduce the stress shielding among these three architectures. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state-of-the-art bio-implants, and provide pertinent results that are instrumental in the design of porous femoral prostheses under normal walking loading conditions

An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed

Free vibration analysis of functionally graded porous plates in contact with bounded fluid

This study investigates the free vibrations of functionally graded porous (FGP) plates in contact with fluid. As an illustrative problem, a rectangular FGP plate is considered as the vertical wall of a rigid tank containing liquid. The plate displacement field is approximated based on the first-order shear deformation theory (FSDT). Thus, the expressions of its strain and kinetic energy are obtained. The fluid is assumed to be incompressible, inviscid, and irrotational. Its velocity potential functions are obtained by applying suitable boundary and compatibility conditions. By using the Rayleigh–Ritz method with two-variable orthogonal polynomials series expansion, the natural frequencies of the FGP plate in contact with fluid are calculated. To validate the method, the results obtained for the natural frequencies are compared with those available in the literature for FGP plates without fluid and isotropic plates with fluid. Then, three different types of porosity distribution are considered to evaluate their effects on the natural frequencies of the plate. Besides, the effect are investigated of different parameters, such as the fluid depth, side-to-thickness ratio, length-to-width (aspect) ratio

Dynamic analysis of a laminated composite plate coupled with a piezoelectric energy harvester and traversed by a moving vehicle

The dynamic analysis is carried out of a laminated composite plate coupled with a piezoelectric energy harvester under the action of a moving vehicle. The finite element method along with Newmark’s method are applied to solve the discretized equations. Results are presented for two main cases: (i) free and forced vibrations of the laminated composite plate with no harvester and (ii) forced vibrations of the plate coupled with the energy harvester. Several parameters–such as the symmetric and anti-symmetric layups, length of the harvester, and piezoelectric material parameters–are considered to study their effects on the electrical output