Flexural motions under accelerating loads of structurally prestressed beams with general boundary conditions

Abstract

The transverse vibration of a prismatic Rayleigh beam resting on elastic foundation and continuously acted upon by concentrated masses moving with arbitrarily prescribed velocity is studied. A procedure involving generalized finite integral transform, the use of the expression of the Dirac delta function in series form, a modification of the Struble's asymptotic method and the use of the Fresnel sine and cosine functions is developed to treat this dynamical beam problem and analytical solutions for both the moving force and moving mass model which is valid for all variant of classical boundary conditions are obtained. The proposed analytical procedure is illustrated by examples of some practical engineering interest in which the effects of some important parameters such as boundary conditions, prestressed function, slenderness ratio, mass ratio and elastic foundation are investigated in depth. Resonance phenomenon of the vibrating system is carefully investigated and the condition under which this may occur is clearly scrutinized. The results presented in this paper will form basis for a further research work in this field.

Response characteristics of a beam‐mass system with general boundary conditions under compressive axial force and accelerating masses

“…However, situation arises when the mass accelerates by a forward force or decelerates, reduces speed, and come to rest at any desired position on the structure, causing the friction between the mass and the structural elements to increase considerably. Under such condition, the vibrating system exhibits dynamic behavior, which may be more complicated . Among few authors in recent times who made effort to tackle the problem of the elastic beam undergoing flexural vibrations under the passage of accelerating loads are, Wang who studied the dynamical analysis of a finite inextensible beam with an attached accelerating mass.…”

“…In a more recent development, Oni and Omolofe considered flexural motions under accelerating loads of structurally prestressed beams with general boundary conditions. The method of generalized integral transform in conjunction with a modification of the asymptotic method of struble was employed to treat this dynamical beam problem.…”

“…Under such condition, the vibrating system exhibits dynamic behavior, which may be more complicated. 34 Among few authors in recent times who made effort to tackle the problem of the elastic beam undergoing flexural vibrations under the passage of accelerating loads are, Wang 35 who studied the dynamical analysis of a finite inextensible beam with an attached accelerating mass. He employed the Galerkin procedure in conjunction with the method of numerical integration to tackle the partial differential equations, which describe the transient vibrations of the beam-mass system.…”

Generalized integral transform solution for free vibration of orthotropic rectangular plates with free edges

“…The boundary conditions at free edges of the rectangular plate were treated exactly by carrying out integral transform of the boundary conditions along the free edge direction. Generalized integral transform technique is a hybrid analytical-numerical method that has been applied successfully in a wide range of flow and heat transfer problems [17][18][19][20], as well as in static and dynamic structural analyses [21][22][23][24][25][26][27][28][29][30][31][32][33][34]. In this work, the free vibration of orthotropic thin rectangular plates with a pair of opposite edges clamped and one or two free edges (CSCF, CCCF, CFCF) is studied analytically by using generalized integral transform technique.…”

Vibration under variable magnitude moving distributed masses of non-uniform Bernoulli-Euler beam resting on Pasternak elastic foundation

“…Force vibration of elastic bodies (stretched string, spring mass system, rods, etc.) have been extensively studied by several authors [1][2][3][4][5][6][7][8][9][10][11]. The vibrations may be due to (i) a force (load) which is a function of the space coordinates only or (ii) a force which c 2019 Vietnam Academy of Science and Technology varies in both space and time.…”