Search results for "free vibration"
showing 10 items of 12 documents
A regular variational boundary model for free vibrations of magneto-electro-elastic structures
2011
In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffne…
Free vibrations of anisotropic panels
2004
A meshfree approach, called Displacement Boundary Method, for the analysis of in-plane and out-of-plane free vibrations of anisotropic plates is presented. The discretization process is based on the use of a modified variational principle and the static fundamental solutions of the problem operators. The stiffness and mass matrices are frequencyindependent, symmetric and positive definite and their computation requires boundary integrations of regular kernels only. Thus, the final resolving system can be solved with classical approaches by using standard numerical procedures. Numerical results are presented to show the accuracy and effectiveness of the method.
Mechanically Based Nonlocal Euler-Bernoulli Beam Model
2014
AbstractThis paper presents a nonlocal Euler-Bernoulli beam model. It is assumed that the equilibrium of a beam segment is attained because of the classical local stress resultants, along with long-range volume forces and moments exchanged by the beam segment with all the nonadjacent beam segments. Elastic long-range volume forces/moments are considered, built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the nonlocal effects are introduced. The motion equations are derived in an integro-differential …
A closed-form solution for natural frequencies of thin-walled cylinders with clamped edges
2016
Abstract This paper presents an approximate closed-form solution for the free-vibration problem of thin-walled clamped–clamped cylinders. The used indefinite equations of motion are classic. They derive from Reissner׳s version of Love׳s theory, properly modified with Donnell׳s assumptions, but an innovative approach has been used to find the equations of natural frequencies, based on a solving technique similar to Rayleigh׳s method, on the Hamilton׳s principle and on a proper constructions of the eigenfuctions. Thanks to the used approach, given the geometric and mechanical characteristics of the cylinder, the model provides the natural frequencies via a sequence of explicit algebraic equat…
On the vibrations of a mechanically based non-local beam model
2012
The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …
An equivalent single-layer model for magnetoelectroelastic multilayered plate dynamics
2012
Abstract An equivalent single-layer model for the dynamic analysis of magnetoelectroelastic laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static and the first-order shear deformation theory is used. The formulation of the model provides for a preliminary fulfillment of the electro-magnetic governing equations, which allows to determine the electric and magnetic potential as functions of the mechanical variables. Then, by using this result, the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-elect…
Nonlinear free vibrations of composite structures via the X-Ritz method
2020
The analysis of large amplitude vibrations of thin-walled cracked structures build as plate assembly is considered in this study. The problem is addressed via a Ritz approach, called X-Ritz, based on the first order shear deformation theory and von K´arm´an’s geometric nonlinearity assumptions. The trial functions are expressed as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour; boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions. Results are presented, which illustrate the influence of cracks on the stiffening effect due to large amplitude vibrations.
Nonlinear free vibrations analysis of cracked composite stiffened plates via X-Ritz approach
2019
Thin and moderately thick composite multi-layered plates are widely employed in naval and aerospace structures. They can experience the presence of cracks, generated for example by corrosion, fatigue or accidental external causes, which aect their static and dynamic behaviour. As regard the dynamic characteristics of plates, many studies have focused on the linear vibration analysis of both isotropic and composite thin and thick plates, providing for a comprehensive knowledge of the plate dynamic behaviour. However, for an accurate appraisal of the plate dynamics, in some applications it is needed to investigate the nonlinear free vibration problem; a literature survey evidences that the la…
On the critical velocities and free vibrations of axially moving elastic webs
2014
On the shear influence on the free vibration behavior of magneto-electro-elastic beam
2009
A magneto-electro-elastic Timoshenko beam model is presented and employed to study the effect of the shear strain on the free vibration behavior of the beam. Once the differential governing equation for Timoshenko magneto-electro-elastic beam is derived, the Euler-Bernoulli model is obtained by letting be zero some of the governing equation coefficients. Results for the Timoshenko and Euler- Bernoulli beam are presented in comparison with two-dimensional finite element computation.