Forced vibrations of a cantilever beam

Abstract

The theoretical and experimental solutions for vibrations of a vertical-oriented, prismatic, thin cantilever beam are studied. The beam orientation is ‘downwards’, i.e. the clamped end is above the free end, and it is subjected to a transverse movement at a selected frequency. Both the behaviour of the device driver and the beam's weak-damping resonance response are compared for the case of an elastic beam made from PVC plastic excited over a frequency range from 1 to 30 Hz. The current analysis predicts the presence of ‘pseudo-nodes’ in the normal modes of oscillation. It is important to note that our results were obtained using very simple equipment, present in the teaching laboratory.

Small‐sized specimen design with the provision for high‐frequency bending‐fatigue testing

“…The above is the equation for dynamic Euler-Bernoulli beam or the Euler-Lagrange equation for a beam with variable cross-section in length (x direction) and the applied external distributed force of f x,t ð Þ in length of the beam. 51,52 The term c x ð Þ ∂w x,t ð Þ ∂t may be added to the left side of the Equation 5 in order to consider the damping coefficient of c x ð Þ over the length of the beam. 51 For a homogeneous beam with uniform cross-section area along the length-where E, I, and A are not dependent on x-the dynamic Euler-Bernoulli turns to the following equation.…”

Medición de frecuencias de resonancia, factor de pérdida y módulo de Young dinámico de varillas empotradas

“…7 se muestra la amplitud de oscilación del extremo libre de la varilla en función de la frecuencia evaluada con la Ec. (25), usando c = 0.38 m/s y γ = 2 s −1 [7]. Las posiciones de los picos de amplitud nos dan las frecuencias de resonancia del sistema predichas por el modelo (los valores obtenidos figuran en la segunda columna de la Tabla 1).…”

“…Con γ ≪ ω y ω ≈ ω n , se puede mostrar [7] que ∆, en las cercanías de la resonancia, puede aproximarse por…”

Novel techniques for laser doppler vibrometry for vibrating shiny and mirror surfaces

“…Secondly, the vibration response of the cantilevered mirror follows the excita tion input force [168]. Here, the response was a sinusoidal velocity response whose maximum velocity occurs when the cantilevered mirror is at the equilib rium.…”