Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods

Kaplunov, Julius; Приказчиков, Д. А.; Sergushova, Olga

doi:10.1016/j.jsv.2015.12.008

Cited by 37 publications

(45 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…At the same time the softer parts, subject to fixed ends boundary conditions, undergo quasi-static deformation, which is almost homogeneous for a rod. The observations in [11] are also relevant for imposing conditions on material parameters of a threelayered strongly inhomogeneous plate, leading to the first shear cut-off tending to zero and thus justifying two-mode low-frequency approximations, see [14], and [15].…”

Section: Introductionmentioning

confidence: 78%

“…Another research strand is oriented mainly towards twoor three-component structures. For example, in [11], the low-frequency vibrations of a three-component elastic rod are studied, revealing the conditions on material parameters resulting in the so-called "global" low-frequency regime, associated with polynomial eigenforms, along with the "local" low-frequency regime, for which the displacements of certain components demonstrate oscillatory behaviour. Vibrations of a two-component string on an elastic foundation over the near-cut-off frequency range are analysed in [12].…”

Section: Introductionmentioning

confidence: 99%

“…The proposed approach relies on the concept of "almost rigid body motion", see e.g. [11]. In this case the stiffer components, subject to free ends boundary conditions, perform rigid body motion at leading order.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The lowest vibration spectra of multi-component structures with contrast material properties

Kaplunov

Приказчиков

Prikazchikova

et al. 2019

Journal of Sound and Vibration

View full text Add to dashboard Cite

The paper is concerned with the lowest vibration modes of multi-component rods and cylinders with alternating high contrast material properties of the components. It is demonstrated that these modes correspond to almost rigid body motions of the "stiffer" components. A general perturbation scheme is developed. At leading order polynomial frequency equations are derived, along with linear algebraic equations for the associated eigenforms. In addition, for multi-component rods, higher order corrections are also obtained. Examples of three-and five-component structures are presented, illustrating the efficiency of the proposed approach.

show abstract

Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The lowest vibration spectra of multi-component structures with contrast material properties

Kaplunov

Приказчиков

Prikazchikova

et al. 2019

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…The inhomogeneous rods are known to provide a suitable distribution of strength and weight for engineering structures [2]. A study of the vibration characteristics of these rods is a subject of considerable scientific interest that has wide applications in aerospace, civil and mechanical engineering [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Pillutla¹,

Sudheer²,

Yerikalapudy³

2018

J. vibroeng.

View full text Add to dashboard Cite

In this work, the problem of free longitudinal vibration of rods with variable cross-sectional area and material properties is investigated using the pseudospectral method. With the gradation of material properties like modulus of elasticity and mass density in the axial direction, the results corresponding to a functionally graded axial bar are obtained using the proposed pseudospectral formulation. The pseudospectral formulation used is relatively easy to implement and powerful in analyzing vibration problems. With the help of several numerical examples, the non-dimensional natural frequencies of rods obtained using the pseudospectral method are compared with those obtained by the analytical solution, generalized finite element method, the discrete singular convolution method and differential transformation method. The numerical results obtained show that the proposed technique allows boundary conditions to be incorporated easily and yields results with good accuracy and faster convergence rates than other methods.

show abstract

“…For rods and rod systems, which elements have a variable cross-section, finding exact methods for calculating frequencies and principal modes of vibration is a very difficult problem. Therefore, it is urgent to develop and use approximate methods for solving such problems [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Bending vibrations of stepped rods

Chernyaev¹

2017

Vib. proced.

View full text Add to dashboard Cite

Abstract. Manufacturing stepped rods with segments of sizes proportional to stresses induced in operation is often used to reduce the material consumption in various fields of technology, for example, in the aircraft industry, where the requirements for the weight of structural elements are high. The vibration problems of continuous systems, i.e. systems which masses are considered distributed, are close to the resistance of materials and elasticity theory problems. They are described by partial differential equations. In this case, we consider a homogeneous isotropic material, obeying Hooke's law. Of all the vibration problems of continuous systems, the transverse vibration problems of shafts and beams is of greatest practical importance. The simplest examples of vibrations of prismatic rods were studied in the 18th century in works on acoustics. But before solving problems of practical importance, the problems of stepped beams, it had taken another two hundred years and the development of approximate methods of solving differential equations. The paper presents a solution to the problem of determining the fundamental frequencies of bending vibrations of two-stepped rods with various boundary conditions, using the approximate Lagrange-Ritz method. The calculation error does not exceed 2.6 %. The fundamental frequency of vibration is defined considering different lengths and stiffness ratios of stepped rod segments. The obtained results can be used in solving practical problems in various fields of technology.

show abstract

Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods

Cited by 37 publications

References 14 publications

The lowest vibration spectra of multi-component structures with contrast material properties

The lowest vibration spectra of multi-component structures with contrast material properties

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Bending vibrations of stepped rods

Contact Info

Product

Resources

About