Free and forced vibrations of shear deformable functionally graded porous beams

• Free and forced vibration characteristics of porous beams are presented.
• Forced vibration analysis is conducted under three different loading conditions.
• The influence of graded and uniform porosity distributions is compared.
• The effects of porosity coefficient and slenderness ratio are discussed.
• The symmetric FG porosity distribution gives the largest beam stiffness.

This paper investigates the free and forced vibration characteristics of functionally graded (FG) porous beams with non-uniform porosity distribution whose elastic moduli and mass density are nonlinearly graded along the thickness direction. Both symmetric and asymmetric porosity distributions are considered. The relationship between coefficients of porosity and mass density is determined based on the typical mechanical property of an open-cell metal foam. Within the framework of Timoshenko beam theory to include the effect of transverse shear strain and by employing Lagrange equation method together with Ritz trial functions, the equation of motion is derived then solved by using Newmark-β method in the time domain. Natural frequencies and transient dynamic deflections are obtained for porous beams under different loading conditions, including a harmonic point load, an impulsive point load and a moving load with constant velocity. A detailed numerical study is conducted to examine the effects of varying porosity distribution, porosity coefficient, slenderness ratio and boundary condition, shedding important insights into the design of functionally graded porous beams to achieve improved dynamic behavior.