A jury found Melvin Jones guilty of the felony murder of his three-month-old daughter while in the commission of the offense of[*885] cruelty to children. The trial court entered a judgment of conviction on the jury’s verdict and sentenced Jones to life imprisonment. The trial court denied Jones’ motion for new trial, and he appeals. ^[1]

1. Construed most favorably for the State, the evidence shows that, before the victim was born, Jones beat her mother, Tonya Andrews, in an effort to cause a miscarriage. He also used a belt or his hands to strike the three other young children in the family. Jones testified that, while Ms. Andrews was out, he grabbed the victim from her crib by one of her arms and dropped her about 15 inches above the bed, as he had done before. After Ms. Andrews returned, Jones threatened and yelled at her. When the baby began to cry, Jones went to check on her, and Ms. Andrews fell asleep. When Ms. Andrews awoke, Jones told her that the child was not breathing. Paramedics could not resuscitate the victim, who had been dead for about 30 minutes. Jones began crying and said it was his fault. The medical examiner testified that, although the victim otherwise was in good health, one of her ribs was broken within the 24 hours preceding her death, and two others were broken two to three weeks earlier. The cause of death was a subdural hematoma, resulting from a blunt trauma to the head likely occurring between 12 and 16 hours prior to death. There was also evidence of shaken baby syndrome, which probably contributed to the victim’s death. The evidence is sufficient to support a finding that, while the victim was in Jones’ care, he fatally struck or shook her. Carter v. State, 269 Ga. 420, 422 (1) (499 SE2d 63) (1998). Accordingly, a rational trier of fact could have found proof beyond a reasonable doubt of Jones’ guilt of felony murder while in the commission of child cruelty. Jackson v. Virginia, 443 U. S. 307 (99 SC 2781, 61 LE2d 560) (1979); Johnson v. State, 269 Ga. 632 (501 SE2d 815) (1998); Carter v. State, supra. Compare Johnson v. State, 269 Ga. 840 (506 SE2d 374) (1998).

2. After Jones expressed dissatisfaction with the public defender appointed to represent him, the trial court released her but refused to appoint another attorney. Thereafter, the public defender and Jones reconciled, but Jones again became dissatisfied, and the trial court required that Jones either accept representation by the public defender or represent himself. Jones chose to act as his own attorney, but contends on appeal that he did not validly waive his right to counsel and that the trial court should have appointed a new attor[*886] ney to represent him.

Jones denies that he engaged in any dilatory tactics and he relies upon the trial court’s failure to establish, as suggested by Raines v. State, 242 Ga. App. 727, 729 (1) (531 SE2d 158) (2000), that he apprehended the nature of the charges, the range of allowable punishments, potential defenses and mitigating circumstances, and any possible lesser included offenses such as voluntary or involuntary manslaughter. However, this Court has held that it is not incumbent upon the trial court to make each of these inquiries. “The record need only reflect that the accused was made aware of the dangers of self-representation and nevertheless made a knowing and intelligent waiver. [Cits.]” Wayne v. State, 269 Ga. 36, 38 (2) (495 SE2d 34) (1998). The trial court was authorized to find that Jones set forth no justifiable basis for dissatisfaction with the public defender and, therefore, that he “was attempting to use the discharge and [appointment] of other counsel as a dilatory tactic, which was ‘the functional equivalent of a knowing and voluntary waiver of appointed counsel.’ ” Bryant v. State, 268 Ga. 616, 617 (2) (491 SE2d 320) (1997). See also Hobson v. State, 266 Ga. 638 (2) (469 SE2d 188) (1996). “ ‘The essential aim of the Sixth Amendment is to guarantee effective assistance of counsel, not to guarantee a defendant preferred counsel or counsel with whom a “meaningful relationship” can be established.’ [Cits.]” Battle v. State, 234 Ga. App. 143, 144 (2) (505 SE2d 573) (1998). Furthermore, the public defender testified that she made Jones fully aware of the nature of the charge, the possible sentences, and the dangers of self-representation. According to Jones’ own testimony, he completely understood that, if he rejected appointed counsel, he would have to represent himself. The trial court endeavored to convince Jones to accept the public defender, informing him and his mother about his right to counsel and the qualifications of the public defender. Under all the circumstances, we conclude that Jones knowingly and intelligently waived his right to counsel after he was made aware of the dangers of self-representation. Simpson v. State, 238 Ga. App. 109, 111-112 (1) (517 SE2d 830) (1999).

Jones further urges that the prosecutor’s failure to take a more active role invalidates the waiver of counsel. In making this contention, however, Jones erroneously assumes that he has the right to receive effective legal assistance from the prosecutor. The trial court is responsible for ensuring a valid waiver of counsel, and did so. See Wayne v. State, supra.

3. Jones urges that the trial court erred in failing to instruct on involuntary manslaughter. Throughout the trial, however, Jones took the position that he did not cause the fatal injury. See Mills v. State, 187 Ga. App. 79, 80 (3) (369 SE2d 283) (1988). Thus, there was no evidence to support such a charge. Moreover, Jones did not request[*887] an instruction on involuntary manslaughter. A trial court does not err in failing to give, sua sponte, an instruction on a lesser included offense in the absence of a written request therefor. Gadson v. State, 264 Ga. 280, 281 (2) (444 SE2d 305) (1994). Compare Tarvestad v. State, 261 Ga. 605 (409 SE2d 513) (1991) (failure to charge without request on sole defense, rather than lesser included offense).

4. Jones also contends that the trial court erred by admitting similar transaction evidence, because the State’s notice of intent to introduce this evidence was untimely under Uniform Superior Court Rule 31.3 and because the trial court made no specific findings in compliance with Williams v. State, 261 Ga. 640 (409 SE2d 649) (1991). Jones made no objection at trial on either of these grounds and, thus, has waived appellate review thereof. Murphy v. State, 270 Ga. 72, 73 (2) (a) (508 SE2d 399) (1998); Williams v. State, 267 Ga. 308, 310 (3) (477 SE2d 570) (1996).

Judgment affirmed.