Classical solutions of forced vibration of rod and beam driven by displacement boundary conditions

2005 ◽  
Vol 279 (1-2) ◽  
pp. 481-486 ◽  
Author(s):  
S.R. Wu
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Classical Solutions ◽  
Displacement Boundary

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

Linear second order elliptic equations with Venttsel boundary conditions

1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Yousong Luo ◽  
Neil S. Trudinger
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence Result ◽  
Boundary Value ◽  
Second Order ◽  
Classical Solutions ◽  
Schauder Estimate ◽  
Second Order Elliptic Equations

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

Forced Motions of Composite Conoidal Shell Roofs with Complicated Boundary Conditions

2010 ◽  
Vol 123-125 ◽  
pp. 89-92
Author(s):  
Kaustav Bakshi ◽  
Hari Sadhan Das ◽  
Dipankar Chakravorty
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Forced Vibration ◽  
Vibration Characteristics ◽  
Finite Element Code ◽  
Isoparametric Finite Element

An eight noded isoparametric finite element code is applied to study static bending, free and forced vibration characteristics of composite conoidal shell roofs with complicated boundary conditions which are often encountered in the industry.

A Mixed Method in Elasticity

1977 ◽  
Vol 44 (1) ◽  
pp. 51-56 ◽  
Author(s):  
N. S. V. Kameswara Rao ◽  
Y. C. Das
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Elastic Body ◽  
Mixed Method ◽  
Forced Vibration ◽  
Three Dimensional ◽  
Dynamic Problems ◽  
Partial Differential ◽  
Theory Of Plates

A mixed method for three-dimensional elasto-dynamic problems has been formulated which gives a complete choice in prescribing the boundary conditions in terms of either stresses, or displacements, or partly stresses and partly displacements. The general expressions for the responses of the elastic body have been derived in the form of transcendental partial differential equations of a set of initial functions, which can be evaluated in terms of the prescribed boundary conditions. The method so-formulated has been illustrated by applying it to the theory of plates. Only plates subjected to antisymmetric loads have been considered for illustration. Some examples of free and forced vibration of plates have been presented. Results are compared with solutions from existing theories.

Nonlinear longitudinal forced vibration of a rod undergoing finite strain

2017 ◽  
Vol 232 (12) ◽  
pp. 2229-2243
Author(s):  
Batool Soleimani Roody ◽  
Ali R Fotuhi ◽  
Mohammad M Jalili
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Governing Equation ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Finite Strain ◽  
Multiple Time Scales ◽  
Different Boundary Conditions ◽  
Resonance Frequencies

Rods are one of significant engineering’s structures and vibration analysis of a rod because of extended application of it in engineering is very important. Due to large amplitude or to excitations at frequencies close to their resonance frequencies, these structural elements can experience large amplitude, hence nonlinear vibration. Therefore, understanding of longitudinal nonlinear vibration of rods with different boundary conditions and large amplitude is very useful to reach an appropriate designing. In this paper, vibration of a rod with different boundary conditions undergoing finite strain, without simplification in strain–displacement equation, is investigated. For obtaining governing equation, Green–Lagrange strain, structural damping and Hamilton principle are used and then Galerkin method is employed to convert nonlinear partial differential equation to nonlinear ordinary differential equation. In spite of many papers that only use of cubic term for nonlinearity, the governing equation has quadratic and cubic terms. At the first, free vibration equations are solved with multiple time scales method and for verifying the accuracy of this method, the results are compared with results of Runge–Kutta numerical method, which have good accuracy. Then, forced vibration is investigated in the cases of primary resonance and hard excitation including sub-harmonic and super-harmonic resonances. Analytical expressions for frequency responses are derived, and the effects of different parameters including nonlinear coefficients, damping coefficient and external excitation are discussed.

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