A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam
نویسندگان
چکیده
In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.
منابع مشابه
Three-dimensional Vibration Suppression of an Euler-bernolli Beam via Boundary Control Method
In this paper, the general governing equations of three-dimensional vibrations of an Euler-Bernoulli Beam under influences of system dynamics are derived by the Hamiltonian method. Then two fundamental cases of a cantilever beam and a rotating beam are considered. The conventional methods for vibration suppression debit to expenses and make new problems such as control spillover because they ar...
متن کاملInvestigation of Thermoelastic Damping in the Longitudinal Vibration of a Micro Beam
In the design of high Quality factor (Q) micro or nano beam resonators, different dissipation mechanisms may have damaging effects on the quality factor. One of the major dissipation mechanisms is the thermoelastic damping (TED) that needs an accurate consideration for prediction. In this paper, thermoelastic damping of the longitudinal vibration of a homogeneous micro beam with both ends clamp...
متن کاملNonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force
This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time ...
متن کاملDynamic Stability of Step Beam Carrying Concentrated Masses under Follower Force
This paper investigates the dynamical behavior of an assembled beam like structure with tip masses modeling a two stage space rocket structure. The beam like structure is composed of two beams connected together carrying two masses at the free ends to model the payload, and the stabilizing fins mass properties. The effect of non-homogeneity of the structure due to different cross section proper...
متن کاملA Survey on Buckling and Vibrations of a Viscoelastic Beam under Distributed Lateral and Axial Loads
In this paper, based on Kelvin and Linear Standard Solid models, dynamic response and the buckling load of a viscoelastic beam under lateral and axial loads have been determined. The governing equations have been extracted using Euler and Timoshenko theories and their analytical solutions have been obtained by using the eigenfunctions expansion method. Buckling load have been calculated by us...
متن کامل