On the deflection of a cantilever beam

Large deflections and large‐amplitude free vibrations of straight and curved beams

“…If the flexural rigidity of the beam is small, it is possible for the elastic axis to form a curve with large slopes. In the case of beams under concentrated loads, solutions to equation (1) can be obtained in the form of elliptic integrals (see, for example, References 1-3). For uniformly distributed loads, solutions to equation (1) cannot be obtained in a closed form.…”

“…In the case of beams under concentrated loads, solutions to equation (1) can be obtained in the form of elliptic integrals (see, for example, References 1-3). For uniformly distributed loads, solutions to equation (1) cannot be obtained in a closed form. This leads to the use of approximate analytical solutions to equation (1).…”

“…Numerical solutions of beams under various loads have been considered by Wang,8'' but the analyses are in error due to the commutation of the derivatives dldx and d/ds. Correcting the error in Reference 6, Holden'' presented numerical solutions for large deflections of uniform beams using the Bernoulli-Euler equation (1). A rather complete survey of developments in the finite deflection analysis up to 1971 is given by Schmidt and DaDeppo.…”

“…I n most engineering problems the slope of the beam is small and its square can be neglected compared to unity. This amounts to linearizing equation (1) to yield the classical equation d2w dx…”

Cantilever Beam Vibration

“…If beams sti!ness and mass are determined experimentally, the properties of the beam need not be known. Barten [9], Prathap and Varadan [10], Takahashi [11] and Verma and Murthy [12] all found that the natural frequency of cantilever beams was essentially independent of amplitude of tip de#ection for tip de#ections less than¸/4.…”