id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-6326	Rajneesh Kumar	Effect of Linearly Distributed Sources in Normal Loading of a Dual-Phase-Lag Thermoelastic Diffusion with Non-Local Formulation 	2025	14	.pdf	application/pdf	4636	255	62	− 𝐾₁₃𝐾₂₆𝜔2 − 𝐾₂₂𝐾₁₅𝜔² − 𝐾₁₁𝐾₂₃𝐾₂₅ + 𝐾₃₃𝜁²𝐾₂₅𝜔² + 𝐾₃₅𝜍²𝐾₂₃𝜔² + 𝐾₂₁𝐾₂₆ − 𝐾₂₃𝐾₂₄ − 𝑏₃𝐾₂₁𝐾₂₅ + 𝑏₃𝐾₂₂𝐾₂₄ , 𝐾₀₃ = 𝜔2𝐾₂₆𝐾₂₂ − 𝜔²𝐾₂₃𝐾₂₅ , 𝐾₁₁ The roots of the characteristic equations (20), (21) are mᵢ (i=1,2,3,4) and 𝐴𝑖(i=1,2,3,4) are the corresponding amplitude coefficients determined from boundary conditions and 𝑅𝑖 ∗ and 𝑆𝑖 ∗ are derived as follows: 𝑅𝑖 ∗ = (𝑚ᵢ2 − 𝜉₁²)³(𝐾₃₃𝐾₃₄𝜁²𝜍² − 𝐾₃₁𝜁²𝐾₁₅) + (𝑚ᵢ2 − 𝜉₁²)²(𝐾₃₁𝜁2𝐾₂₆ + 𝐾₂₁𝐾₁₅ −𝐾₃₃𝜁2𝐾₂₄ − 𝐾₃₅𝜍²𝐾₂₁) + (𝑚ᵢ2 − 𝜉₁²)(𝐾₂₁𝐾₂₆ − 𝐾₂₃𝐾₂₄) (𝑚ᵢ2 − 𝜉₁²)² (𝐾₁₃𝐾₁₅ − 𝐾₃₃𝐾₃₅𝜁²𝜍²) + (𝑚ᵢ2 − 𝜉₁²)(−𝐾₂₂𝐾₁₅ − 𝐾₁₃𝐾₂₆ + 𝐾₃₃𝜁²𝐾₂₅ +𝐾₃₅𝜍²𝐾₂₃) + (𝐾₂₂𝐾₂₆ − 𝐾₂₃𝐾₂₅) 𝑆𝑖 ∗ = (𝑚ᵢ2 − 𝜉₁²)³(𝐾₃₁𝐾₃₅𝜁²𝜍² − 𝐾₃₄𝐾₁₃𝜍²) + (𝑚ᵢ2 − 𝜉₁²)²(𝐾₁₃𝐾₂₄ + 𝐾₃₄𝜍²𝐾₂₂ − 𝐾₃₁𝜁²𝐾₂₅ −𝐾₃₅𝜍²𝐾₂₁) + (𝑚ᵢ2 − 𝜉₁²)(𝐾₂₁𝐾₂₅ − 𝐾₂₂𝐾₂₄) (𝑚ᵢ2 − 𝜉₁²)² (𝐾₁₃𝐾₁₅ − 𝐾₃₃𝐾₃₅𝜁²𝜍²) + (𝑚ᵢ2 − 𝜉₁²)(−𝐾₂₂𝐾₁₅ − 𝐾₁₃𝐾₂₆ + 𝐾₃₃𝜁²𝐾₂₅ +𝐾₃₅𝜍²𝐾₂₃) + (𝐾₂₂𝐾₂₆ − 𝐾₂₃𝐾₂₅) i=1,2,3 5.	cache/cana-6326.pdf	txt/cana-6326.txt