Free Vibration Analysis of Double Curvature Thin Walled Structures by a B-Spline Finite Element Approach

2007 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Numerical Solutions ◽  
Free Vibration Analysis ◽  
B Spline ◽  
Thin Walled Structures ◽  
Double Curvature ◽  
Spline Finite Element ◽  
Element Approach ◽  
Shell Formulation

This paper presents a free vibration analysis of general double curvature shell structures using B-spline shape functions and a refinement technique. The shell formulation is developed following the well known Ahmad degenerate approach including the effect of the shear deformation. The formulation is not isoparametric, as a consequence the assumed displacement field is described through non-uniform B-spline functions of any degree. A solution refinement technique is considered by means of a high continuity p-method approach. The eigensolution of a plate, and of single and double curvature shells are obtained by numerical simulation to test the performance of the approach. Solutions are compared with other available analytical and numerical solutions, and discussion follows.

Dynamical Analysis of Shell Structures by Means of B-Spline Shape Functions

2007 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Numerical Solutions ◽  
Ritz Method ◽  
Computational Cost ◽  
Free Vibration Analysis ◽  
Shell Structures ◽  
Dynamical Analysis ◽  
Free Form ◽  
Shape Functions ◽  
B Spline ◽  
Double Curvature

This paper presents a free vibration analysis of double curvature free form shaped shell structures using the B-spline shape functions approximation method. It is based on the Ritz method. The shell formulation is developed following the well known Ahmad degenerate approach including the effect of shear deformation. The assumed displacement field is described through non-uniform B-spline functions of any degree. The effect of locking is investigated and both reduced and modified quadrature integration rules are considered with the purpose of increasing the solution accuracy and diminishing the computational cost. Numerical simulation is reported for the evaluation of the eigensolution of plates, and of single and double curvature shells to test the effectiveness and the efficiency of the approach. The presence of spurious zero energy modes both at local and global level was investigated. The solutions are compared with other available analytical and numerical solutions, and discussed in detail.

Influence of dynamic temperature variation and inplane varying loads over post-buckling and free vibration analysis of sandwich composite beam

2020 ◽  
pp. 2050012
Author(s):  
Achchhe Lal ◽  
Kanif Markad
Keyword(s):  
Free Vibration ◽  
Shape Memory ◽  
Temperature Variation ◽  
Vibration Analysis ◽  
Numerical Solutions ◽  
Shape Memory Polymer ◽  
Free Vibration Analysis ◽  
Sandwich Composite ◽  
Dynamic Temperature ◽  
Post Buckling

In this study, nonlinear post-buckling and free vibration analysis of shape memory polymer sandwich composite (SMPSC) under dynamic temperature variation is performed. For the analysis, simplified Co continuity based on higher-order shear deformation theory (HSDT) has been adopted to perform finite element analysis (FEA). Numerical solutions are obtained by iterative Newton–Raphson method considering Von-Karman nonlinear kinematics. Material properties of SMPSC, with Shape Memory Polymer (SMP) as matrix and carbon fiber as reinforcements, have been calculated by theory of volume averaging. The effect of dynamic temperature variation and axial variable inplane loadings (AVIL) on SMPC and SMPSC has been evaluated for various parameters such as beam thickness ratio, layer variation, boundary conditions (BCs), position of core, thickness of core in sandwich structures for the first time. Apart from these, this study also clearly reveals the difference in magnitude of buckling and free vibration parameters between the shape memory polymer composites (SMPC) and SMPSC, before and after glass transition region of material.

A New Static Analysis Approach for Free Vibration of Beams

2018 ◽  
Vol 10 (01) ◽  
pp. 1850004 ◽  
Author(s):  
C. W. Lim ◽  
Zhenyu Chen
Keyword(s):  
Free Vibration ◽  
Static Analysis ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
Free Vibration Analysis ◽  
Concentrated Force ◽  
Static Approach ◽  
Beam Bending ◽  
The Relationship

This study deals with a new method for the free vibration analysis of beams under different boundary conditions. We show that it is possible to apply a static approach for solving free vibration systems, i.e., we obtain natural frequencies for free vibration of beams by analyzing static beam bending problems. Specifically, the basic governing equation for beams with harmonic loadings and resting on an elastic foundation is solved and the solutions are used directly to yield the beam free vibration solutions. In the free vibration analysis, the natural frequency can be a real number or an imaginary number while in the static analysis, the foundation stiffness can be either positive or negative. We show that one can solve the deflection of a beam subjected to a given concentrated force and subsequently deduce the possible infinite deflection when the stiffness becomes zero or negative. In such cases, there exists an equivalent relationship between the free vibration frequencies and the negative stiffness. Consequently, determining the natural frequencies becomes a problem of determining an appropriate negative foundation elastic constant. In general, the numerical vibration solutions can be obtained by analyzing the relationship between loadings and frequencies. For comparison, a comparison with the classical free vibration solutions is presented and excellent agreement is illustrated. We further show that this static approach for free vibration solutions has a clear edge over the classical free vibration approach in computational beam vibration solutions. Very accurate and convergent numerical solutions can be obtained using a very simple numerical solution method. This static approach for free vibration problems can be extended for plate, shell and other structural systems.

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