Dynamic analysis of rigid roadway pavement under moving traffic loads with variable velocity

Dynamic Response of a Rigid Pavement Plate Based on an Inertial Soil

“…p ( x , y , t ) = p o [1 + (1/2)cos⁡( ω · t )] δ [ x − x ( t )] δ [ y − y ( t )] is the load transmitted to the pavement [14]. Here x ( t ) = v o t + (1/2)acc( t 2 ); y ( t ) = (1/2) b are the geometrical position of load at the time t ; p o is the magnitude of the moving wheel load; acc is the acceleration of the load; ω is the angular frequency of the applied load; δ is the Dirac function; a , b , and h are the dimensions of the finite plate and D is the flexural stiffness of the plate.…”

“…(i) The restriction of the elastic vertical translation is characterized by the four equations [14]:$\begin{array}{c}T20V_{x=\mathrm{0}}-D\left[\frac{{\partial }^{\mathrm{3}}w\left(\mathrm{0},y,t\right)}{\partial x^{\mathrm{3}}}+\left(\mathrm{2}-\upsilon \right)\frac{{\partial }^{\mathrm{3}}w\left(\mathrm{0},y,t\right)}{\partial x\partial y^{\mathrm{2}}}\right]\\ =k{s}_{x\mathrm{1}}w\left(\mathrm{0},y,t\right),\end{array}$ $\begin{array}{c}{V}_{x=a}-D\left[\frac{{\partial }^{\mathrm{3}}w\left(a,y,t\right)}{\partial x^{\mathrm{3}}}+\left(\mathrm{2}-\upsilon \right)\frac{{\partial }^{\mathrm{3}}w\left(a,y,t\right)}{\partial x\partial y^{\mathrm{2}}}\right]\\ =k{s}_{x\mathrm{2}}w\left(a,y,t\right),\end{array}$ $\begin{array}{c}{V}_{y=\mathrm{0}}-D\left[\frac{{\partial }^{\mathrm{3}}w\left(x,\mathrm{0},t\right)}{\partial y^{\mathrm{}}}\right]\end{array}$…”

“…The free vibrations solution of the problem is set as [14, 20] $\begin{array}{c}T1w\left(x,y,t\right)=\underset{m=\mathrm{normal1}\hspace{0.17em}}{\overset{\infty }{{\displaystyle false\sum }}}\underset{\hspace{0.17em}n=\mathrm{normal1}}{\overset{\infty }{{\displaystyle false\sum }}}{W}_{mn}\left(x,y\right)\sin \left({\omega }_{mn}t\right).\end{array}$ …”

“…From that, many researchers base theirs works on using this type of soil [12, 13]. Alisjahbana and Wangsadinata [14] looked at the dynamic analysis of a rigid pavement under mobile load resting on Pasternak soil type. Based on this model, the determination of soil parameters is only based on the elasticity modulus and Poisson's ratio.…”

Damped Vibrations of Rectangular Plate of Variable Thickness Resting on Elastic Foundation: A Spline Technique

“…In reality all the vibrations are damped vibration, as free vibrations are ideal and can't be practically possible, so no vibration can be thought of being in existence without damping. In a series of papers, recently DJO'Boy [3] have analyzed the damping of flexural vibration and Alisjahbana and Wangsadinata [4] discussed the realistic vibrational problem incorporating dynamic analysis of rigid roadway pavement under moving traffic loads. In the demand of modern science, a study dealing with damped vibrations of homogeneous isotropic rectangular plate of linearly varying thickness along one direction and resting on elastic foundation is presented employing classical plate theory.…”