Vibration Analysis Of Sandwich Beams Research Articles

Free vibration analysis of sandwich beam carrying sprung masses

In this paper, free vibration of three-layered symmetric sandwich beam carrying sprung masses is investigated using the dynamic stiffness method and the finite element formulation. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. Applying the effect of sprung masses by replacing each sprung mass with an effective spring on the boundary condition of the element, the element dynamic stiffness matrix is developed. These matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the well known Wittrick–Williams algorithm. Free vibration analysis using the finite element method is carried out by increasing one degree of freedom for each sprung mass. Finally, some numerical examples are discussed using the dynamic stiffness method and the finite element formulation. After verification of the present model, the effect of various parameters such as mass and stiffness of the sprung mass is studied on the natural frequencies.

Free vibration analysis of sandwich beams using improved dynamic stiffness method

Abstract In this paper, free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness and finite element methods. To determine the governing equations of motion by the present theory, the core density has been taken into consideration. The governing partial differential equations of motion for one element contained three layers are derived using Hamilton’s principle. This formulation leads to two partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are combined to form one ordinary differential equation. Closed form analytical solution for this equation is determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. They are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the known Wittrick–Williams algorithm. After validation of the present model, the effect of various parameters such as density, thickness and shear modulus of the core for various boundary conditions on the first natural frequency is studied.

Free vibration analysis of sandwich structures with a flexible functionally graded syntactic core

A new model based on high-order sandwich panel theory is implemented to free vibration analysis of sandwich beams with syntactic foam as a functionally graded flexible core. The formulation uses the classical beam theory for the face sheets and an elasticity theory for the FG core. By considering the flexibility of the sandwich core, the model can achieve to high-order effect caused by the nonlinearity of the longitudinal and vertical deformations of the soft FG core. The behavior is presented in terms of internal resultants and displacements in the faces, peeling and shear stresses in the face–core interface and stress and displacement field in the core. A numerical analysis of free vibration of simply supported beams including higher modes that cannot be detected by other models is carried out and a parametric study that investigates the effect of distribution of functionally graded core’s properties is presented.

Free vibration analysis of sandwich beam with FG core using the element free Galerkin method

In this paper, free vibration analysis of sandwich beams with functionally graded material as core material is investigated. For the analysis, the element free Galerkin method and Galerkin formulation for two dimensional elasticity problems are considered. Penalty method is used for modeling of interface between the face sheets and the core in the sandwich beam. Using the similarity of materials for the face sheets and core, applicability of the model is tested. The first ten natural frequencies of sandwich beam with elastic core are derived. The results have shown good agreement with those obtained by the finite element method. Finally, the natural frequencies of sandwich beam with functionally graded core are obtained and discussed.

Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator

This paper provides a basic mechanics model for the flexural analysis of a sandwich beam coupled with a piezoelectric layer. The Euler beam model for a long and thin beam structure is employed, together with the electric potential satisfying the surface free charge condition for free vibration analysis. The distribution of the piezoelectric potential is obtained by including the Maxwell equation in the formulation. Based on the results of vibration analysis, it is shown that the dynamic characteristic of the entire structure is related to the position of the piezoelectric layer. More importantly, the mode shape distribution of the electric potential in the piezoelectric layer in the longitudinal direction is related to the transverse displacement, or more accurately the curvature, of the sandwich beam, and the latter is dependent on the boundary conditions. Hence, the commonly adopted assumption of uniform electric potential in the longitudinal direction needs to be carefully re-examined. The distribution of electric potential obtained serves as a guide for selecting the trial function for the mode shapes of the electric potential required in numerical methods, such as FE modelling, for coupled piezoelectric structures.